Talk:Conservation of energy/Archive 2

Mechanics
Under the subheading Mechanics it states:


 * In mechanics, conservation of energy is usually stated as 


 * $$E=T+V\ $$


 * where T is kinetic energy and V potential energy.

I disagree. E=T + V looks like an expression for the principle of conservation of mechanical energy, not the principle of conservation of energy.

It also states:
 * For this particular form to be valid, the following must be true:
 * The system is scleronomous (neither kinetic nor potential energy are explicit functions of time)
 * The potential energy doesn't depend on velocities.
 * The kinetic energy is a quadratic form with regard to velocities.
 * The total energy E depends on the motion of the frame of reference (and it turns out that it is minimum for the center of mass frame).

Again, I disagree. For $$E=T+V\ $$ to be conserved, all forces must be conservative forces.

The current information is unsourced. I think it needs to be re-written so that it addresses conservation of energy rather than conservation of mechanical energy. Do you agree? Dolphin ( t ) 06:05, 18 February 2013 (UTC)


 * There being no comment after a week I deleted the section Mechanics - see my diff. I plan to do further writing for Conservation of energy in coming days. Dolphin  ( t ) 11:22, 25 February 2013 (UTC)

transfer of energy between open systems
At issue is the quantity of energy transferred between two open systems. In particular, what is the scope of the concepts of heat and work as modes of transfer of energy between two systems? Smith 1980 offers an answer that I am here saying is not adequate.

Smith offers a "process", illustrated in his Figure 1. His "process" has two stages, first the removal of a partition between two interior systems, second the doing of work and passage of heat from the overall surroundings to the surroundings of the interior systems.

I say that this format is not of the proper form for general process of exchange between a system and its surroundings to which it is open. Smith's process has four systems, and is conducted in a particular way. This is not a general proces of the required form.

The required form has two systems, the system of interest, and its surroundings. Between the systems there are no external force fields or relative motion, and no long range forces. The interaction of these two open systems is represented by removing the boundary between them when initially it was rigid and impermeable.

I offer what I think is a process in proper format. It defines the initial state as consisting of two systems, 0′ and 0′′, with internal energies $U_{0}′$ (the system of interest) and $U_{0}′′$ (its surroundings) separated from each other by a rigid impermeable wall, and jointly isolated from the rest of the universe. The final state consists of two systems 1′ and 1′′ with internal energies $U_{1}′$ and $U_{1}′$, still jointly separated from the rest of the universe, etc.. The final state system 1′ consists of the system produced by removing the boundary between the initial systems, and including the regions of space formerly occupied by the initial systems 0′ and 0′′, surrounded by the final system 1′′, which is now empty, with internal energy $U_{1}′′ = 0$ as a convenient reference value. Then for this process, the change in internal energy of the system of interest is given by $ΔU′ = U_{1}′ − U_{0}′$, and the change of internal energy of the surroundings is given by $ΔU′′ = U_{1}′′ − U_{0}′′$. The first law of thermodynamics then says that $ΔU′ + ΔU′′ = 0$.

Then $ΔU′′ = − U_{0}′′$ and so $ΔU′ − U_{0}′′ = 0$, and thence $ΔU′ = U_{0}′′$.

For someone starting from the usual textbook scenarios of the first law, which are explicitly only for exchange of energy between two closed systems, this is not merely trivial, because removal of a partition is not an admissible process for such scenarios. This present version for an open system is plausible for those who believe in the law of conservation of energy.

This much is indeed used by Smith 1980, who attributes the idea to Gillespie, Coe (1933). I intend that what I have written here is also a rendering of Münster's 1970 p. 51 statement of the first law for open systems. There is here no attempt to split the internal energy change into heat and work. Smith acknowledges that "No progress can be made until we have some notion of adiabatic processes for these systems." I say that the notion he chooses is arbitrary, not uniquely general, and that he offers no justification for it.

I conclude that something like the above, a version of Münster 1970 p. 51, would count as a reliably sourced statement of the first law for open systems.Chjoaygame (talk) 16:20, 15 March 2013 (UTC)

new edit on simple open systems
I would like ask for careful consideration of the new edit that adds a statement of the first law of thermodynamics for simple open systems, with its attached definition of a simple open system.

In various texts and research articles there are statements that propose to state the first law of thermodynamics for open systems, in terms that include heat and work. The heat and work are in each case defined by some proviso, stated more or less explicitly, depending on the rigour of the text or research article, that restricts the kinds of process to which the statement applies, so as to make the system virtually closed. Many texts simply leave out a statement for open systems.

The only satisfactorily thoroughly discussed and rigorous statement of which I am aware is by A. Münster (1970, Classical Thermodynamics, Wiley—Interscience, London, pp. 50–51). I know of other discussions of this question, but they do not seem to me to match Münster in thoroughness and reliability. I would be glad to be advised of other careful and thorough statements, that might match Münster's rigour and might support or oppose what he says.

Münster concludes that the classical definition of adiabatic work, and the notion of heat that depends on it, are not applicable to any open system. As I read it, he intends this to refer to statements without some kind of proviso that restricts the kinds of processes allowed so as to make the system virtually closed. As I read this, it applies to simple open systems as defined in the new edit; the proviso of simplicity in the new edit does not exempt its statement from the above-mentioned inapplicability. If this reading is right, then it seems to follow that the new edit conflicts with Mŭnster's discussion. The new edit cites no source.Chjoaygame (talk) 22:53, 18 February 2013 (UTC)

response 1

 * As for references, see for example, the Alberty and Callen references in the thermodynamic potential article (Alberty Equation 1.1-1, Callen Equation 2.6 on page 36). Also see the de Groot reference (Equation 2 of Appendix II "On Thermodynamic Relations") in the Boltzmann equation article.


 * This statement is found in most books on thermodynamics. To dispute this is out of the mainstream (although not necessarily wrong). Can you give a short description of Munster's reasoning? PAR (talk) 15:07, 20 February 2013 (UTC)

response 1a
The response 1 above contains several elements and I will to some degree address them separately.Chjoaygame (talk) 03:54, 21 February 2013 (UTC)

response 1a(i)
response to "As for references, see for example, the Alberty and Callen references in the thermodynamic potential article (Alberty Equation 1.1-1, Callen Equation 2.6 on page 36). Also see the de Groot reference (Equation 2 of Appendix II "On Thermodynamic Relations") in the Boltzmann equation article."

The new edit contains the equation
 * $$\mathrm{d}U = \delta Q - \delta W+\mu dN,\,$$

Alberty Equation 1.1-1 on page 1352 reads
 * $$dU=TdS - PdV+\sum_{i=1}^{N}\mu_i dN_i\, .$$

Callen Equation 2.6 on page 36 reads:
 * $$dU=TdS - PdV+\mu_1 dN_1+ ... + \mu_r dN_r\, .$$

These two cited equations do not mention $δQ$ or $δW$.

It is true that on page 36 Callen goes on to consider his equivalent of $δW$, but in doing so he relies on his equation 1.1, which refers to volume work for a closed system. This is not work in general for a closed system, because it does not include isochoric work. Isochoric work includes friction which can be important for open systems. Callen makes further remarks, for example that in the special case of constant mole numbers (virtually a closed system requirement) one can write $đQ = T dS$. But they are not general statements and are not decisive for the present discussion.

Appendix II on page 457 of my copy of de Groot & Mazur (1963 reprint of 1962 original) has equation (2) as
 * $$\mathrm {d}G= - S \mathrm {d}T+V\mathrm {d}p+\sum_{k=1}^{n}\mu_k \mathrm {d}M_k\, .$$

This equation does not mention $δQ$ or $δW$. It is true that in another place de Groot & Mazur 1962/1963 offer a definition of heat flux in an open system, but the literature abundantly points out that in doing so they make special assumptions that mean that this is not a uniquely adequate general definition.

It seems that the new edit has made some assumption such as that $T dS = δQ$ and that $P dV = δW$. This particular assumption is not suitable for the de Groot & Mazur formula. This assumption is not part of mainstream thinking and is not generally right for an open system, though it is right for a closed system under particular conditions.Chjoaygame (talk) 03:54, 21 February 2013 (UTC)

response 1a(ii)
response to "This statement is found in most books on thermodynamics."

The new edit contains the equation
 * $$\mathrm{d}U = \delta Q - \delta W+\mu dN,\,$$

I think this statement is not found in most books on thermodynamics. Indeed I think it is not easily found in any reliable source that I can recall. I think it is fair for me to say I will deal with such a sourced statement on its merits in its context, if someone produces one here. Failing this, I think it fair to say that the statement referred to in this subsection is unfounded.Chjoaygame (talk) 03:54, 21 February 2013 (UTC)

response 1a(iii)
response to "To dispute this is out of the mainstream (although not necessarily wrong)."

Response 1 above asserts that my point, that the edit is not justified, is out of mainstream thinking. Evidence that it is the edit that is out of mainstream thinking is right here, that these sources do not offer general statements about $δQ$ or $δW$ in this context, where it would be expected if it were part of the sources' thinking.Chjoaygame (talk) 03:54, 21 February 2013 (UTC)

response 1a(iv)
response to "Can you give a short description of Munster's reasoning?"

It is dangerous for me to try to make short description of a source, because the source has its context, which I will hardly be able to reproduce.

But I will take the risk, and have a go at it, subject to the proviso that I do not claim to give an adequate account of what Münster says, and that I may say more later if necessary.

Münster writes on page 50: "As explained in §14 the classical point of view (equivalence of heat and work) as well as Carathéodory's point of view (definition of heat) are meaningless for open systems."

We here in our Wikipedia articles from the physical viewpoint usually use what Münster refers to as the Carathéodory point of view for defining heat. It relies on processes of pure adiabatic work, which is impossible in an open system, by definition. On page 46 Münster writes: "It is, therefore, not generally possible fo define clearly the 'volume work' done on an open phase." He also writes: "... adiabatic work as required by §8 cannot, by definition, be done on an open phase."

Münster is not alone in this. R. Haase 1971 writes on page 35: "But the total work done on the open system remains indefinite. We shall not try to extend the general concept of work to open systems, since such an extension would not serve any useful purpose."

L. Tisza (1966) in paper 2 considers what he calls the "macroscopic theory of equilibrium", which is essentially the Gibbs presentation of classical thermodynamics. On page 63 he defines work, but only for the case of unchanging mole numbers, that is to say only for the case of closed systems. He associates four kinds of work with the four usual thermodynamic potentials, respectively adiabatic-isochoric work, isothermal-isochoric work, adiabatic-isobaric work, and isothermal-isobaric work, with respectively the internal energy, the Helmholtz free energy, the enthalpy, and the Gibbs free energy. He does not mention 'chemical work'. He considers a piston released from an initial position of pressure unbalance. The final position of the piston depends on the details of the dissipation process. For an open system these details include transfer of matter. In section 4 he considers the idea of generalized work, but does not include here the idea of work in an open system.

L. Tisza (1966) points out on page 139 that "An interesting distinction between energy flow and mass flow is connected with the availability of restrictive walls." There are walls restrictive of mass flow but not of energy and entropy flow, but generally not walls non-restrictive of flow of some chemical species but restrictive of energy and entropy flow. Thus for walls that transmit matter, processes generally involve simultaneous independent variations of mole numbers and of entropy. An exception is that fine capillaries transmit the superfluid but not the normal fluid of helium II; such walls transmit the superfluid but not entropy.

There is a small literature on this subject, some of of which I have read. It contains efforts to define work for open systems, but they all rely on special assumptions that restrict the kinds of process allowed, so as virtually to require closed systems. As I read this literature, it is, however, acknowledged that there is no general, adequate, and unique definition of work for open systems.Chjoaygame (talk) 03:54, 21 February 2013 (UTC)

response 1a(v), conclusion
I conclude that the defence offered above, headed 'response 1', is not adequate.Chjoaygame (talk) 03:54, 21 February 2013 (UTC)

To the above, there seems to be no response. This seems to be a sufficient reason to undo the new edit.Chjoaygame (talk) 20:45, 5 March 2013 (UTC)

Please note that I gave the wrong formula number for the de Groot reference. I should have said equation 9. This is given without any qualifications, and, yes, PdV is the work done by a simple system in which velocities are negligible, and thus viscosity effects ("friction") is negligible. The statement in Alberty is likewise without qualification. Callen states that the PdV term for open systems is the work, and the fact that he notes that it is the same term found in the closed system statement does not constitute a "qualification". Unless you understand Munster's reasoning and can explain it, and can explain why these three reputable sources seem to be in conflict with Munster, please don't modify the statement.

Another reference: "The differential equations of thermodynamics" by V.V. Sychev. His equation 3.144 (page 56 in my copy) states the same thing again. Here he uses $$\varphi dG$$ where dG is mdN, where m is the mass of a particle, and $$\varphi=\mu/m$$. I could go on and on. PAR (talk) 16:08, 6 March 2013 (UTC)


 * Lifted from the immediately above response by editor PAR: "Please note that I gave the wrong formula number for the de Groot reference. I should have said equation 9. This is given without any qualifications, and, yes, PdV is the work done by a simple system in which velocities are negligible, and thus viscosity effects (″friction″) is negligible."


 * My response to this is as follows.
 * Equation (9) of de Groot & Mazur 1962 reads
 * $$T\, \mathrm d S= \mathrm d U+p\, \mathrm d V- \sum_{k=1}^{n}\mu_k \mathrm {d}M_k\, .$$


 * This cited equation is correct as it stands, of course.
 * But it does not mention the quantities $δQ$ or $δW$, which are the quantities that appear in the new edit. It is the presence of these quantities in the new edit that is in question here.
 * As far as I can see, it seems that the new edit has made some assumption such as that $T dS = δQ$ and that $P dV = δW$. This editorial assumption is not explicitly and adquately supported by reliable sources in the response below by editor PAR under the subheading response 1a(v), conclusion.


 * It is not part of mainstream thinking and is not generally right for an open system, though it is right for a closed system under particular conditions, namely that isochoric work is not permitted. As I read, and agree with, the immediately above response by editor PAR, it says that the cited equation does not refer to viscosity effects. Viscosity effects are classified as isochoric work and are thus not considered in the cited equation. The cited equation therefore does not cover work in general, which includes both pressure-volume work and isochoric work. Logically speaking, it is true that some pressure-volume effects are work effects. But what is implied in the new edit is that all work effects are pressure-volume effects, and the above response agrees that such is not the case. This means that the new edit is not justified in its use of the terms $δQ$ and $δW$.


 * This is not the only reason why the cited equation does not cover work effects in general. When matter is transferred, internal energy is also transferred, but that quantity of energy cannot in general be uniquely split into a "heat" component and a "work" component. This is the burden of the argument of Münster and of Haase. Some texts simply use the word 'heat' here to refer to this kind of transfer of internal energy. This usage of the word 'heat', meaning internal energy, though quite commonly found, including in texts of kinetic theory, and more or less traditional, is not in accord with our usage here, and to assume that by 'heat' these texts mean what we mean by heat would be inaccurate. Other texts give other definitions of 'heat' transfer, but in each case they are arbitrary as to the kinds of process that they allow, and do not supply in general unique definitions of heat, or definitions that accord with our definition of heat. Our definition of heat requires that adiabatic work be possible for the system, and this is not so for open systems, which is stated by Münster. This decisive point, previously stated here, is ignored by the immediately above response by editor PAR.Chjoaygame (talk) 03:32, 7 March 2013 (UTC)


 * Lifted from the immediately above response by editor PAR: "This is given without any qualifications, and, yes, PdV is the work done by a simple system in which velocities are negligible, and thus viscosity effects ("friction") is negligible. The statement in Alberty is likewise without qualification."


 * My response to this is as follows.
 * Alberty Equation 1.1-1 on page 1352 reads
 * $$dU=TdS - PdV+\sum_{i=1}^{N}\mu_i dN_i\, .$$
 * This cited equation is of course correct as it stands It does not mention $δQ$ or $δW$, which are the quantities that appear in the new edit. It is the presence of these quantities in the new edit that is in question here. The immediately above response by editor PAR does not address this decisive point.Chjoaygame (talk) 03:32, 7 March 2013 (UTC)


 * Lifted from the immediately above response by editor PAR: "Callen states that the PdV term for open systems is the work, and the fact that he notes that it is the same term found in the closed system statement does not constitute a ″qualification″."
 * My response to this is as follows.
 * Callen on page 36 starts with the equation
 * $$dU=TdS - PdV+\mu_1 dN_1+ ... + \mu_r dN_r\, .$$
 * which does not mention $δQ$ or $δW$.
 * Callen goes on to give a pedagogic discussion of the cited formula. In particular he considers the term $−P dV$ as identified as the quasi-static work as given for the case of a closed system. This is not work in general, as is implied in the new edit. It is a special case, the quasi-static case. Callen also considers the term $T dS$ as representing the quasi-static heat flux. This is not heat flux in general, as is implied in the new edit. Again, it is a special case, the quasi-static case. The immediately above response by editor PAR says that this is not a "qualification". That word "qualification" is his. I am saying that the pedogogic account given by Callen does not pretend to cover heat in general or work in general; it just illustrates the correct general formula in a special case that is easy for the student to grasp. The use of the terms $δQ$ and $δW$ in the new edit implies that what is being referred to is heat and work in general; this is not justified by Callen's pedogogic discussion of a special case.Chjoaygame (talk) 03:32, 7 March 2013 (UTC)


 * The defence of the new edit does not actually explicitly cite a source for the terms $δQ$ and $δW$, though it obviously intends Callen's equation (2.10) on his page 37: $dU = đQ+đW_{M}+đW_{c}$, where $đW_{c}$denotes what Callen in his pedagogic discussion chooses to call the quasi-static chemical work. This equation of Callen refers to quasi-static processes only and is a special case, not the general case implied by the new edit when it uses the terms $δQ$ and $δW$. The implication of this pedagogical special case is that the processes of transfer of internal energy as heat and as work and with the transfer of matter are conducted separately and seriatim. This is not a general process for an open system.Chjoaygame (talk) 03:32, 7 March 2013 (UTC)


 * Lifted from the immediately above response by editor PAR: "Another reference: The differential equations of thermodynamics by V.V. Sychev. His equation 3.144 (page 56 in my copy) states the same thing again. Here he uses $$\varphi dG$$ where dG is mdN, where m is the mass of a particle, and $$\varphi=\mu/m$$. I could go on and on."


 * My response to this is as follows.
 * I am sorry that I do not have quick access to this text. It may take me some time to get access. It may speed things up if editor PAR would very kindly explicitly cite here the exact equation to which he refers in this text.
 * I am sorry that editor PAR feels that he has to write "I could go on and on."Chjoaygame (talk) 03:32, 7 March 2013 (UTC)


 * Lifted from the immediately above response by editor PAR: "Unless you understand Munster's reasoning and can explain it, and can explain why, please don't modify the statement."


 * This request is an attempt to reverse the burden of proof. The normal Wikipedia burden of proof is that the new edit, if challenged, must supply reliable sourcing. This request is an attempt to evade this by asking me to understand and explain Münster's reasoning, and by implying that I haven't already done so, and that I have an obligation to do so.
 * I have above stated Münster's argument, that heat is properly defined for systems in which work is properly defined, and that proper definition of work requires that the system can participate in adiabatic work, and that adiabatic work is impossible for an open system; therefore heat is not uniquely and properly defined for open systems. The immediately above response by editor PAR has not responded to this; it is as if the edit has simply ignored it. It does not matter whether I have understood or explained Münster's reasoning. What matters is the the new edit has an obligation to provide reliable sourcing, which it has not done. The above request is an attempt to reverse this burden of proof. The immediately above response by editor PAR seems to assume that $T dS = δQ$ and $P dV = δW$, but does not prove it. I say that, though it may be so in special cases, it is not true in general. The general case is in question here, and that is the one that needs to be proved by reliable sources in order to justify the edit.Chjoaygame (talk) 03:32, 7 March 2013 (UTC)


 * Lifted from the immediately above response by editor PAR: "these three reputable sources seem to be in conflict with Munster." In my reading, the "three reputable sources" do not seem to be in conflict with Münster. It is not what the sources say, but what editor PAR reads for himself into the sources that conflicts with Münster. In brief, editor PAR seems to read into the sources some proposition such as that in general $T dS = δQ$ and that $P dV = δW$, though that is not stated in the sources.Chjoaygame (talk) 03:32, 7 March 2013 (UTC)


 * As a general comment, it seems to me that editor PAR's response here is trying to evade or ignore the fact that our definition of heat refers to a closed system which has its internal energy defined by the adiabatic work it does, and that adiabatic work is impossible for an open system, as noted by Münster and others. Editor PAR seems to wish for another definition of heat.Chjoaygame (talk) 03:32, 7 March 2013 (UTC)


 * In summary, I again conclude that the defence of the new edit is not adequate.Chjoaygame (talk) 03:32, 7 March 2013 (UTC)

response 2

 * I think that I have partially misunderstood your objections and that I partially agree with you. You are right, the new edit certainly should not say that, for a simple system, $$dU=\delta Q-\delta W+\mu\,dN$$ without specifying that, for a simple system $$\delta Q=T\,dS$$ and that $$\delta W=P\,dV$$. Or, perhaps it should simply read $$dU=T\,dS-P\,dV+\mu dN$$ and then specify that $$T\,dS$$ and $$P\,dV$$ are the heat and work terms. I thought the problem was with the $$\mu\,dN$$ term and I am sorry for the misunderstanding.


 * I won't list the Sychev reference, it basically repeats the others.


 * I take issue with the idea that adiabatic work is impossible for an open system, or that one cannot separate the contribution of heat and work when the internal energy of an open system is changed. Not having access to Munster, I will state my reasoning and perhaps you can clarify. For a simple open system, $$dU=T\,dS-P\,dV+\mu dN$$. U, T,S,P,V,$$\mu$$ and N are all well defined for a simple system so that each term in the equation has a definite value. An adiabatic transformation is one in which there is no heat transferred or, equivalently, dS=0, since the change in internal energy by heating is $$\delta Q=T\,dS$$. Likewise, the work done by the system is just $$\delta W=P\,dV$$. The change in the internal energy as a result of particle transfer is then $$\mu\,dN$$. In other words, for a simple open system, the contributions to the change in internal energy CAN be divided up into that due to heat, work, and particle transfer. PAR (talk) 04:54, 7 March 2013 (UTC)


 * Thank you for this response.
 * You write that "For a simple open system, $$dU=T\,dS-P\,dV+\mu dN$$. U, T,S,P,V,$$\mu$$ and N are all well defined for a simple system so that each term in the equation has a definite value." That is what the sources say. I agree. That is not at issue.
 * At issue is the terms $δQ$ and $δW$, which do not appear explicitly as such in this formula, though you feel that they are necesarily implicit.
 * You propose that "An adiabatic transformation is one in which no heat is transferred, or equivalently, dS=0". This is not the Wikipedia definition. The Wikipedia definition is that an adiabatic process is one that occurs when the walls of the system are adiabatically isolating. Heat is then defined as a residual between two ways of conducting the process of interest, one a reference way with purely adiabatic work permitted so as to fix the change of internal energy, the other the way of actual interest that allows non-adiabatic transfer of energy as well as the work done in the process of actual interest. Adiabatic walls do not allow transfer of matter. In general, walls that allow transfer of matter allow also transfer of internal energy and with the one exception noted by Tisza they also allow transfer of entropy; they are not adiabatically isolating. On the other hand, for an open system, when matter is transferred there is also transfer of internal energy to be considered, and this is not simply attributable to heat transfer in the Wikipedia sense. Thus, for an open system, dS=0 is not necessarily equivalent to a transfer in which no heat is transferred. Also, in general, work is not confined to pressure-volume work, but in general includes isochoric work. The formula $dU = δQ − δW + μ dN$ in the new edit is not well defined for heat and work in general, but as written it gives an appearance of referring to them in general. The requirements $δQ = T dS$ and $δW = P dV$ are special requirements, not generally true.


 * For open systems, in general, one needs to consider second law factors such as entropy. As noted by Münster and by others, the Gibbs formulation that covers open systems, simply postulating that $U = U(S, V, N)$, is therefore a real generalization beyond the Clausius-Kelvin(-Carathéodory) discussion. It is not evident to me that this needs to be gone into at this point in the article on conservation of energy. I think it likely that this is better omitted from here than elaborated here.Chjoaygame (talk) 07:52, 7 March 2013 (UTC)


 * Maybe I understand the problem here. You cannot in general have a wall that is both permeable to particles yet allows no transfer of the thermal energy of those particles. The fundamental law for a simple system states that dU=TdS-PdV+µdN. Suppose we have a system (system A) whose thermodynamic parameters are being changed as the result of being connected by a wall to another system. Lets assume the volume of system A is held fixed, so that dU=TdS+µdN. You cannot in general have a permeable wall for which the entropy of system B does not change. In other words, you cannot generally have a wall such that dU=µdN. So, basically you cannot have a wall that is permeable to particles, yet impermeable to heat. It is not true that an adiabatic wall permits no particle transfer. To say that a wall is adiabatic says nothing about its permeability. An adiabatic wall may or may not be permeable to particle transfer. So I agree, walls that permit particle flow cannot generally be adiabatic. As I said in the heat article, I also agree that, for a simple system, it must be specified that $$\delta Q=TdS$$ and $$\delta W=PdV$$. PAR (talk) 05:21, 8 March 2013 (UTC)


 * You write: "for a simple system, it must be specified that $$\delta Q=TdS$$ and $$\delta W=PdV$$."


 * Instead of "it must be specified" I would say "one might wish to specify". It remains the case that for an open system, in general, work is not uniquely defined, and so heat is not uniquely defined. The use of the terms $$\delta Q$$ and $$\delta W$$ then is hardly rational.Chjoaygame (talk) 12:17, 8 March 2013 (UTC)


 * Editor PAR writes above: "An adiabatic wall may or may not be permeable to particle transfer." It may save some time if I observe here that this statement is contrary to the uniform usage of established authorities on thermodynamics. For example, Carathéodory initially takes an 'adiabatic wall' as impermeable to everything. Following that, as contrary to adiabatic walls, he considers "permeable walls", including those "permeable only to heat". I think the term 'adiabatic' was introduced to physics by Rankine, who used it in the context of closed systems. In general in thermodynamic texts, adiabatic work is discussed in the context of closed systems, and not in the context of open systems. Münster writes that adiabatic work is impossible for open systems, obviously taking it that an adiabatic wall is impermeable to matter. In the strict thermodynamic definition of adiabatic work, mention of the word 'heat' is forbidden, so that one cannot properly read the word adiabatic as intended to mean 'impermeable to heat'; much effort goes into defining it without reference to heat. A typical example of an adiabatic wall is sometimes given as the wall of a thermos flask. The Greek origin of the word bespeaks simply impermeability, with no mention of heat.Chjoaygame (talk) 17:59, 8 March 2013 (UTC)


 * This discussion is about definition of terms, and I do not mind altering what I see as a definition of a particular word in order to facilitate discussion, as long as we remain consistent. We are talking about a partition, or wall, between two simple systems. By simple, I mean a system composed of one type of particle, which is very close to being in equilibrium. The wall can be characterized by its thermal conductivity (k), its diffusion coefficient (D) (i.e. its permeability to mass or particle transfer), and its mobility (&eta;) (i.e., its ability to move, altering the volume of the system). Let's not be too concerned with how exactly to characterize its "mobility", other than to say that it may not move at all (&eta;=0, or rigid, or inflexible) or, that in response to a pressure difference, it will move.


 * I wish to speak about a wall which has a thermal conductivity of zero, but makes no claim as to the mobility or diffusion coefficient of that wall, what I have been calling adiabatic. Lets characterize a wall by its three coefficients (k,&eta;,D). Lets define * as some number greater than zero. Lets define ? as some number greater than or equal to zero (possibly infinite), and let ∞ stand for infinity. In other words, a (∞,∞,∞) wall represents no wall at all. I have been defining an adiabatic wall as a (0,?,?) wall. What is your definition of an adiabatic wall?. Lets use the notation to avoid any misunderstanding. You say that work cannot be defined for an open system. By an open system, what kind of wall do you mean? Do you mean a (?,?,*) wall, one that allows diffusion but makes no claim to mobility or thermal conductivity? Or do you mean perhaps a (*,*,*) wall, one which is open to all kinds of transfer. Or do you mean a (∞,∞,∞) wall, which means effectively no wall at all? Or perhaps a (?,?,∞) wall, one that allows completely free transport of particles across the wall? We must define exactly what we are talking about in order to have a meaningful discussion.


 * What do you mean by a diathermal wall? I would say it is a (*,?,?), one with a positive thermal conductivity, with its mobility and permeability to matter unspecified. Perhaps you mean a (*,0,0) wall, a rigid wall, impermeable to matter, but with a positive thermal conductivity.


 * You say that adiabatic work is impossible for an open system. To me, this says that PdV cannot be defined for a wall that is permeable to particles - a (?,?,*) wall. Again, I need to know exactly what you mean by an adiabatic wall before I can address your statement. PAR (talk) 06:10, 9 March 2013 (UTC)


 * Thank you for this response.


 * You ask: "I need to know exactly what you mean by an adiabatic wall before I can address your statement."


 * I do not see myself as a source. I see my remit as reporting what reliable sources say. For me, an adiabatic wall is what reliable sources say it is. I have tried to say just above that reliable sources say that an adiabatic wall is movable according to the usual mechanical rules about pressure and volume, but impermeable to matter and energy.


 * You ask me to use your notation to define a diathermal wall. I am not sure why you ask about this, when the question at issue is about an adiabatic wall.


 * You have set up a notation that presumes the answer to the question at issue. You have presumed that the wall has a defined thermal conductivity. That presumes that heat is already defined, when its definition is in question. Once I accepted your notation, it would be assumed that I accepted your presumption. Sometimes such a presumption is called petitio principii.


 * Thermal diffusion is a phenomenon of nature in which a temperature difference drives diffusion of matter even when there is zero concentration gradient of matter. Your notation seems to rule out this phenomenon of nature, because your notation seems to presume that transfer of internal energy driven by temperature gradient is indifferent to the presence or absence of a concentration gradient that could drive transfer of matter. You seek to ignore what are often called 'cross-effects'.


 * You allege that I say that adiabatic work is impossible for an open system. This is making things personal.


 * It is not me who says that adiabatic work is impossible for an open system.


 * Münster 1970, p. 46 writes: "The situation is, however, quite different when we try to include open systems and chemical reactions in the discussion. We note immediately that the definition of the fundamental concepts of work and heat run into difficulties." He goes on to illustrate with an example. I do not think it appropriate that I quote verbatim the whole of his discussion. I will paraphrase the first part. Münster tells of a phase of interest with fixed volume and a semi-permeable membrane. Matter is forced from the surroundings through the membrane into the phase. According to Münster, "Work is obviously done", but is not reflected as pressure-volume work in the deformation coordinates of the phase of interest. I would hardly be sure that it was work done on the phase of interest. It is not captured by the formula in terms of $P dV$. But I feel that it put internal energy into the phase of interest. Is it a kind of isochoric work? Münster says "It is, therefore, not generally possible to to define clearly the 'volume work' done on an open phase. This removes, at the same time, the basis for the definition, according to §8, of the heat absorbed. This state of affairs may be expressed somewhat more precisely by saying that the adiabatic work required by §8 cannot, by definition, be done on an open phase." Some energy went into the phase of interest with the matter, and I would say that was internal energy added to the phase of interest, but I don't see how it can be split into heat and work. I think that is what Münster means.Chjoaygame (talk) 11:58, 9 March 2013 (UTC)


 * Haase 1971 writes on page 34: "On the other hand, work and heat are not functions of state; they essentially relate to interactions of the system with its surroundings. Hence, these quantities as defined heretofore have no definite meaning for open systems (cf. Defay (1929). See also Haase (1956a).)" He goes on to list exceptions and to offer restricted definitions of work and heat, but he still says on page 35 that "the total work done on the open system remains indefinite." He speaks of "the trivial case of a closed phase".


 * Not exactly to the point of your case of a single constituent, but still to some degree related, is info from Prigogine and Defay 1954. They are interested in chemical reactions. They do their examination in terms of affinity. On page 34, however, they refer to irreversible mechanical processes, such as viscosity. They write: "The idealization of changes as reversible involves the suppression of all phenomena such as those just listed, and very often this is quite impracticable." On page 43 they compare their approach with that of Schottky, Ulich, and Wagner, Thermodynamik, Berlin, 1929, which uses concepts of work. They say that their approach, and that of SUW, are based on chemical reaction, while Gibbs' approach is based on the components of the phase and their chemical potentials. They say that theirs and SUW's approaches are based on the fact that all chemical reactions are irreversible, "except for the special limiting case of equilibrium reactions". They find that their approach differs from the SUW approach in the case of non-isothermal changes. For the SUW approach, "The reversible work done between two given states depends, by virtue of (3.37) on the path taken, and it cannot be defined unequivocably [sic].* foot note reads: For a further discussion of this point cf. R. Defay and I. Prigogine, Bull. Ac. Roy. Belg. (Cl. Sc.), (5), 33, 222 (1947)."Chjoaygame (talk) 11:58, 9 March 2013 (UTC)


 * You ask "I need to know exactly what you mean by an adiabatic wall before I can address your statement." By an adiabatic wall I mean what reliable sources say it means. Perhaps Carathéodory 1909 is the locus classicus for this. Translated, he says: "A vessel $Γ$ of this kind can have, for example, the property that the phases present in it are in equilibrium and the numerical values (2) established for them remain constant when the bodies present outside the vessel are modified with the single restriction that $Γ$ remains at rest and retains it original shape. A thermos flask constitutes a handy example of such a vessel. ... A vessel provided with such properties is called adiabatic and the phases enclosed in it are referred to as adiabatically isolated." Other sources follow this. For example, Callen on page 16 also writes of "a Dewar wall (consisting of two silvered glass sheets separated by an evacuated interspace)." These adiabatic walls are impermeable to matter.


 * You wish to ignore these reliable sources and to re-define the term adiabatic wall, but I think that is not appropriate for dealing with established concepts like this for the present purpose. Much effort on this page has gone into accepting the Carathéodory definition. I mostly recall Count Iblis as champion of this, but I think others agree. It is not appropriate to ditch that effort without proper work. You are seeking to ditch it in order to criticize a particular edit that you find objectionable. You do not offer a properly relevant explicit quote from a source to support your case.


 * On the talk page for the Wikipedia article on heat there is more about closely related matters. An answer to your concern about 'heat' for open systems is there partly supplied by the edit about Beris.Chjoaygame (talk) 09:03, 9 March 2013 (UTC)


 * At the risk of being over-chatty, perhaps I can suggest an interpretation of the Prigogine & Defay 1954 comments quoted above. The Gibbs approach is about demonstrating the convexity property of the equilibrium surface. Just geometry. Rates don't come into it. For this, one can rely on quasi-static "processes", conceptual entities that are not naturally occurring. They are just virtual "processes". They are convenient and enlightening manifolds to which naturally occurring processes may approach. Nice quasi-static formulas tell about the virtual quasi-static work. Prigogine & Defay focus on naturally occurring physical processes especially including those that are essentially non-quasi-static; they use an affinity method. Rates matter here. The naturally occurring "work" is not given by nice quasi-static formulas. The virtual work approach of SUW doesn't always deliver the goods. Just guessing, not having read more than a snatch of Beris, it seems that he prefers the affinity method, but is not as particular about the rigorous definition of heat as are Münster and Haase. When it comes to "heat" current, Prigogine & Kondepudi 1998 on page 348 say something about different definitions. This is partly to do with the difference between the energy representation and the entropy representation, and partly to do with substantially different notions of "heat" current.Chjoaygame (talk) 00:27, 10 March 2013 (UTC)

response 3
It may be useful for me to offer some more interpretive comments here.Chjoaygame (talk) 04:25, 13 March 2013 (UTC)

Closed systems
On page 121, Atkins, P., de Paula, J. (1978/2010), Atkins' Physical Chemistry, ninth edition, Oxford University Press, Oxford UK, ISBN 978-0-19-954337-3, discuss the combination of the first and second laws for closed systems in the absence of isochoric work. They say "that the first law of thermodynamics may be written $dU = dq + dw$ [their notation and sign convention]". For a reversible process, they write $dw_{rev} = − p dV$ and $dq_{rev} = T dS$. Then

$dU = dq_{rev} + dw_{rev}


 * = T dS − p dV$

They call $dU = T dS − p dV$ "the fundamental equation". Its value is independent of path. True for both reversible and irreversible processes with the same end-states. Then they write: "The fact that that fundamental equation applies to both reversible and irreversible processes may be puzzling at first sight. The reason is that only in the case of a reversible change may $T dS$ be identified with $dq$ and $− p dV$ with $dw$ ." For an irreversible change, the Clausius inequality holds, so that $T dS > dq_{irr}$ and $− p dV < dw_{irr}$ [their sign typo corrected]; the identifications of $T dS$ with $dq$ and of $− p dV$ with $dw$ are not valid.

With this same sign convention, that work done on the system has a positive sign, Prigogine & Defay 1954 on page 44 note that $dW_{irr} > dW_{rev}$.

On page 75, Adkins, C. (1968/1983), Equilibrium Thermodynamics, third edition, Cambridge University Press, London, ISBN 0-521-25445-0, discusses "the entropy form of the first law" for closed systems. His account is nearly the same as the above one from Atkins & de Paula 2010. "For any change of state, however it occurs, ..., $dU = đQ + đW$ [his sign convention, again the same]." For reversible changes $dU = T dS − p dV$. But this depends only on the initial and final states and the variables here are all state variables, so that this holds for both reversible and irreversible changes. For reversible changes, $đW_{rev} = − p dV$ and $đQ_{rev} = − T dS$, while for irreversible changes, $đW_{irr} ≥ − p dV$ and $đQ_{irr} ≤ − T dS$. When, in addition, isochoric work is allowed, in the form of friction for example, it is always irreversible, and again the identifications of $T dS$ with $đQ_{irr}$ and of $− p dV$ with $đW_{irr}$ is not valid.Chjoaygame (talk) 04:25, 13 March 2013 (UTC)


 * Yes, I agree. What we want is the best expression of the first law (conservation of energy) for an open system. The above discussion is for closed systems.


 * I have been carefully reading "Definition of heat in open systems" by Smith (1980) and I now agree with you, my latest edit, $$dU=\delta Q+\delta W+\mu\,dN$$, in which I just tacked on the chemical potential, is simply incorrect, even though, as we both agree, $$dU=T\,dS-P\,dV+\mu\,dN$$ is correct.


 * In reading Smith, however, I see that for a reversible simple system, work and heat CAN be defined. Smith clearly states that, for a simple (1-component) system, reversible or irreversible,


 * $$dU=\delta Q+\delta W+u'\,dM$$


 * where u' is the internal energy per unit mass of the added mass. This makes sense. The main point is that the addition of mass to the system may change its volume, but this volume change multiplied by pressure does not constitute work, so $$\delta W\ne -P\,dV$$. In fact, in the reversible case, $$\delta W= -P\,(dV-v\,dM)$$ where v is the volume per unit mass of the added mass, and the heat $$\delta Q$$ is the remainder. I have altered the offending equation to reflect this. Does this agree with your view of the situation? PAR (talk) 22:33, 13 March 2013 (UTC)


 * We are now looking at fine points. Münster gives a very carefully considered general statement of the first law of open systems. It is couched in more abstract or fundamental terms than the Smith account, and for that reason may be preferable. I think it best right now that I just say I am not sure.Chjoaygame (talk) 23:34, 13 March 2013 (UTC)


 * I will have to get hold of a copy of Münster. PAR (talk) 00:47, 14 March 2013 (UTC)


 * Ok. It is a pity there is not a bit more about this easily accessible.Chjoaygame (talk) 05:51, 14 March 2013 (UTC)


 * Thinking it over some more. I think that Smith 1980 is not a reliable source. It is primary research, not cited so far as I know in a secondary source. And it is not adequate for the purpose for which it is cited.


 * What is wrong with Smith 1980?


 * (1) Smith writes: "We choose to define adiabatic processes ..." If this is a real choice, then it is arbitrary. Smith makes no attempt to provide explicit justification for it. Classical and established terms such as adiabatic are not playthings. We are not here about putting up an arbitrary notion as a definition of heat.


 * (2) "it is possible to have workless adiabatic processes". This is an insignificant play on words. Work is properly defined as a kind of transfer of energy between two closed systems. Smith's "workless process" is not a process of transfer of energy between two closed systems. It is an amalgamation of two closed systems into one. It is a "workless process" only because it is in the strict sense not a process of the kind that has a defined quantity of energy transferred as work. This "workless process" might be regarded, under some other definition of a process, as a process of transfer of internal energy. But that is just the point, we are trying to resolve a process of transfer of internal energy uniquely and in general into a work component and a heat component. It is as I were to say "Here is my resolution in A and B: so much A, so much B, some not classified as A or B". Smith requires a concept not considered in the usual statement of the first law for closed systems, namely transfer of unclassified internal energy associated with matter. Strictly, the ordinary definition of adiabatic work is not applicable here, and so Smith's term $dW$ is not properly defined, while he supposes, without explicit discussion, that it is properly defined.


 * As a more general comment, I think that the concepts of heat and work in thermodynamics are properly limited to a particular theoretical context, and that it is not useful to try to force against the grain beyond that context. This is not too surprising. Originally one thought of heat as always driven by temperature gradient, but I now think probably that one can speak of heat transfer in a violent process in which temperature is defined only for some of the way, especially for the initial and final states; but it is overdemanding to think of a process of heat transfer only when temperature is defined throughout the internal course of the process. In this case it is temperature that is undefined. But it is a precedent for admitting that there may be cases when heat is not defined. In both cases, the undefined quantities belong to the internal course of a process, not to initial and final states.Chjoaygame (talk) 21:58, 14 March 2013 (UTC)


 * Smith (1980) is not original research, it is an analysis of the various terms for heat found in the literature. For multicomponent systems, he shows that the terms basically boil down to two types which he refers to as "P" for Prigogine, and "H" for Haase. He demonstrates that both agree in the case of a single component system. He examines the points that recommend each type, showing in particular that the Haase definition is invariant when the standardized values are changed, while Prigogine's does not, which is a strong point in Haase's favor. He does not declare either form to be wrong or inconsistent. He does declare that both yield the same definition of heat and work for the case of a single component open system.


 * An increment of work is a clearly defined concept, it is force times the increment of distance. To say that adiabatic work is undefined does not mean that the work, Smith's $dW$, is undefined, it means that "adiabatic" is undefined. Smith supposes, without explicit discussion, that work $dW$ is properly defined, and rightly so. He then discusses a system consisting of the system in question before the mass is added and the added mass before it is added. This system constitutes a closed system, and the term "adiabatic" has meaning. He then considers how that closed system evolves in time, yielding an expression which clearly defines work and heat for the open (sub)system. He further shows that the disagreements in the literature regarding heat in the case of open multicomponent system disappear in the case of the open single component system and that they also agree with his explanation for the single component system. The fact that he shows this assures that his development explains the literature, and is not original research. PAR (talk) 05:21, 16 March 2013 (UTC)


 * In this context, the phrase 'original research' usually refers to ideas coming from the Wikipedia editor. I wrote not that Smith's paper was original research, but that it was "primary research". In this context it means that it is a journal article, not taken from a standard textbook. In the present context, a secondary source is preferred and that often means taken from a standard textbook, especially in a subject of this degree of maturity and generality.


 * Smith's position is that the internal energy that passes with matter is not safely to be split into heat and work components. I think we all agree with that.


 * Smith, however, in his Figure 2, constructs an at-least-four-system scenario in which external work is done by the outer surroundings on the system of interest, while the inner surroundings, not the the system of interest, receive heat from the outer surroundings; this is not the usual two-system scenario of system-and-surroundings to which the usual statements of the first law apply. Smith has constructed a special case.


 * Smith, moreover, indicates that a notion of adiabatic work for an open system is problematic for him, so that he feels entitled and obliged to fabricate a definition for it. Münster (and I) would say that he is not so entitled or obliged.


 * I wrote that "Smith's term $dW$ is not properly defined". I meant that he defines it in a way not proper for the present problem, not that it is undefined. Smith answers his question only for mass-reversible and for completely reversible processes, of the first kind, idealizations that do not occur in nature, not for general natural processes. General natural processes are the proper setting for the present problem.


 * You write: "To say that adiabatic work is undefined does not mean that the work, Smith's $dW$, is undefined, it means that ″adiabatic″ is undefined." Your sentence is logically faulty in several ways.


 * In pure logic, semantics if you will, that a two-word phrase is undefined does not necessarily entail that either one of the two words separately is undefined. It means that their combination in the phrase is undefined. For example, the phrase 'banana heat' is undefined, but that does not imply that either of the words banana or heat is undefined.


 * But beyond mere semantics. Substantially, your sentence implies that someone said that adiabatic work is undefined. The nearest we have to that is Smith saying that "No progress can be made until we have some notion of adiabatic processes for these systems." This is a problem in Smith's mind, that he feels that somehow he can and must fiddle with the term 'adiabatic work'. But that doesn't mean that he is logically entitled to such fiddling. Far from it. It is a snow job. For an open system, adiabatic work is impossible, as pointed out by Münster and implied by Haase. This leaves the term heat as inapplicable. Yes, I did write above that "there may be cases when heat is undefined". I should more safely have written 'there may be cases when heat is not an applicable term'. But that does not amount to Münster's (or my) having said that adiabatic work is undefined.


 * More generally, your comments are not engaging effectively with the arguments against your position.Chjoaygame (talk) 15:59, 16 March 2013 (UTC)

an increment of work

 * You write above: "An increment of work is a clearly defined concept, it is force times the increment of distance." The problem here is that the force and the increment of distance are not clearly identifiable. So their product is also not clearly identifiable. For a concept of transfer of energy as work, say from the surroundings to the system, some of the force is on the bulk of the system, and some of it on the matter that is diffusing through the semi-permeable membrane from the surroundings to the system. The diffusing matter is moving and so has kinetic energy. How far does it move under the influence of what force? This makes it impossible to name a single quantity work in terms of macrocscopic variables such as are admissible in thermodynamics. On the other hand, transfer of internal energy is identifiable. That is why for kinetic theory, people speak of "heat" transfer, but when one reads their writings one finds that what they really mean is internal energy transfer, not heat transfer as defined in macroscopic thermodynamics. The Prigogine 1947 definition of "heat" transfer for open systems refers actually to internal energy transfer. That is why it does not agree with Haase's "reduced heat"; neither is heat transfer as defined for closed systems; that they differ in quantity does not mean that one is right and the other wrong; it means that they differ in intent and use of language.Chjoaygame (talk) 13:57, 30 March 2013 (UTC)

the dog that didn't bark

 * The following is not proposed as a valid physical argument, but is intended to raise a question in the reader's mind.


 * There is a small literature on the estimation, calculation, or definition of irreversible volume work. Not radically exciting physics, just routine stuff. But there is a small literature nevertheless. Some people care about this.


 * For example, Gislason and Craig (J. Chem. Educ., 64: 660–668) wrote in 1987: "A thoughtful writer on this topic has said (9) [Levine (1983) second edition, p. 40] For mechanically irreversible volume changes, we usually cannot calculate the work from thermodynamic considerations." The logic here is that mechanical work is a concept presupposed prior to thermodynamics and one cannot in general demand of thermodynamics that it provide an algorithm to calculate a quantity of work; thermodynamics expects to be provided with such an algorithm as a prior presupposition. Levine did not ignore this. His text has over 1000 pages and he has space to say what he likes. In his sixth edition (2009, Levine,I.N., Physical Chemistry, McGraw-Hill, New York, ISBN 978–0–07–253862–5) he followed it up with three references including one to Gislason and Craig (2007, ibid. 84: 499–503). Levine writes on page 45 of his text: "The work $w$ in a mechanically irreversible volume change sometimes cannot be calculated with thermodynamics." I will not here list further references to this small literature; Gislason and Craig provide some. Levine cares about this.


 * But in contrast to this concern about the details of calculation of irreversible mechanical work, little is widely discussed about our current problem, the existence of a unique general definition of work for open systems.


 * For example, Levine in his 2009 sixth edition writes on page 43: "We implicitly assumed a closed system in deriving (2.26) [volume work for a closed system, reversible process]. When matter is transported between system and surroundings, the meaning of work becomes ambiguous; we shall not consider this case." Two points here. Levine did not initially flag that he was dealing with a closed system for his discussion of work; he implicitly assumed it. Many other writers do the same, but, unlike Levine, they do not later remark on having done so. But if you notice, statements about work for open systems are conspicuous by their absence from many texts. Given that Levine cares about the detail of calculation of irreversible volume change work for closed systems, it is perhaps surprising that he offers nothing about such things for open systems, unless one guesses that he doesn't have much of an answer about them; which he seems to say directly. That is the dog that didn't bark.Chjoaygame (talk) 13:03, 31 March 2013 (UTC)

concerning Smith's position
Regarding the "original research" comment - point taken. But primary sources are not automatically disqualified.

Concerning Smith's position that the internal energy that passes with matter is not safely to be split into heat and work components, we do not agree. In the case of multicomponent systems, yes. In the case of a single component system, no. But why do we disagree?

The statement of Smith you seem to have a problem with is "We choose to define adiabatic processes in these (single component) systems by requiring that the process for the original system plus its infinitesimal added mass, which together form a closed system, is adiabatic in the usual sense." Can we agree that IF this convention can be justified to your satisfaction, you would agree that heat and work CAN be distinguished for an open system? I'm not asking this because I think I can justify it to your satisfaction, I ask it only to clarify the nature of our disagreement. PAR (talk) 05:10, 18 March 2013 (UTC)


 * For the present I will defer the hypothetical question just above, and just consider your comment "Concerning Smith's position that the internal energy that passes with matter is not safely to be split into heat and work components, we do not agree. In the case of multicomponent systems, yes. In the case of a single component system, no. But why do we disagree?"


 * It seems what I wrote was not explicit enough. By writing "Smith's position is that the internal energy that passes with matter is not safely to be split into heat and work components. I think we all agree with that," I meant as follows. Smith proposes the formula $dU = dW + dQ + dR,   (1)$. This formula refers to three physical terms. The first two refer to transfers of energy as work and as heat. The third, $dR$, called by Smith "changes by addition of mass", is a term that contributes to the internal energy increment and I read it as consisting of the internal energy that passes with matter, not splittable into heat and work components; he says it is both "workless" and "adiabatic". I do not see him try to split it anywhere later in the paper. Now I recall, however, that you said at one stage that, because it was "workless", it was all heat contrary to Smith who said it was transferred in way that is both "workless" and "adiabatic". If had forgotten that when I thought this was agreed.Chjoaygame (talk) 09:39, 18 March 2013 (UTC)Chjoaygame (talk) 19:03, 18 March 2013 (UTC)


 * As for your hypothetical question. If I were to let you keep nagging long enough, and continue to answer your leading questions as if I were a witness in a box letting himself be bagdered by a barrister, presumably at some stage you would wear me down and trick me into contradicting Münster, who says that adiabatic work is impossible for an open system. Not yet.


 * Carathéodory is put by Tisza 1966 together with Clausius and Kelvin, as a leader of the CKC theory, in distinction from the MTE (macroscopic theory of equilibrium) largely represented by Gibbs. The CKC theory is only about closed systems. Gibbs introduced open systems in order to account for the chemical potential. Carathéodory includes the scenario of Smith Figure 1 as a "simple system". It is a closed system even though its internal "phases" are allowed to exchange matter. Work and transfer of internal energy are defined across the external walls that confine it from the surroundings; they can be adiabatic, or "permeable only ″to heat″", or can allow non-adiabatic work transfer, transmitting work as well as "heat". But matter does not penetrate those external walls. Only transfer of internal energy is defined between the internal "phases". Smith puts an adiabatic wall around his system of interest plus its incremental system; that should mean that through that wall no heat enters the system of interest plus its incremental system. All the heat, $dQ$, that penetrates from the external surroundings ends up in the internal surroundings, none of it reaching the system of interest. It has nothing to do with the system of interest. Why does he mention it? Smith is just playing games with the term "open system", and tacitly admits that Münster is right to say that adiabatic work, defined in the usual way, is impossible for an open system. This problem was not dreamed up by Münster. It is discussed for example by Defay 1929, Gillespie & Coe 1931, Prigogine 1947, Haase 1951, and Tolhoek & de Groot 1952, and de Groot & Mazur 1962.Chjoaygame (talk) 19:03, 18 March 2013 (UTC)


 * You are taking me wrong yet again. I am not nagging, not trying to trick you, and my question was not a leading question, and even if it were, leading questions are not dishonest. I tried to make that clear when asking it. I am trying to tie down the nature of our disagreement, and you could have answered "yes", in which case our point of disagreement would have been clear, or "no", in which case our point of disagreement would be elsewhere. If at some later time you realize you gave the wrong answer, then change it, I don't care, I do it all the time, because I am not interested in victory here, apparent or otherwise, I am interested in understanding your objection in order to write a better article, and every once in a while, contained in your blizzard of irrelevant quotations is a valid point and I learn something. I mean, how is the fact that "Tisza puts Caratheodory together with Clausius and Kelvin as a leader of the CKC theory" relevant to this discussion?


 * Again, Smith says "We choose to define adiabatic processes in these (single component) systems by requiring that the process for the original system plus its infinitesimal added mass, which together form a closed system, is adiabatic in the usual sense." Do you agree that this is an unambiguous statement? If you do, what is the reason you object to it? Is it because you feel it is a statement that is concocted by Smith, not discussed in other reliable sources? I'm throwing out guesses here, because I cannot seem to clarify the problem that you have with this statement.


 * I think you have misinterpreted Smith's intent on his Figure 1. Its a poor figure - the appearance of an adiabatic wall which does not follow the contours of the system(s) in question is not intended to show three systems, but rather two. Read the caption carefully and you will see that this is true.


 * I would like to follow up on the references you mentioned. The one I have at hand is de Groot and Mazur 1962. Can you tell me where in this book this scenario is discussed? I will try to find the other references in the next few days and give a more informed response. PAR (talk) 06:57, 19 March 2013 (UTC)


 * My problem is that you are reversing the onus of proof. You put up a dodgy post, that you started by making up off the top of your head without any research into sources and without citing a source, and you are in effect demanding that I spend time providing proof that it is faulty. The onus is on you to do proper research in sources and provide a well-sourced post, not on me to spend time proving your post faulty when it is prima facie dodgy as it is.


 * At best this post is hardly notable in this article: it is really helpful to tell our readers that, in the case when the boundaries of the isolated system referred to in the law of conservation of energy are hard to define because it is not clear whether one is talking about boundaries that are moving, a formula in terms of limited applicability can be written for a special scenario?


 * It is not my objection, it is Münster's, and others'. It is simple. Adiabatic work is impossible in an open system. To define the heat transferred in a process defined by its end-points, one must perform the process by two paths. A reference path is by adiabatic work, that determines the difference in internal energy. The path of interest is then followed and the work done is determined. The difference between the two amounts of work is the quantity of energy transferred as heat. For an open system, the reference path is not available. The definition of quantity of energy transferred as heat is inapplicable. Why is the reference path not available? Because one cannot guarantee that it will transfer the right amount of matter.


 * I concede that I was careless just above in reading Smith's Figure 1. He draws a time lapse as a space difference, which I did not notice. As I noted, if you keep at me long enough, at some stage I will have to make a mistake.


 * Smith's Figure 1 process is carried out in two steps. Step 1 is to keep the two systems in combination adiabatically isolated. The partition is removed. I agree that this is covered by the first law for closed systems, though heat and work are not defined for it. Step 2 is removing the adiabatic isolation and then doing some non-adiabatic work on the unpartitioned combined system, for which heat and work are defined. But the order of these two steps is important. If it is reversed, how much of the heat and work go into the separate systems before the partition is removed? In general the path of a physical process cannot be demanded to be decomposable into two steps like this. The physical process has its own path with its own determination of how the heat and work are distributed between the two separate systems. That that cannot be fiddled with. Different paths will in general have different outcomes. The process is defined by its initial and final states, and it cannot be guaranteed that a path defined simply by amounts of work and heat will take the given initial state to the given final state.


 * Smith's process of combining the two subsystems into one by simply removing a partition is not a general open system process. In Smith's process one of the subsystems has to finish up empty. In a general open system process, the two subsytems stay as two non-empty subsystems.


 * Smith avoids this to some extent by using infinitesimal increments and restricting his result to special cases. He says that this is partly an arbitrary device. A partly arbitrary device is an arbitrary device. It may be that Smith has enough apparatus to determine the change of state variables between the end-points of the process, but that does not mean that it is enough to define work and heat for a general path between the end-points.


 * Now I have to struggle with the logic of your question. Smith gives the first stage of his path, the removal of the partition between the two initial systems, jointly adiabatically isolated from the surroundings. I don't see why for Step 1 they can't be just simply isolated, as far as his path is concerned. Why bring in adiabaticity? No heat or work come into Step 1. Adiabaticity seems to have nothing to do with it. When for Step 2 he wants to let in the heat and work he will remove the isolating wall, and for two paths, replace it respectively with an adiabatic wall for the reference process and with a non-adiabatic wall suitable for the path of interest. Now I have to ask myself a two-fold question: can Smith's convention be justified? How do I react if it can be justified? The relevance of adiabaticity comes in when for Smith's step 2, after the two subsystems have been combined by removal of their partition. The adiabaticity has nothing to do with it for Step 1, for which simple isolation is required. Smith's sentence is: "We choose to define adiabatic processes in these (single component) systems by requiring that the process for the original system plus its infinitesimal added mass, which together form a closed system, is adiabatic in the usual sense." Why does he feel he need a special convention to deal with the combined de-partitioned system? Does his sentence refer to Step 1 or to Step 2? Because Smith's sentence doesn't answer that question, as Smith words it, it therefore seems to me that his sentence is nonsense. How can I respond to a demand that I say what I think would be the case if nonsense were justified?


 * Smith writes: "Hence for open systems the first law of thermodynamics must be of the form ..." He is proposing that we accept as an argument that because removal of a partition cannot be analysed as a heat − work process, the first law must be extended from closed systems to open systems by adding a pure internal energy term, assuming that his invented use of the term 'adiabatic' will permit the definition of heat and work for an arbitrary process of an open system. I don't buy it.


 * If I were to locate the problem here, I would say it was that you haven't engaged with Münster's proposition that adiabatic work is impossible for an open system, by definition, a proposition that I accept as obviously valid. Instead, you are playing a word game of trying to re-define 'adiabatic' so as to shoe-horn a usage of 'heat' and 'work' into a shoe that doesn't fit. And I don't think it is important that that shoe should be filled right here.


 * Is there anything physically important here? Well, for the local thermodynamic equilibrium version of non-equilibrium thermodynamics, one is interested in transport that is driven by several factors, including a flow of one thing as a driver of the flow of another. One of the things said to be such a driver is the flow of 'heat'. But what really is 'heat' for this purpose. One may assume all kinds of things, but I don't know how much the assumptions have been tested. The assumptions matter because of the existence of cross effects. De Groot & Mazur 1962, and Prigogine in the earlier days, simply read 'heat' to mean internal energy. In a sense they are just saying to themselves, it seems, 'Oh, diffusive thermal energy flow is "heat flow", thermal energy is internal energy, therefore "heat flow" is diffusive internal energy flow', or somesuch. For example, de Groot & Mazur 1962 on page 18 write "and finally a ″heat flow″ $J_{q}$ : ..." Glansdorff & Prigogine 1971 say they are using he same definition as de G & M and they write on page 9: "Again the flow of internal energy may be split into a convection flow $ρev$ and a conduction flow. This conduction flow is by definition the heat flow $W$." As I read this they do not try to follow the Carathéodory-Born story for "heat" here, though in other places they cite it. There is no attempt to say that heat flow is other than internal energy flow due to conduction, whatever that might be. Is heat flow driven by $grad T$ or by $grad ln T$ or by $grad (1/T)$ ? De G & M discuss this a bit in § 3 on pages 25–27. Lebon, Jou, Casas-Vázquez (2008), Understanding Non-equilibrium Thermodynamics, Springer, Berlin, 978-3-540-74251-7, on page 54 for example seem to follow also this definition of "heat flux". Later, however, Kondepudi & Prigogine 1998 seem to have taken to the Haase 'reduced heat flow', but I can't say whether they have done it rightly. Smith gives reasons why the different definition by Haase is better, but this is not very decisive, because on must ask the question "better for what purpose?" Statistical mechanics people use the internal energy definition, not the Haase definition, as far as I can see. In our language, the "heat flow" definition of these people is not a definition of heat flow and doesn't pretend to be. They simply don't define heat flow in our language for open systems. In our language, for open systems they define conductive flow of internal energy and do their things with that.


 * The relevance of the Tisza reference is that it shows that it is mainstream thinking that Carathéodory's story is, like Clausius-Kelvin, a closed system story, not an open system story, though it permits flow of matter within the simple system.


 * I suppose there are mistakes in the above.Chjoaygame (talk) 12:20, 19 March 2013 (UTC)


 * Thank you for "going out on a limb" and addressing the problem directly. As for any mistakes, I hope there are none, and if there are, I hope to find them and point them out, and offer a counter explanation. As for mistakes, I hope your attitude (and mine) is a combination of disappointment and enlightenment. And then we move on. I will read the above more carefully, go looking for references, and respond in a few days. PAR (talk) 16:46, 19 March 2013 (UTC)


 * Ok.Chjoaygame (talk) 05:00, 20 March 2013 (UTC)

Going through Smith slowly
I'm going thru Smith slowly. What he has is a very small system with internal energy density u ' and mass dM so that its internal energy is $$u' dM$$. This small system is separated from a large system (the system of interest) which has internal energy U. The partition is removed, and the combined system is now the system of interest. By removing the partition, no work is done on the system dW=0 and no heat is passed to the system dQ=0. Clearly the change in the internal energy of the system of interest is $$dU=u' dM$$. This is Smith's equation 2, with work and heat set to zero. Are we in agreement so far? PAR (talk) 06:27, 27 March 2013 (UTC)


 * Though you are going through Smith slowly, it seems you are doing so with disregard for what I have written above and below here about his paper. As I wrote above, it seems you are not engaging effectively with arguments against your position. And I think it fair to say also that you are doing so apparently without what you promised above, that you would "go looking for references". It seems that you feel you are entitled to make it up off the top of your head, and to continue to try to lead me through Smith's paper.


 * Your comment above uses the concept of "the partition is removed". This is a very potent concept, for which neither Smith nor you offer any hint of justification, or even recognition of its potency.


 * From classical thermodynamics, we are familiar with the idea that energy may pass across a partition from one system to another, and that the passage may be as heat or as work or as a combination. And we are familiar with the idea that the character of the partition may be changed, so as to produce a different process. But the idea of removing it and creating a new system from two old systems needs proper theoretical establishment. Without a proper theoretical establishment of the concept of the removal of a partition like this, of course I cannot agree with your above comment at all.


 * On page 120, Tisza 1966 tackles the difficulty that one might try to think of an isolated system, initially not in its own internal thermdynamic equilibrium, then approaching thermodynamic equilibrium as manifest in a progressive increase of its entropy, but that the entropy is defined only for a system already in its own internal thermodynamic equilibrium. He writes "This difficulty is resolved in a natural way by the artifice of composite systems." The problem is solved by considering the combined entropy of two systems, initially in their own respective separately isolated thermodynamic equilibria, with their respective separate entropies, but then allowed to interact so as to have a combined entropy. Soon, on page 121, he writes "The concept of composite systems plays an essential part in Carathéodory's theory (3; Carathéodory 1909) and is widely used in more recent works (18; Planck 1935 [I failed to find this reference and I think perhaps it might be mistaken][Added note 18 Apr 2013: Tisza did not make a mistake here. I have now found this reference. The reference is 'Bemerkungen über Quantitätsparameter, Intenstitätsparameter und stabiles Gleichgewicht', Physica, 2: 1029–1032.Chjoaygame (talk) 00:15, 18 April 2013 (UTC)]). However, the systematic incorporation of this concept into the foundations of the theory necessitates a considerable revision of the classical conceptual framework. ... In particular, we have to consider thermodynamic operations as well as thermodynamic processes." (Münster 1970 on page 376 recommends Tisza 1966 as a source for thermodynamic axiomatics.)


 * Removal of a partition is a thermodynamic operation, not a thermodynamic process. Carathéodory deals systematically with such operations by including them in his scheme of simple systems. The internal walls of Carathéodory's simple systems, as I remarked above, do not define heat or work, but only demarcate regions that have internal energy. It is only the external walls that define heat and work. So it is insignificant speech to say that "By removing the partition, no work is done on the system dW=0 and no heat is passed to the system dQ=0."


 * In an intuitive way, one might say that Smith's very small system appears out of nowhere and moves by magic. It got into the closed system without passing through its walls; truly magical. Perhaps Smith feels that by making it infinitesimally small, he can make it also able to do magical things, or that we won't ask awkward questions about operations that decreate it; but I think more likely he just hasn't thought it through or taken int account what Carathéodory did, or what Tisza had to say about it. I also expressed this below by saying that Smith moves the goal-posts while the ball is in mid-flight.Chjoaygame (talk) 08:19, 27 March 2013 (UTC)


 * Do you then disagree with the analysis of the Joule expansion article? Do you then disagree with the analysis of the Entropy of mixing article? Each of these articles make use of the removal of a partition in their analysis, and they are suitably sourced. I neglected to state in my above statement that the partition was thermally insulating, immovable and admitted no material transfer. PAR (talk) 20:40, 27 March 2013 (UTC)


 * I mentioned before that I felt like a witness being cross-examined, nay, badgered, by a barrister. You are now asking me to read other articles in the Wikipedia and assess them. You are in effect asking me to accept the Wikipedia as a reliable source, and telling me that you have no real intention of carrying out your promise that you would "go looking for references". I have here given plenty of argument on the matter in hand, and you are practically ignoring it. Why would I expect you to take notice of what I think about an altogether other article?


 * The proper Carathéodory way to deal with this is that the overall system is the one that can describe heat and work; it is a closed system, with two subsystems, the whole being classified as simple in his scheme. The two subsystems (with masses $dM$ and $M$) have internal energies; but heat and work are not defined for them. In the process of interest here, the partition between the two subsystems, initially impermeable, is made permeable to all quantities, and then internal energy, you claim, passes from the subsytem with mass $dM$ to the subsystem with mass $M$, and you thereafter want to ignore the existence of the subsystem with mass $dM$. Why did the internal energy pass from the subsytem with mass $dM$ to the subsystem with mass $M$? Because Smith waved his hands and ordered it do so?


 * I repeat, removal of a partition is not a thermodynamic process in the relevant sense. The consequences of treating removal of a partition as a thermodynamic process are set out clearly in Defay 1929: nonsense is the result that Defay finds. Smith cites Gillespie and Coe 1933, who cite Defay 1929, but Smith does not cite him; apparently Smith did not digest the physical meaning of Defay 1929, and bring it bear for his own 1980 paper. The result derived in Defay 1929 is nonsense because it is not properly done as set out by Carathéodory or by some other proper procedure.


 * Perhaps you might like to ask yourself why Gibbs is regarded as one of the greats, while few have heard of Gillespie and Coe 1933? It may help your questioning to observe that G&C remark that Gibbs gives a physical interpretation of his equations, but "as usual, deals with entropy rather than heat". Did Gibbs really not understand the importance of heat for closed systems? Why did he not talk about it for open systems?Chjoaygame (talk) 22:08, 27 March 2013 (UTC)


 * Perhaps it will be useful for me to respond to your concern about the Wikipedia articles on the Joule expansion and the entropy of mixing.


 * As to the article on the Joule expansion. The entire system is isolated from its surroundings; it is not an open system. The entire system consists of two subsystems, initially isolated from one another by a partition. This set-up is classified by Carathéodory as a simple system. The process of interest is set going when the partition is made completely permeable, or removed if you like. Quantities of matter, energy and entropy pass from the initially filled system to the initially empty system, significant amounts remaining in the initially filled system. The final state is one in which the two subsystems have reached a common temperature and pressure. This is a thermodynamic process. The two subsystems retain their identity; they are not combined into a new system, with de-creation of one of them. Because of the isolation of the entire system from its surroundings, no work or heat was transferred between system and surroundings. Carathéodory says that the sum of the internal energies of the two subsystems is unchanged by the process. He does not attempt to define the work or heat transferred between the two subsystems. Neither does the Wikipedia article.


 * You are concerned that the partition was removed, and that Tisza would say that would be a thermodynamic operation, rather than defining a thermodynamic process. The thermodynamic operation would be the merging of the two subsystems into one, with de-creation of one of them. This does not happen here. The two subsystems retain their volumes unchanged, and have their own respective internal energies in the initial and final states.


 * The Wikipedia article on the Joule expansion also considers another scenario. There is only one initial system, with its surroundings. The initial system is allowed to expand slowly and adiabatically against a resisting pressure and to do work on its surroundings. Then heat is supplied by the surroundings to the system to compensate for the work done, so that the internal energy of the system is restored to its initial value. Again, this is a process of a closed system, not of an open system.


 * As to the article on entropy of mixing. Again, following Carathéodory, one considers an entire closed system consisting of two subsystems with a partition between them; not an open system. In the conventional case, the pressures and temperatures of the two subsystems are equal, controlled and constant over the course of the process. For the process, the partition is made completely permeable, or removed if you like. The two subsystems continue to have their respective volumes, though the values of these may change during the process. The two subsystems also have their respective initial and final internal energies. In this case, work and heat may be transferred between the entire closed system and its surroundings, which are the constant temperature and pressure bath. Carathéodory now says that the sum of the internal energies of the two subsystems may be changed by the process. In the final state, also the respective internal energies of the two subsystems may be changed. These internal energies are functions of state of the respective subsystems, and their total change is governed by the first law, which talks about the work done by the entire system on its surroundings, and the heat transferred from the surroundings to the entire system. Carathéodory does not attempt to define the work or heat transferred between the two subsystems. Neither does the Wikipedia article. Again, it is a case of a thermodynamic process. The two subsystems are not merged into one, with de-creation of the other, as would be the case for the relevant thermodynamic operation.


 * In contrast, Smith's scenario involves two initial systems with masses $M$ and $dM$, which are then merged into a final common system of interest with mass $M + dM$, with de-creation of the initially infinitesimal subsystem. This is a thermodynamic operation. The internal energies of the two initial systems sum to the internal energy of the final common system. There is no talk of heat or work for the merger. Perhaps you would like to say that the initially infinitesimal subsystem changed its volume and contents to zero, and that it was not de-created; and that this would be a thermodynamic process. For your case, it would not do for some volume and contents finally to remain in the initially infinitesimal subsystem. It would be essential for your case that the final volume and contents be strictly zero. It would be a very special and restricted kind of thermodynamic process, practically indistinguishable from Tisza's thermodynamic operation.


 * If one were interested in open systems here, and wanted to take one of the two initial subsystems as the system of interest and the other as its surroundings, one could consider transfers between the system of interest and its surroundings. Matter, internal energy and entropy may pass. Work and heat in the passage are not defined in the articles on the Joule expansion or on the entropy of mixing.


 * In summary, it is not just what happens to the partition that defines Tisza's thermodynamic operation. It is what happens to the systems as a result.Chjoaygame (talk) 14:05, 29 March 2013 (UTC)


 * First, please note that my post made no reference to heat or work, only that the internal energy of the closed combined system is equal to the energy of the large system (U) plus the energy of the infinitesimally small system (udM). All discussions concerning work and heat in your response are superfluous.


 * I think you misunderstand the concept of a system. A system is a contiguous volume in space that you define, and that's all it is. It does not matter if there is a physical discontinuity at the boundary. If you have a simple gas in equilibrium, and define a volume inside it and another, infinitesimally different volume, there will be a difference in volume dV, a difference in internal energy dU, a difference in entropy dS, and a difference in mass dM, and the fundamental equation holds: dU=TdS-PdV+µdM. Systems can be created and "de-created" at will without logical problems.


 * For example, in Joule expansion, you have a single system with a physical discontinuity, conceptually "maintained" by a partition. Or not, if you choose. You also have two systems, one either side of the discontinuity. You could have a third system which divides the left system in half, but it does not help the analysis, so such a system is not used. The volume, mass and internal energy of the single system before expansion is equal to the sums of the volumes, masses, and internal energies of the two systems, because volume, mass and internal energy are extensive variables, and therefore additive. The entropy of the final system is not the same, since entropy is not conserved. The two subsystems are "created" for the purpose of the analysis.


 * In the entropy of mixing, the same reasoning applies. In Joule expansion one of the two systems is evacuated, in the mixing problem it is not, it has the same temperature and pressure as the other system.


 * In Smith's case, the same reasoning applies but the thermodynamic parameters of each subsystem are different and the internal energy, mass and volume of one system are infinitesimally small. I said the partition is removed as a conceptual device, you can just as well say that there is only one system - its volume is the large system before equilibration, the large and the infinitesimal volume after equilibration. The large system is open, or equivalently the system composing both systems is closed, it doesn't matter and that's the whole point. You analyse the open system by choosing a different closed system and analyse the closed system in order to derive conclusions about the open system. In my post, I am only trying to establish agreement that the internal energy is conserved. The system of interest consists of the large system before equilibration and the large system and the infinitesimal system after equilibration. The large system is open before equilibration, closed afterwards, and no heat or work is added to either system during the equilibration process. I am only trying to establish agreement that the internal energy of the large system plus the internal energy of the small system is equal to the internal energy of the combined system after equilibration. Equivalently, the internal energy of the system of interest increases by the amount of internal energy of the infinitesimal system before equilibration. PAR (talk) 14:12, 30 March 2013 (UTC)

response to the above comment on Going through Smith slowly
The above comment has several sections and I will quote them here in blue type and respond bit by bit.Chjoaygame (talk) 20:49, 30 March 2013 (UTC)


 * First, please note that my post made no reference to heat or work, only that the internal energy of the closed combined system is equal to the energy of the large system (U) plus the energy of the infinitesimally small system (udM). All discussions concerning work and heat in your response are superfluous.

Your post read: "What he has is a very small system with internal energy density u ' and mass dM so that its internal energy is $$u' dM$$. This small system is separated from a large system (the system of interest) which has internal energy U. The partition is removed, and the combined system is now the system of interest. By removing the partition, no work is done on the system dW=0 and no heat is passed to the system dQ=0. Clearly the change in the internal energy of the system of interest is $$dU=u' dM$$. This is Smith's equation 2, with work and heat set to zero. Are we in agreement so far?"

I count several mentions of heat and work here. Yes, they are assigned zero values, but that does not mean they are not mentioned. My response was to the effect that such mention of heat and work was inappropriate. At least we seem to agree to this. I disagree with your assertion that it was "superfluous" that I registered objection to what you wrote.


 * I think you misunderstand the concept of a system. A system is a contiguous volume in space that you define, and that's all it is. It does not matter if there is a physical discontinuity at the boundary. If you have a simple gas in equilibrium, and define a volume inside it and another, infinitesimally different volume, there will be a difference in volume dV, a difference in internal energy dU, a difference in entropy dS, and a difference in mass dM, and the fundamental equation holds: dU=TdS-PdV+µdM. Systems can be created and "de-created" at will without logical problems.

You write: "Systems can be created and "de-created" at will without logical problems." You are there simply contradicting the doctrine of Tisza 1966. I agree with Tisza on this point. If you want to insist that Tisza is mistaken about this, for me you will need to provide sound argument in support. Your comment above does not for me provide sound argument in support. As things stand, I contend that your statement "Systems can be created and "de-created" at will without logical problems" is one that you have made up off the top of your head, and contradicts a reliable source, Tisza 1966. Tisza is recommended by Münster 1970 as a text on axiomatics of thermodynamics. Münster 1970 is cited by Smith 1980. Tisza 1966 is also cited by Lieb & Yngvason 1999 as follows: "The simplest solution to the foundation of thermodynamics is perhaps that of Tisza (1966), and expanded by Callen (1985)..."Chjoaygame (talk) 12:13, 31 March 2013 (UTC)

In effect Smith does create and de-create systems at will. That is what I meant by using the metaphor that Smith moves the goal-posts while the ball is in mid-flight. Transfer of energy as heat and work is between two systems, but Smith tackles the problem by re-defining his systems in the mid-course of the process. That is the fault I am pointing out. Removal of the partition, as Smith does it, is just de-creation of a system, and is a thermodynamic operation, not a thermodynamic process, in Tisza's language. I think you are following Smith down his ill-starred path.


 * For example, in Joule expansion, you have a single system with a physical discontinuity, conceptually "maintained" by a partition. Or not, if you choose. You also have two systems, one either side of the discontinuity. You could have a third system which divides the left system in half, but it does not help the analysis, so such a system is not used. The volume, mass and internal energy of the single system before expansion is equal to the sums of the volumes, masses, and internal energies of the two systems, because volume, mass and internal energy are extensive variables, and therefore additive. The entropy of the final system is not the same, since entropy is not conserved. The two subsystems are "created" for the purpose of the analysis.


 * In the entropy of mixing, the same reasoning applies. In Joule expansion one of the two systems is evacuated, in the mixing problem it is not, it has the same temperature and pressure as the other system.

You use your own concepts here, for purposes that I have been recommending that one use the concepts set out systematically by Carathéodory. Tisza is of the view that it is of conceptual and historical importance that Carathéodory introduced the idea of a "simple" system with partitions as he did. I accept Tisza on this. In your conception, indeed, as you write "The two subsystems are ″created″ for the purpose of the analysis." Since it lacks the systematic background supplied by Carathéodory's presentation, I contend that such "″creation″", in your conception, as it is used by Smith, is misleading and should not be used as Smith uses it.


 * In Smith's case, the same reasoning applies but the thermodynamic parameters of each subsystem are different and the internal energy, mass and volume of one system are infinitesimally small. I said the partition is removed as a conceptual device, you can just as well say that there is only one system - its volume is the large system before equilibration, the large and the infinitesimal volume after equilibration. The large system is open, or equivalently the system composing both systems is closed, it doesn't matter and that's the whole point. You analyse the open system by choosing a different closed system and analyse the closed system in order to derive conclusions about the open system. In my post, I am only trying to establish agreement that the internal energy is conserved. The system of interest consists of the large system before equilibration and the large system and the infinitesimal system after equilibration. The large system is open before equilibration, closed afterwards, and no heat or work is added to either system during the equilibration process. I am only trying to establish agreement that the internal energy of the large system plus the internal energy of the small system is equal to the internal energy of the combined system after equilibration. Equivalently, the internal energy of the system of interest increases by the amount of internal energy of the infinitesimal system before equilibration.

I find your just above comment faulty in conceptual disorganization. It seems largely conceived in terms that I characterized above by writing "You use your own concepts here, ..." I followed that by commenting "... for purposes that I have been recommending that one use the concepts set out by Carathéodory. You now write: "I am only trying to establish agreement that the internal energy of the large system plus the internal energy of the small system is equal to the internal energy of the combined system after equilibration. Equivalently, the internal energy of the system of interest increases by the amount of internal energy of the infinitesimal system before equilibration." This is vague as to its conceptual setting. It does not say anything about the fate of the initial systems after equilibration, or of the exact origin of the combined system. I am objecting to that vagueness. In Carathéodory's conceptual system, I have many times said that the internal energy of the entire closed system is the sum of the internal energies of the two subsystems.Chjoaygame (talk) 22:19, 30 March 2013 (UTC)


 * To condense your response, you say that my statements conflict with your understanding of Caratheodory, Tisza, and Munster and that, in effect, I must engage them rather than you in any discussion of the physics of the situation. For me to do otherwise is to "make things up". So we are back to my need to track down these sources, which I will do in a matter of days or perhaps a week. PAR (talk) 04:08, 31 March 2013 (UTC)


 * Hmm. I think it fair that you engage for yourself directly with the respected authorities rather than just how I read and report them. I have offered several direct physical discussions off my own bat more or less freehand here, but you have not responded to them. I respond to your arguments, I agree, often by referring to authorities; but at least I respond to your arguments somehow. I do not think that only Carathéodory, Tisza, and Münster can be consulted here; I just mention them as particularly relevant to how I see it; I have learnt from them. I think it fair to say that you do at significant times make things up off the top of your head. For example: "Systems can be created and "de-created" at will without logical problems." That does not mean that I think that the only way you can avoid a criticism that you are making things up is that you cite those three authorities; you might prefer others, but mostly you cite none.Chjoaygame (talk) 04:53, 31 March 2013 (UTC)


 * Yes. My livelihood depends on, among other things, my understanding of physics and ability to apply that understanding to novel problems whose solutions are not to be found in references. My boss doesn't care if I can provide references for each step in the solution, only that it works. I can fail 10 times in trying to solve the problem, as long as the 11th time works. I know that's not the right attitude to bring to editing a Wikipedia page, but at least it explains my process. I piece together a unified understanding from a number of references, write down an explanation, and then go searching thru the references to back up my statements. Sometimes (rarely, hopefully) its wrong, so I fix it.  To me, you appear reference bound, dealing only with quotations from references, rarely engaging in a discussion of your understanding of the physics and your editing reflects this. Your "physical discussions" are basically saying that my understanding is faulty or vague because you cannot verify it word for word in some reference or other. Our opposite approaches are the reason these discussions are so frustrating for both of us, but to me, the discussions are sometimes constructive rather than destructive, because in answering your objections, every once in a while I realize that you have a point. Otherwise, I wouldn't even bother. Its just very difficult for me to clarify the point in your blizzard of quotations. I have to take a week off to deal with some much more frustrating, difficult and complicated mathematical problems like balancing my checkbook and doing my taxes, etc. so I will rarely be able to think about this for about a week. PAR (talk) 07:41, 31 March 2013 (UTC)


 * You write: "Your ″physical discussions″ are basically saying that my understanding is faulty or vague because you cannot verify it word for word in some reference or other." You focus here on your understanding. Your understanding is not my focus. My intention is to persuade you to accept deletion of an entry that you put in the article, because I think the entry is mistaken and contrary to reliable sources. You have not responded to my effort below in this section of this talk page, headed some comments about an open system, to provide a physical discussion of my own; it does not refer to your understanding.Chjoaygame (talk) 12:01, 31 March 2013 (UTC)


 * The matter is simple. You have put up an edit that seems to imply that work and heat transfer can be uniquely and generally defined for an open system; I think this is a mistake. Your edit is restricted to a system with only one component, but I think this is a red herring. Your main argument in support of your edit seems to be that Smith 1980 claims to be talking about a process in which work and heat are transferred between an open system and its surroundings, with only one component. But Smith doesn't do so. He talks about a process in which heat and work are transferred between a closed system and its surroundings. Yes, he prepared his closed system by an operation that he regards as a process with an open system. But how he prepared his closed system, between which and its surroundings he actually allowed heat and work transfer, does not affect the simple fact that it was a closed system when that transfer was allowed to occur. Smith does not in fact talk about a process of transfer of heat and work between an open system and its surroundings. You are trying to make out that he does; I think you are mistaken in this. Reliable sources say that there is no unique general definition of heat and work transfer between an open system and its surroundings. I think all this amounts to valid reason why your edit should be deleted.


 * You are asking for more. You want me to provide a physical account of why there is no unique general definition of heat and work transfer between an open system and its surroundings, a physical account that would satisfy your intuition. However virtuous and admirable might be your desire for understanding, I don't think your unsatisfied desire for such an account is a valid reason that stands in the way of deletion of your edit.Chjoaygame (talk) 15:45, 31 March 2013 (UTC)


 * My edit does not imply that heat transfer can be uniquely and generally defined for an open system. It ONLY applies to a single component open system. One of the main reasons this is true is because when dealing with the continuum hydrodynamic equations in a single component system with varying thermodynamic parameters, the heat flux vector is uniquely defined. (de Groot and Mazur p 17-19, and also p26 Eq. 24 where $$\mathbf{J}_k=0$$ for a single component system, as can be seen from the definition of $$\mathbf{J}_k$$ p 13, Eq 9, where, for a single component, k=1 only and therefore $$\mathbf{v}_k=\mathbf{v}$$). For such a continuum, there are no infinitesimal systems except those defined arbitrarily as having volume dV located at point $$\mathbf{r}_k$$. You can pick a volume dV, or dV'=dV/2, or whatever, your choice. These systems are totally open, yet the heat flux vector is defined uniquely. The choice of the size or location is arbitrary, and that's what I mean when I say systems are created at will for the purpose of analysis. You refer to "my" understanding, but this only in contrast to "your" understanding of the applicability of the quoted references, and "your" estimation of their reliability, not to the references themselves. You have no special standing because you can quote references. Understanding the theory is indispensable to an editor, if only to judge the applicability of a source, and ultimately that boils down only to the editor's understanding, no way out of that. You shy away from demonstrating an understanding, you only declare that you know what is a reliable source and what that source says. To this extent your edits or deletions are lacking and your discussion is deficient. PAR (talk) 00:39, 1 April 2013 (UTC)


 * Yes, it does not imply. I did not write that it did. I wrote that it "seems to imply". The point is, what would a naive reader read into your edit? Your edit is in a place where a reader would expect generality, and is likely to read a simplified version as a device to make it easier to read. This is not an article about heat flux in thermodynamic systems; it is an article about the conservation of energy, where generality would be expected.


 * Yes, as I have long and repeatedly pointed out here, and you have apparently entirely ignored, De Groot and Mazur 1962 talk of "heat flux", but they don't use the term as we do, strictly according to the Carathéodory-Born definition, as especially championed by Count Iblis. De Groot & Mazur's "heat flux" is actually flux of internal energy, as I have repeatedly pointed out here. Besides ignoring what I write here, it also seems you have hardly read De Groot and Mazur carefully. As you are partly aware, their definition in general is not that of Haase's "reduced heat flux", which on one occasion you seem to have preferred here. It seems you just ignore much of what I write and you just perseverate with your mistaken story that contradicts reliable sources.


 * To be precise, the edit which I want to delete is not about "heat flux" to which you refer here. It is about transfer of energy between a finite system and its surroundings. For this, for a closed system, transfer of internal energy as heat is here defined as transfer of internal energy that is not transfer as work. De Groot and Mazur do not define their "heat flux" like this. For example, they do not mention a "work flux" vector, complementary to their "heat flux" vector.


 * You talk of my "deletions". No, on this occasion I have refrained from deleting your edit, preferring to talk it out here.


 * You are getting personal now, with your attack on my understanding and my habit of abiding by the Wikipedia rule that requires reliable sources. I referred above to your understanding in response to your raising of the topic; you used the word six times. I did not insult you when I responded, in contrast to what you have written just above.Chjoaygame (talk) 22:13, 1 April 2013 (UTC)Chjoaygame (talk) 23:10, 1 April 2013 (UTC)


 * It is usually thought that the internal energy is safely defined for an open system. Following this assumption, for example, we find Glansdorff & Prigogine (1971, Thermodynamic Theory of Structure, Stability and Fluctuations, Wiley, London, ISBN 0-471-30280-5, on page 4 writing:


 * "We have therefore


 * "For example, the heat flow $j = j_{cond} + j_{conv} = j_{cond} + fv         (1.15)$ is the conduction current associated with the internal energy (cf. §4). ......


 * "Let us now apply this formalism. ... We shall follow closely the procedure one of us outlined some years ago (Prigogine, 1947). ... Supplementary information may also be found in other textbooks (e.g. De Groot and Mazur, 1962)."


 * This just quoted material makes it clearer than do De Groot & Mazur 1962 themselves that their "heat flow" (of their page 18 cited above by Editor PAR) is a flow of unsplit internal energy, not a heat flow as defined in these Wikipedia pages, as a residual amount of internal energy left after a work part is split off.


 * This way of using the term 'heat flow' is also followed by I. Gyarmati (1967/1970, Non-equilibrium Thermodynamics. Field Theory and Variational Principles, translated from Hungarian, Springer, New York). On page 68 he writes "the heat flow introduced in (3.35) is identical with the substantial current density of the internal energy: $$\boldsymbol J _{\mathrm{q}} \,\equiv\,\boldsymbol J_{\mathrm{u}}\, .\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(3.38)$$ ."Chjoaygame (talk) 23:25, 6 April 2013 (UTC)

summary of objection

 * A summary of my objection to the edit on "heat" and "work" for open systems may be in order.


 * The edit rests on Smith 1980. I claim that the edit uses not the rigorous and uniquely general definition of heat for closed systems agreed upon in the present Wikipedia articles, but that it rests upon another definition that is new and arbitrary and not even explicitly recognized or stated in the edit. Smith discusses the arbitrary definition, based on previous work by others. I contend that Smith does not even claim to establish that this definition is uniquely general. Smith writes "However, this reduction to closed system thermodynamics can only be made after agreement has been reached on a suitable definition of heat." His paper then goes on to "attempt to provide physical motivation for these [previously proposed] definitions". I contend that this is not an adequate justification for the edit on "heat" and "work" for open systems.Chjoaygame (talk) 21:20, 3 April 2013 (UTC)

less is more
I am sorry I have written so much above. It is rendered redundant by the following.

The diagram and set-up of Smith for Figure 1 is announced by Smith to be about an "open system with one component".

Looking at it, one sees that it would be called a simple system by Carathéodory. He does not actually use the word closed to describe it, but that is what it is. (I mentioned Tisza as authority for that.) The simple system of Carathéodory has internal partitions which are allowed to be changed. Work and heat are not defined with respect to them. Such changes accord with simple principles and conservation relations which just reduce the number of independent variables. There is only one work variable, and the one heat quantity is be defined as the difference for that variable between a reference adiabatic work path and the path of interest. Smith's one-component "open" system is a closed system according to the locus classicus definition. He is hardly opposed to that when he writes: "Thus in homogeneous one-component systems the mass is almost an irrelevant variable; all changes can be described by using the laws of closed-system thermodynamics." It is not the one-componentness, but is the closedness, with just one work variable and just one heat quantity, that is decisive here.

For an open system, matter crosses the boundary between the system and its surroundings, which is the decisive boundary. Transfers of matter within the system are not across that decisive boundary. Smith puts the matter-permeable boundary within his system, not on the boundary between the system and its surroundings. He does not define heat and work with respect to his matter-permeable boundary; actually that is impossible, as noted by Münster and by Haase; Smith defines heat and work with respect to the outer boundary, between system and surroundings, a boundary that is not permeable to matter.

In spite of his announcement, Smith is not talking about an open one-component system; he is talking about a closed one-component system. No more needs to be said.Chjoaygame (talk) 11:25, 20 March 2013 (UTC)Chjoaygame (talk) 11:55, 20 March 2013 (UTC)

P.S. I note that I said more or less the same thing just above, as copied and pasted just below. It is a pity I let myself get distracted from this, and wrote a whole heap more that appears above.

"Carathéodory is put by Tisza 1966 together with Clausius and Kelvin, as a leader of the CKC theory, in distinction from the MTE (macroscopic theory of equilibrium) largely represented by Gibbs. The CKC theory is only about closed systems. Gibbs introduced open systems in order to account for the chemical potential. Carathéodory includes the scenario of Smith Figure 1 as a "simple system". It is a closed system even though its internal "phases" are allowed to exchange matter. Work and transfer of internal energy are defined across the external walls that confine it from the surroundings; they can be adiabatic, or "permeable only ″to heat″", or can allow non-adiabatic work transfer, transmitting work as well as "heat". But matter does not penetrate those external walls. Only transfer of internal energy is defined between the internal "phases". Smith puts an adiabatic wall around his system of interest plus its incremental system; that should mean that through that wall no heat enters the system of interest plus its incremental system. All the heat, $W$, that penetrates from the external surroundings ends up in the internal surroundings, none of it reaching the system of interest. It has nothing to do with the system of interest. Why does he mention it? Smith is just playing games with the term "open system", and tacitly admits that Münster is right to say that adiabatic work, defined in the usual way, is impossible for an open system. This problem was not dreamed up by Münster. It is discussed for example by Defay 1929, Gillespie & Coe 1931, Prigogine 1947, Haase 1951, and Tolhoek & de Groot 1952, and de Groot & Mazur 1962."

In a word, Smith moves the goal-posts while the ball is in midflight.Chjoaygame (talk) 00:16, 21 March 2013 (UTC)

Putting it another way. The Smith 1980 account defines heat and work with respect to a combined system and its surroundings, the combined system being the combination of the two initially defined subsystems. The transfer of matter is not defined with respect to that same combined system, but is defined with respect to the two subsystems separately, one as system, the other as surroundings, if you like. With respect to the combined system, there is no transfer of matter. The "matter transfer term", $dQ$, that Smith says is adiabatically workless is also matter-transferless. Stretching meanings, it might be described as having a zero value, but really it does not exist as a transfer term at all, with respect to the combined system for which heat and work are defined, and has no value, not even zero. This is partly hidden by the appearance of the two subsystems as one substantial subsystem and an infinitesimal incremental subsystem.Chjoaygame (talk) 07:26, 21 March 2013 (UTC)

In spite of his announcement, Smith is not talking about an open one-component system; he is talking about a closed one-component system. No more needs to be said.Chjoaygame (talk) 11:25, 20 March 2013 (UTC)Chjoaygame (talk) 11:55, 20 March 2013 (UTC)

another comment about transfer of internal energy between an open system and its surroundings
It would have been better if I had long ago cited the following, from Fitts, D.D. (1962) ''Nonequilibrium Thermodynamics. Phenomenological Theory of Irreversible Processes in Fluid Systems'', McGraw-Hill, New York, p. 28.


 * "There exists an arbitrariness in the definition of heat flow for open systems, so that is is impossible to separate the internal energy flux $dR$ into a diffusive term and a purely conductive term by any unique method. Consequently, we may split $j_{E}$ into a diffusive term and a conductive term in several ways and thereby define a number of heat fluxes for the system.
 * "When the molecular mechanism for energy transport is considered, the difficulty of the separation of these two effects, heat transport by diffusion and by pure heat conduction, becomes apparent. ..."

Fitts continues with more detail about this.

The uniqueness intended here is at the stage of development of the reasoning process before the arbitrary selection of the definition. Once the definition has been selected, there is no further problem of uniqueness. It seems from the above comment "These systems are totally open, yet the heat flux vector is defined uniquely" that the uniqueness there intended is from a stage of development of the reasoning process after selection of the arbitrary definition; no problem there.Chjoaygame (talk) 00:26, 5 April 2013 (UTC)


 * This is true, and totally irrelevant to the present question. There is no diffusion term in a one-component system. PAR (talk) 14:08, 5 April 2013 (UTC)


 * The above comment is framed for a discussion of heat flow for a process for an inhomogeneous system distributed over time and space, not for a process in equilibrium thermodynamics; in this sense, yes, it can be said to be irrelevant. It seems that Editor PAR regards it as totally irrelevant when I mention it, but as the source of a main reason, centrally relevant when he brings it up. Above, he considered it relevant to cite De Groot & Mazur 1962: "One of the main reasons this is true is because when dealing with the continuum hydrodynamic equations in a single component system with varying thermodynamic parameters, the heat flux vector is uniquely defined. (de Groot and Mazur p 17-19 ...)". In this case, if there is no diffusion, then all transport is by bulk flow, and the term 'open system' is also irrelevant or not notable; the process is fully described by routine ordinary closed-system theory. It is insignificant play with words then to speak of an open system.


 * It is hard or perhaps impossible to define relevance for the present version of the edit, because the edit is vague does not properly describe its proposed 'process'. The edit is a confabulatory word game that lacks thermodynamic physical meaning.


 * The present version of the edit is ostensibly framed in terms of equilibrium thermodynamics for a process specified by the flowless initial and final states of internal thermodynamic equilibrium of the subsystem of interest. Ostensibly, internal energy, entropy, and matter are transferred between the system of interest and its surroundings. Ostensibly, in general, when there are differences of pressure, temperature, and molar concentration between the system and surroundings, then the material diffuses through the partly permeable membrane between the system of interest and its surroundings.


 * But this ostensible frame is specious and not really used by the edit.


 * The edit is actually framed in terms of four systems, not just the two systems required for the proper specification of a thermodynamic process, namely the system of interest and its surroundings. The four systems of the frame of the edit are (1) the surroundings with respect to which the work and heat are considered, denoted here by $j_{E}$, (2) the initially defined system of interest, denoted here by $S_{0}$, (3) the infinitesimal incremental system which supplies the transferred matter, denoted here by $S_{i}$, and (4) the finally defined system of interest, denoted here by $s_{0}$. The edit does not say how the infinitesimal incremental system, $S_{f}$, is related to the work-heat surroundings, $s_{0}$. This is a fatal failure to adequately describe the proposed 'process'. Is $S_{0}$ part of the surroundings $s_{0}$, with respect to which the work and heat are considered? How does $S_{0}$ 'merge' with $s_{0}$? The 'merging' is workless and heatless because work and heat are undefined for it, not because they are defined and have zero values. Where does $S_{i}$ go to? Does it simply disappear into cyberspace? Where does $S_{i}$ come from? Out of cyberspace? The idea that $S_{f}$ could 'come from' $S_{f}$ and $S_{i}$ is conveniently and speciously invented ad hoc for the present concerns, but is not admitted as a description of a physical process in ordinary thermodynamics, in which merging of systems is not considered to be a physical process, though it may be considered to be a logical operation. The edit does not mention this.


 * In the special case in which $s_{0}$ is controlled so as to make both the relevant properly defined heat and work zero, the only ostensible non-trivial candidate left for a proposed 'process' is the merging of $S_{0}$ with $s_{0}$. This candidate is proposed to proceed by "removal" of the partition between the initially defined system of interest. This is not a properly defined thermodynamic process, because a properly defined thermodynamic process has respective initial and final states both for a really existing system and for its really existing surrounds, and no other systems.


 * A proper thermodynamic account must say which, if any, of the four systems $S_{0}$, $S_{0}$, $s_{0}$, and $S_{i}$ is the system and which its surroundings. Without this, the edit is too vague to consider, and has no physical meaning.


 * In proper thermodynamic terms, the edit's reference to open systems is a specious and trivial word game with no physical import, insignificant semantics if you like. A naive reader would reasonably assume that a Wikipedia entry was not a nugatory semantic game with no physical import. He would get from the edit the mistaken impression that there is a properly defined account of transfer of heat for open systems. Indeed, the reader would not even have to be very naive to get that impression. Editor PAR himself started the present train of editing with just that impression, saying "to dispute this is out of the mainstream". Later, he greatly revised it to the present edit, citing Smith 1980, which I regard as not a reliable source for the present purpose. The present edit is meaningless, misleading, or not notable. It should be deleted.Chjoaygame (talk) 02:43, 6 April 2013 (UTC)

why the Smith 1980 scheme fails to do the task it is here advertised to do and doesn't make sense as physics
The Smith 1980 scheme fails to do the task it is here advertised to do. This is largely because it splits its "process" into two temporally serial steps which must be performed in the sequence prescribed by the scheme.

The first step deals ostensibly with an open system, but simply transfers internal energy which it fails to split into work and heat moieties, because heat and work are not defined for the transfer; they do not exist; they do not merely have zero values. There is a very good reason for this: Smith has no unique general way of defining the split, not even for a scenario with only one chemical constituent. The Smith scheme is being used by the edit as a hand-waving word-game intended to hide this important physical fact.

The second step of Smith's scheme follows a thermodynamic operation that converts the open system into a closed system, and then allows a process of transfer of internal energy distinctly as heat and work. No heat and work are thus defined for an open system. If perchance the closed-system heat and work are left at zero values, then the previous transfer of internal energy remains unsplit, and it is merely trivial to speak of heat and work for the whole sequence.

In thermodynamics, it is usually desired to develop a finite process out of indefinitely many infinitesimal incremental processes, and the edit speaks of "the reversible case". For the development of a finite process of transfer of matter, the closed system needs a thermodynamic operation to open it up again for another increment of matter transfer, but the original infinitesimal incremental system has disappeared. Where will the new opening be? Is there hidden in the background a matter reservoir in the surroundings? Or indefinitely many infinitesimal incremental matter-supplying systems? How does one account for a finite amount of matter transferred? What effect does the matter transfer have on the physical state of the so-far unidentified sources?

It is said in the Smith scheme that the system is opened by removal of a partition. Unless the infinitesimal incremental system is at the same temperature and pressure as the system of interest, this will be irreversible. This implies a severe restriction on permissible reversible "processes", even with only one chemical constituent.

When it comes to reversing the Smith scheme, the system must start off closed and the work and heat have to be transferred first, and then the system must be opened for the transfer of matter. Where and how will this opening operation take place? Is there a trace of the previous but now disappeared infinitesimal incremental system? Is there some way that the infinitesimal extruded increment can have a temperature and pressure other than those of the system of interest? It seems such a reverse "process" cannot do so spontaneously; this would be a very severe restriction to place on intended physical processes. The Smith scheme is designed for addition of matter to the system, but not for removal of matter from it.Chjoaygame (talk) 05:35, 8 April 2013 (UTC)

general physical criticism of Smith 1980
I will criticize Smith 19880 in two ways here. One is specific to the detail of his scheme, the other more general.

Specifically, Editor PAR and I agree, I think, that, however one might define or not define heat here, mainstream thinking includes the validity of Gibbs' formula $S_{f}$. I now offer the criticism of Smith 1980 that it does not demonstrate that this formula can in general and uniquely be segmented into the two temporally serial steps on which the Smith formula is based. I think this is a serious weakness in Smith 1980.

More generally, it is often so that when a thesis has faults, they can be spotted in the first sentence or two of its presentation. I now look at the first two paragraphs of Smith 1980.

Smith starts by saying that the definition of heat transfer for open systems is unsettled. (Agreed.) His next sentence cites Münster's saying that "a real generalization of closed-system thermodynamics is required". (Agreed. I observe that this is also said explicitly by Landsberg 1978, and not quite so explicitly by Tisza 1966.) Smith 1980 then adds an apodosis that I contend is meaningless or nonsensical. "Thus it is possible to increase the internal energy of an open system without doing work and without heat flowing simply by adding more mass at the same temperature and pressure under adiabatic conditions." The implication here is that this is a thermodynamic process. No, it is a thermodynamic operation. It is not an account of physical happening: it is an account of a change of analytical framework which does not involve anything happening physically. That these two things are tacitly conflated by Smith's apodosis makes it nonsense. When nothing happens, of course no work or heat transfer occurs. Smith's scheme changes analytical frameworks during the course of a "process" and carries on as if the change of framework were part of a real physical process. Moreover, the Smith apodosis directly conflicts with the protasis citing Münster, who says that adiabatic work is by definition impossible for an open system.

Smith's second paragraph announces a main flaw of his scheme. "... a convention is established that the heat flow into an open system is zero when the system, its supply tank and discharge tank are all surrounded by an adiabatic enclosure". The heat and work account is not for the system, it is for the system together with its supply and discharge tanks. The game is over at this point. Smith more or less admits this in his next sentence: "This convention is partly a consequence of conventional notions of heat and partly an arbitrary device." Yes, that is the point: even for one-component systems, Smith is offering an arbitrary device, not a unique general definition.

Another physical consideration is that there might be proposed two different ideas of heat transfer. One is the strict Bryan-Carathéodory-Born idea that is accepted in the present physics articles, suitable for strict equilibrium thermodynamics, and directly relevant for the present edit; the other the perhaps more intuitive idea that heat diffuses because of a temperature gradient according to Fourier's law. The latter idea is verboten in these physics article, but is important for thinking about non-equilibrium systems with local thermodynamic equilibrium and is discussed in Smith 1980 and was brought up here by Editor PAR. For the present edit, the latter is not strictly relevant because the present edit is a statement in terms of equilibrium thermodynamics. But a difficulty with the Fourier idea is that one is interested in entropy production as well as in energy transfer. One thinks in terms of 'generalized thermodynamic "forces"' and fluxes driven by them, through a coupling "constant". The "constant" differs by powers of the temperature depending on the "force" one chooses. Two main choices are for the energy picture $dU = T dS − P dV + Σ μ dN$ and for the entropy picture $U = U(S, V, N)$. For these one might make the force $S = S(U, V, N)$ or $− grad T$. Physically, the choice of $− grad (1/T)$, made by Fourier, has an advantage, seen by looking at some tables of values of the "constant", that the "constant" is indeed often not too far from being independent of temperature, while this is not so for the other choice. Intermediately, a third choice is made by some authors, $− grad T$. Would the real "heat" please stand up? Whatever, this is not directly relevant here.Chjoaygame (talk) 21:18, 8 April 2013 (UTC)


 * First of all, the Gibbs formula is: $$dU=T\,dS-P\,dV+\sum_i \mu_i dN_i$$. The subscripts refer to the particular species in a multicomponent system. For a single component system, the Gibbs formula is $$dU=T\,dS-P\,dV+\mu dN$$ where the µ and dN refer to the one component. I would normally ignore this as a typo, but since the distinction has been confused in previous discussions, I point it out. [This response, with one step from the margin, was posted by editor PAR but not signed.]


 * Yes, I was lazy in writing the formula. Not exactly a typo.Chjoaygame (talk) 23:48, 9 April 2013 (UTC)


 * Having mentioned my abbreviation of the formula, the comment does not address the point that the post made, that Smith does not attempt to link his result to the well agreed formalism established by Gibbs.Chjoaygame (talk) 10:16, 10 April 2013 (UTC)


 * Second, a "system" is defined by the analyst, not by the physics. Choosing a system which simplifies analysis almost always involves taking the physics into account, but the point stands. Its like choosing a coordinate system - if the physical problem has cylinder symmetry, then posing the problem in cylindrical coordinates probably offers the simplest mathematical analysis, but it is not necessary to do so. The laws of thermodynamics describe real physical processes but the description is in terms of systems chosen by the analyst. In hydrodynamics, you can describe the behavior of an infinitesimal volume fixed in space, moving in space at the fluid velocity, or moving in space at the fluid velocity and changing its volume so as to keep its mass constant. The analysis in terms of the different systems all yield the same hydrodynamic equations. There are no naturally defined systems in the equations of fluid dynamics, yet fluid dynamics is analyzed by supposing a set of contiguous systems, each one small enough to be considered homogeneous, yet large enough to be considered a thermodynamic system. Without the ability to "suppose" these systems, you eliminate your ability to analyze fluid dynamics problems. [This response, with one step from the margin, was posted by editor PAR but not signed.]


 * The "system' is indeed defined by the analyst for the purpose of analyis. But his choice has consequences for his analysis. When the choice is changed in them middle of an analysis, it is called a thermodynamic operation, and is not a thermodynamic process. The above comment ignores this point which was central to the post that it was replying to. The post was not denying the analyst the choice of system, as the comment seems to imply. The post was saying that the choice should be suitable for the problem at hand. Thus the above comment is no response.Chjoaygame (talk) 23:53, 9 April 2013 (UTC)Chjoaygame (talk) 00:38, 10 April 2013 (UTC)


 * Smith is not even trying to divide the energy added by the additional mass into heat and work, he explicitly states that the added energy is neither the result of work or heat. This is clearly stated in the sentence which you call nonsense. With regard to "supply" and "discharge" tanks, I am not sure what he means. Referring to the diagram, there are two systems to begin with, one afterwards, and both (or the one) are adiabatically and mechanically closed, before the addition of heat or work. [This response, with one step from the margin, was posted by editor PAR but not signed.]


 * That's right: "Smith is not even trying to divide the energy added by the additional mass into heat and work". That is because he knows it can't be done. This is the point which he is trying to evade by his concoction, and the point which his paper is being cited in order to hide. The nonsensical apodosis is "Thus it is possible to increase the internal energy of an open system without doing work and without heat flowing simply by adding more mass at the same temperature and pressure under adiabatic conditions." It is nonsense because it muddles a thermodynamic process, which is a physical happening and can be adiabatic, with a thermodynamic operation, which is simply an analytical exercise and not a physical happening and so cannot be adiabatic or non-adiabatic. The comment above effectively concedes that the post is right.Chjoaygame (talk) 00:45, 10 April 2013 (UTC)


 * The comment reads "With regard to "supply" and "discharge" tanks, I am not sure what he means." This is saying that the commentor has missed the main point of Smith's article; Smith has not only deceived himself, but has entirely pulled the wool over the commentor's eye's. The "supply" and "discharge" tanks are components of the surroundings of the system of interest. They correspond here to the infinitesimal incremental system that "adds" to the system of interest. Smith has performed the analytic operation of changing the definition of the system of interest, by the procedure of re-labeling the component systems of the surroundings as part of the system of interest. He says of this that he is establishing a "convention". He then uses further components of the surrounds of the newly closed system of interest as the eventual overall surrounds that support the heat and work that could not be distinguished when matter was purported, by a thermodynamic process, to be transferred between the open system and its surrounds; but there was no physical process of transfer of matter; instead there was an operation of re-labeling of component systems of the surrounds as "part of the system of interest".Chjoaygame (talk) 10:16, 10 April 2013 (UTC)


 * It's really simple what Smith is saying in the beginning. First he expands the large system to include the small system, which has volume $$\Delta V$$. Then he performs reversible work on that system changing its volume by $$dV_w$$, lets say. Now, rather than express the work as $$\delta W=-P dV_w$$ he simply expresses it in terms of the total volume change $$dV=\Delta V+dV_w$$ or $$\delta W=-P(dV-\Delta V)$$. In the reversible case, the densities are only infinitesimally different, so $$\Delta V=v\Delta N$$ where v is the specific volume and $$\Delta N$$ is the mass of the small included system. This is Smith's equation 6. [This response, with one step from the margin, was posted by editor PAR but not signed.]


 * The notion of "expanding the large system to include the small system" is an intellectual operation, not a physical process. The "expansion" is a verbal and conceptual change in the way the physics is described, not a physical expansion such as is considered in thermodynamics. That the small system is infinitesimal might conceal this from a reader glancing at the paper for a first time, but does not conceal it from a careful examiner. It seems that Smith is deceived by his own words, and fails to  see what they imply. The comment in reply does not refute the post.Chjoaygame (talk) 00:52, 10 April 2013 (UTC)


 * The distinction between $$\nabla T$$, $$\nabla (1/T)$$ and $$-\nabla \ln T$$ is superfluous. Instead of the more complicated three-dimensional case involving the $$\nabla$$operator, consider the one dimensional case of Fourier's law for a cylinder separated by a diathermal wall. Fourier's law may be stated as:


 * $$J_q=-\lambda(T)(T_2-T_1)$$


 * where $$J_q$$ is the heat flux vector (one component only since the problem is one-dimensional), $$\lambda(T)$$ is the thermal conductivity (watts/m^2/K, generally a function of temperature!) and the T's are the temperatures on either side of the wall. The *main point* is that the equation is approximate, it only holds in the limit as $$\Delta T=T_2-T_1$$ approaches zero, and does a very good job for $$\Delta T$$ sufficiently small. For $$\Delta T$$ very small, it doesn't much matter whether you use $$T_1$$, $$T_2$$ or any other nearby temperature as the argument $$\lambda(T)$$.


 * $$\lambda(T)$$ is "constant" only in the sense that it not a function of the temperature difference $$\Delta T$$. If the heat flux is $$\lambda_0(T) dT$$ then it's also $$\lambda_1(T)\Delta (1/T)$$ where $$\lambda_1(T)=-\lambda_0(T)/T^2$$, since $$\Delta T$$ is infinitesimally small. [This response, with one step from the margin, was posted by editor PAR but not signed.]


 * As the post said: "Whatever, this is not directly relevant here."Chjoaygame (talk) 00:57, 10 April 2013 (UTC)


 * I have put up several replies, set far back from the margin. In summary, they say that the above replies by Editor PAR do not refute the post.Chjoaygame (talk) 01:00, 10 April 2013 (UTC)

illustration of distinction between process and operation
The following may help by illustrating the distinction between process and operation.

The distinction between a physical process and an analytic operation was made clearly by Tisza (1966).

In classical thermodynamics, a cyclic process is a different thing from an ordinary thermodynamic process such as was considered by Gibbs, with which we are perhaps more familiar. For example, a heat engine is run through a cyclic process. It has one working body, which corresponds in many ways to the the system of interest in an ordinary thermodynamic process. It has three reservoirs in its surroundings. A well known cycle starts with the working body starting at a known temperature and being brought into thermal connection with the hot heat reservoir. The connection is an operation, and does not in itself change the state of the working body, and so is not a process. What changes is the arrangement of connecting walls of the working body. When the operation is done, the process starts, in which the working body gains internal energy by transfer as heat. Then another thermodynamic operation is done: the thermal connection is broken, and a mechanical connection is made with the work reservoir. When that is done, a thermodynamic process of expansion happens and the working body loses internal energy to the work reservoir. More operations and more processes complete the cycle in the usually described way. In a typical heat engine of classical thermodynamics, the material content of the working body is kept strictly intact throughout the cycle, and is used to keep track of the overall effect of the transfers of energy. This corresponds with a closed system. Also the heat and work transfers are kept track of through the energy changes of the reservoirs.

It is considered in textbooks to be a significant conceptual advance to fully remove the cycles from the conceptual apparatus of thermodynamics, and replace them by the ordinary processes with which we are familiar. In such ordinary processes, there are just two systems, the system of interest and its surroundings. The wall connecting them needs also to be specified. Changes in the wall are operations, not processes. In a non-trivial ordinary thermodynamic physical process, the changes are in the system, not in the wall.

The key point of Smith's thermodynamic operation is that it changes the system of interest, but not as a thermodynamic process. That is why it is workless and heatless. It is not that the work and heat are defined and have zero values. It is that they are not defined, as indicated above by the sentence "Smith is not even trying to divide the energy added by the additional mass into heat and work, he explicitly states that the added energy is neither the result of work or heat." Adding two systems to produce another is a thermodynamic operation, an intellectual and conceptual analytic device, not a physical process. The concept of addition of systems as an operation, as distinct from a process, is considered and used explicitly for example in the axiomatic development of Giles, R. (1964), Mathematical Foundations of Thermodynamics, Macmillan, New York.

Instead of the ordinary arrangement of classical thermodynamics, which works well specifically for equilibrium systems with all flows zero, other arrangements of systems are used. For example, by Attard, P. (2012), ''Non-Equilibrium Thermodynamics and Statistical Mechanics. Foundations and Examples'', Oxford University Press, Oxford UK, ISBN 978-0-19-966276-0. This is an important conceptual step, and opens up non-equilibrium thermodynamics to a systematic development, with direct linkage to a form of statistical mechanics specifically designed for systems with steady non-zero flows. There are three systems, the system of interest, sandwiched between two mutually separate and different surroundings systems. For example transfer of heat is considered for closed systems by making the two surroundings systems have different controlled temperatures. Generalizations of temperature and entropy are possible and practically necessary with this arrangement.

Most relevant here is that when Smith's system of interest is open, its transfers of internal energy associated with matter transfer are not split into heat and work. Heat and work come into Smith's scheme only when the system of interest has been closed by a thermodynamic operation. Therefore, to cite Smith's scheme as indicating heat and work for open systems is misleading.Chjoaygame (talk) 04:32, 10 April 2013 (UTC)


 * Thanks, that is a good clarification of terms. Smith's operation of expanding the system of interest is almost entirely an operation, since the intensive parameters of the small system are only infinitesimally different from those of the large system, in the reversible case. Therefore the equilibration which occurs after the large system is expanded is only infinitesimally different from zero, or, equivalently, equal to zero in the first order. For the non-reversible case, the differences are not infinitesimal and an equilibration process occurs. I don't understand why you think the analysis is misleading. It is simply an analysis which leads to the same well-defined, unique heat flux vector found in the continuum case for a single-component system. I don't understand why you insist on the need to separate the internal energy resulting from the influx of matter to a system into work and heat. It is simply neither - what's wrong with that?. I also think it is incorrect to say that Smith's steps must be carried out in a specific order. Since they are infinitesimal steps, they may be carried out in any order. PAR (talk) 11:08, 10 April 2013 (UTC)


 * Smith's "expansion" of the "system" may or may not have two steps in it. If the matter-incremental body is at the same temperature and pressure as the initial system of interest, then one might say that Smith's expansion was only an operation of re-labeling, and no physical process. If finitely different temperature and pressure, then re-labeling and also a physical process, but not a reversible one. For reversibility, the temperature and pressure must be only infinitesimally different.


 * Smith's procedure to get is result with internal energy of matter transfer and heat and work in the same formula is illegitimate if interpreted, as it is intended to be interpreted, as a representation of a thermodynamic process for an open system. No, it is a procedure for a complex device that contains a simple system that at one stage is open. The complex device is in a sense like an engine, not just a system undergoing an ordinary process; but the result is pretended to be for a simple system undergoing an ordinary process. That is why Münster and Landsberg explicitly point out that a generalization is required, and why Tisza considers two distinct great forms of equilibrium thermodynamics, the Clausius-Kelvin-Carathéodory form and the Macroscopic Theory of Equilibrium, which is practically the Gibbs form (practically postulated by Callen). Smith is in effect saying that he can leap this distinction which none of the usual authors thinks can be crossed without a leap. For careful development, some authors cite Falk G., Jung H. (1959), Axiomatik der Thermdynamik, Handbuch der Physik, volume $− grad ln T$, part 2, editor S. Flügge, Springer, Berlin, but this is not commonly cited in the English-language literature. Are the usual authors fools, that they think they cannot do what Smith does by what I think is hand-waving, when by a bit of effort they could do it? I find Smith's story poorly constructed and so I accept the usual authors.


 * I do not accept the claims about the sequence of the steps in Smith's procedure being indifferent because they are infinitesimal. That argument relies on their being legitimate steps in a process that can be reversible, but that is what is being challenged, and cannot be assumed. I think the infinitesimality is a red-herring, and that a proper argument should be able to work for finite processes. Reversible processes are not physical processes. They are very valuable and useful mathematical fictions that refer to mathematically defined manifolds of states. They are useful for calculating the differences between states, but more is needed for realisable physical processes, which are all irreversible. The edit, to have any useful semblance of generality, which is necessary in the context of an article about conservation of energy, not about the finer points of irreversible thermodynamics, should refer mainly to realisable physical processes.


 * For us, the misleading occurs when Smith's story is interpreted in a particular way. It is the interpretation that is misleading. The interpretation put on Smith by the edit is that 'it shows that it makes sense to speak of heat and work for an open system'. But examination of Smith shows that he does not demonstrate that; indeed he practically demonstrates its negation.


 * You would like to leap from a story about scalar systems to vector systems like a superman who can leap tall buildings. I think it wrong to try to invoke the vectors when there is still major difficulty with the scalars, and make out that the vector and scalar stories are the same. Considered in rigorous terms, the vector story is not the same. For basic stuff like this, rigour is mandatory. We are dealing with the scalar case for the edit, and we must stick to it. Having settled the scalar case by a proper physical development, for another article one might proceed to tackle the vector case, but going from the vector to the scalar case is not development of new physics, it is mere deduction, retracing the steps of the basic development.


 * In the accepted Wikipedia definition of heat and work, in general (excepting the special case of convective circulation within a closed system), internal energy transported by convection is just simply internal energy, which cannot be split into heat and work as state variables of the convected material. This is the basic physics here. It includes the open system case. The edit is trying to deny it.


 * Forgetting this, you write: "I don't understand why you insist on the need to separate the internal energy resulting from the influx of matter to a system into work and heat. It is simply neither - what's wrong with that?." Nothing is wrong with it. It is what Münster is asserting, and what I am saying, and the edit intends speciously to deny. The point is that it is not so by choice, but indeed is so by necessity. The point is not that there is a choice and that it is chosen not to be done, the point is that there is no choice because it cannot be done. But the evident intention of the edit is to say that it can be done, that is to say, that 'it can make sense to speak of heat and work for an open system'. That it cannot be done contradicts the edit. I don't insist that it must be done, I insist that to make the case intended by the edit, it would have to be done, but cannot. Smith is being cited to say that it can be done. But it turns out that in effect he admits that it cannot be done. If he thought it could be done, he wouldn't have concocted his fancy scheme because he would have done it without a fancy scheme.Chjoaygame (talk) 22:12, 10 April 2013 (UTC)


 * The edit does not deny it. The edit says $$\delta W=-P(dV-v\,dM)$$. If the net volume change dV is equal only to the infinitesimal volume added (v dM), the work is zero. There is no attempt to divide the energy added by the additional mass (u' dM) into work and heat. It is explicitly stated that it is neither, because, as you say, it cannot be done. It does not need to be done to justify the edit. I don't understand how you leap to the conclusion that since it is not and cannot be done, therefore the expression $$\delta W=-P(dV-v\,dM)$$ is nonsense. This expression is not dividing up the added energy (u' dM) into work and heat, it is expressing the work done in terms of open system variables (dV and dM) on what has become a closed system, after the addition of the infinitesimal volume. You would obtain the same equations if you first added energy by heat and work on the system of interest and then added the contents of the infinitesimal system. Again, Smith and the edit do not say (u' dM) must be divided into heat and work, and explicitly says that it cannot be and this does not render $$\delta W=-P(dV-v\,dM)$$ nonsense. (Also, I have ordered Munster's book, since I simply cannot find it any other way. Perhaps I should order Tisza as well.) PAR (talk) 23:28, 10 April 2013 (UTC)


 * The edit is ostensibly about transfer for an ordinary open system, but in reality is inescapably about sequence of processes and operations in a complex device which does not represent a general case of an ordinary open system. It is not appropriate to put into the present article something about such a special device in the way that the edit does it. The special device sheds no light on the conservation of energy. It is just a word game intended to rescue an otherwise unjustified reference to work and heat for open systems. The edit does not explicitly state that the internal energy associated with the added mass cannot be split into heat and work. The formula does not split it, but that is not an explicit statement that it cannot be split. Whether it can or cannot be done is a fine point of thermodynamics, hardly central to the law of conservation of energy, which is essentially more general than thermodynamics. The law of conservation of energy for thermodynamics of open systems is happy enough with unsplit internal energy, and mention of heat and work is otiose or I would contend wrong for this context. The heat and work of the formula refer only to a closed system, and that is not made clear in the edit. I would oppose more detail in the article along the lines of Smith's paper, as a further rescue attempt.


 * On a more general approach, I have given some thought to your very beginning comment, that if the Wikipedia definition of heat and work does not do it for open systems, then the Wikipedia definition needs to be put right about that. Since in general you are a rigorous mathematical thinking man, and the Wikipedia definition is recommended by heavy but not universal weight of literature opinion as being the uniquely best rigorous way, I have assumed till now that you would be very much on side with Count Iblis that heat is internal energy transferred in a way other than by work, a statement that is always made in the context of closed systems, with perhaps some contestable exceptions. Examining the record, I learnt yesterday that my assumption was mistaken and that in fact you have hardly expressed any views on this question, and this seems re-inforced by your suggestion that the Wikipedia definition needs revision. Therefore I spent some time thinking about a revision of the definition. My thinking so far has not favoured revision, but I am still thinking.Chjoaygame (talk) 00:31, 11 April 2013 (UTC)


 * Ok, forget Smith for the moment. Please explain to me how a heat flux vector can be defined for a flowing one-component fluid, with temperature and pressure and density gradients, etc. The analysis is done in terms of infinitesimal volume elements which are assumed to be in equilibrium (i.e. the assumption of LTE). Each of these volume elements is an open system, yet the heat flux vector is unique and well defined.


 * Regarding the definition of heat, for closed simple systems we are in full agreement, I agree with Count Iblis's description. Only mechanical quantities are directly measurable (pressure, volume, mass) and so only the work done on a system is directly measurable. The first law says that work adds or subtracts from a system's internal energy which is not directly measurable. By adiabatically isolating the system, we can be sure the only addition to the internal energy is due to work, and we can measure an energy equation of state Utot(P,V)=Uo+U(P,V) which allows us to calculate the internal energy (up to an undetermined constant Uo) in terms of the measurable P and V. If we remove the adiabatic constraint, measure the work, the pressure, and the volume, we can then calculate the change in internal energy via the energy equation of state, and the difference between the work and the internal energy is the change in internal energy due to heating.


 * Smith's first step is that if you have another system, and you then join them, the internal energy of the combined system is equal to the sum of the internal energies of the two original systems. This follows from the first law which effectively states that the internal energy is an extensive variable, and therefore additive. Joining them is a process, while defining the system of interest to include both is a "conceptual operation". The increase in the internal energy of the system of interest is simply equal to the internal energy of the added system. If the energy of the added system is $$\Delta U$$, then the change in energy of the system of interest is likewise $$\Delta U$$. There is no point in going further until we agree on this.[This unsigned item was posted by editor PAR at 12:40 on 11 Apr 2013.]


 * Dear Editor PAR, please take a look at what you are asking and how you are proceeding here. You are asking me to explain to you something that I think is more or less irrelevant to the edit in question, prescribing for me assumptions that I think are not sound enough to deal safely with the question you raise. It is not up to me to explain such things to you. For no evident reason, you are asking to temporarily forget the cited source of the edit in question. You are making a blatant petitio principii by expecting me to accept your assumption that "the heat flux vector is unique and well defined", when the present question is whether for the present problem it is possible or not to define heat. A brief interruption, in which happily you agree with the customary definition of heat for closed systems. And then back to an attempt by you to drive me into following step by step at your dictation the flawed reasoning of the just forgotten cited source of your position.


 * In that attempt to drive me into accepting your position, you offer what I consider to be a muddled and flawed piece of argumentation, that purports to support a conclusion that I have long and repeatedly proposed here, though not on the grounds of your flawed piece of argumentation. And you ask me to agree. If I agreed, it would hide the fact that I reject your muddled and flawed piece of argumentation, which is what you really want me to accept.Chjoaygame (talk) 21:03, 11 April 2013 (UTC)


 * The question at hand is whether heat can be defined for simple open systems, so the question about the heat flux vector is relevant. The heat flux vector is defined in LTE fluid flow, therefore heat is defined. LTE fluid flow is analyzed by dividing the fluid into infinitesimal volume elements which are open systems. Therefore heat is defined for these open systems. Rather than declare my argument muddled and confused and sign off, please point out where the flaw and muddlement occurs, and correct and clarify it. Yes, it is up to you to explain such things to me because it is you who are objecting to the edit. If you refuse to discuss the physics of the situation, declaring the source and my explanation of it "muddled" without offering any correction or clarification, then that's practically an ad hominem argument which is a useless response, not to the point.


 * Even simpler - If you have two equilibrated systems separated by a thermally, mechanically, and materially isolating partition, both having the same single-component composition at equal pressure and volume and then you remove the partition, then the internal energy of the combined system is equal to the sum of the internal energies of the two original systems. Let's stop there. Do you agree or disagree, or is my statement muddled and if so, where and why? PAR (talk) 02:09, 12 April 2013 (UTC)

break for editing
Yes, the question at hand is whether heat can be defined for simple open systems, in the context of macroscopic theory of thermodynamic equilibrium, which has no fluxes. You write, in effect, that you are entitled to require me to explain a matter of continuum theory of non-equilibrium fluxes to you because I am objecting to your edit. First, this is disingenuous; it is an attempt to reverse the burden of proof, as I regrettably have needed to point out here many times; the edit was initially in its first iteration recognizedly faulty, and is now in a rescue phase; the rescue relies on primary research that is manifestly inadequate; it is up to you the editor of the edit to supply sound reason for it; instead you have repeatedly tried to drive me through the faulty reasoning of the cited source; you have not at any stage offered any reasonable physics in support of the edit, and have largely ignored careful and properly argued criticism of it; the rescue has now reached a painfully circular stage. The challenged edit is about macroscopic theory of no-flux thermodynamic equilibrium, not about continuum theory of non-equilibrium fluxes. For that changed, and I contend not strictly relevant, context, you assert that the heat flux vector is defined in LTE flow. First, we have repeatedly discussed this, and I have repeatedly pointed out that there are several definitions for it in the literature. The macroscopic theory uses a definition in terms of work, carefully avoiding specification of the modes of heat transfer, such as conduction or radiation. The continuum flux theories often define heat in a way that has been carefully avoided by the macroscopic theory; the continuum flux theories often specify for example conductive or diffusive mechanisms, though often not mentioning radiative transfer. You seem to be ignoring this important difference in style of definition. Secondly, I have said above that I think the definition needs to be made primarily for the no-flux macroscopic thermodynamic equilibrium case, before the continuum flux case is considered. You seem to be ignoring this.

Even simpler — an improvement omitting your muddled argumentation — which it now seems you didn't really need: you ask me about additivity of internal energy. I have repeatedly said in this talk-page (for example at Talk:Conservation of energy), and have posted as an edit in this article, that under the conditions of your question the internal energies add. Your question appears to me as direct evidence that you do not read what I write here. Why do you ask me this again? Do you think I might give a different answer this time?

In the presence of several complaints from me that you seem to ignore what I write here, in a string of gratuitous demands you offered a muddled piece of argumentation and demanded that I respond to it. It was not the conclusion that I said was muddled, as you are now implying, but it was the argumentation that preceded it that I was complaining about. As part of my reply complaining about your gratuitous demands I am entitled to observe that your argumentation is muddled without detailing exactly why. You are treating me like a witness before an inquisition and yes it is ad hominem that I complain about it.

Trying to break free of your inquisitorial approach I have posted an attempt to provide some physical imagery, which you seem here to have ignored in favour of more inquisition.Chjoaygame (talk) 04:49, 12 April 2013 (UTC)Chjoaygame (talk) 16:14, 12 April 2013 (UTC)Chjoaygame (talk) 21:48, 12 April 2013 (UTC)


 * If you will look above, at my response beginning "Smith's first step is that if you have another system..." I asked essentially the same question, to which you replied that my thinking was muddled, without clarifying how or why, accusing me of trying to drive you into accepting some position or other, refusing to "explain such things" to me, etc. etc. but never really responding to the question. I am not running an inquisition, I am trying to clarify where exactly you think my reasoning is muddled. I wrote the "even simpler" statement to see if you thought it contained any "muddled thinking". Thankfully, you agreed with the statement, albeit with the usual punishment. Will you now give a simple response to the following, nearly identical statement, without an extended analysis of my motives? If you agree, please indicate agreement, if not, please explain why. Unless you can back up your statement that my reasoning is muddled, you should not make that statement.


 * If you have two systems, and you then join them, the internal energy of the combined system is equal to the sum of the internal energies of the two original systems. This follows from the first law which effectively states that the internal energy is an extensive variable, and therefore additive. Joining them is a process, while defining the system of interest to include both is a "conceptual operation". The increase in the internal energy of the system of interest is simply equal to the internal energy of the added system. If the energy of the added system is $$\Delta U$$, then the change in energy of the system of interest is likewise $$\Delta U$$.[This unsigned entry was posted by editor PAR at 01:16, 13 April 2013.]


 * You have the perfect recidivist scheme. You repeatedly misbehave by ignoring what I write, and then cry foul when I complain about it. You want me to let you get away with it scot free.


 * You write "If you have two systems, and you then join them, the internal energy of the combined system is equal to the sum of the internal energies of the two original systems. This follows from the first law which effectively states that the internal energy is an extensive variable, and therefore additive. Joining them is a process, while defining the system of interest to include both is a "conceptual operation". The increase in the internal energy of the system of interest is simply equal to the internal energy of the added system. If the energy of the added system is $$\Delta U$$, then the change in energy of the system of interest is likewise $$\Delta U$$."


 * In relation to this you demand: "Will you now give a simple response to the following, nearly identical statement, without an extended analysis of my motives? If you agree, please indicate agreement, if not, please explain why. Unless you can back up your statement that my reasoning is muddled, you should not make that statement."


 * Ok, here is my response. Your initial clauses "If you have two systems, and you then join them" are the muddle. This is because of your new invention of the notion of "joining". You say that joining them is a process. No, it's most importantly an operation. That's why I say you are muddled. I have carefully tried to explain the distinction, but it hasn't got through to you. I hardly see how I can do better at explaining the distinction than I already have done. But it seems I must try again.


 * Thermodynamics is about a system with its surroundings. Processes are transfers between them. A thermodynamic process starts with a system in contact equilibrium with its surroundings; and then the surroundings are changed and transfers occur between the system and its surroundings until a new contact equilibrium is reached; that new contact equilibrium ends the process.


 * You have ignored that basic scheme when you have "joined" your two systems. Your "joining" exercise so far has said nothing about the surroundings or how they change. For two systems, you are likely in general to need operations. Your "joining" mainly involves an operation because it starts with two systems and ends with one; it may perhaps also involve a process. For your "joining", the initial two respective surroundings and the relevant walls are abandoned. In effect, if you like, your operation starts by making the the two systems into mutual respective surroundings with an isolating wall between them. Then if you operate on the wall so as to make it permeable, you are in effect starting a process that will lead to a new contact equilibrium; it is a process because something is likely to be transferred across the newly permeable wall until a new contact equilibrium is reached. In effect, by changing the wall, you have exposed the respective systems to changes in their respective surroundings. Perhaps, if your newly permeable wall was completely permeable to everything, you also intended a further operation of creating a new surrounds and making the two fully equilibrated systems into the new system of interest. I was upset about what you wrote because you were wrecking the distinction between a process and an operation.Chjoaygame (talk) 03:35, 13 April 2013 (UTC)


 * I think I understand the distinction you make between process and operation. I also think that my statement was not as clear as it should have been. I failed to state that the two systems were isolated from any third "surrounding" system, so that only two systems are being considered. That should eliminate one of the problems. The other is the "joining" of the two systems. The two systems are initially separated by a wall impermeable everything. Then the wall is removed, or, if you like, made permeable to everything. This is an operation. The two systems consist of the same type of single-component gas. Before the removal, one system is the "system of interest". After the removal, the system of interest is bounded by the same isolating walls that previously bounded the two systems (except for the removable wall). This change in the definition of the system of interest is an operation, a "conceptual operation" I believe you call it. Do you now agree that the increase in the internal energy of the system of interest is simply equal to the internal energy of the other system? Do you agree that if the energy of the added system is $$\Delta U$$, then the change in energy of the system of interest is likewise $$\Delta U$$? PAR (talk) 05:40, 14 April 2013 (UTC)


 * I have already answered a properly posed version of this question for you several times. It seems you do not read what I write for you. It is hard to think of a good reason why you persist in asking this question.


 * Your question is posed in an illegitimately loaded way. It talks of an increase in the energy of a system of interest and of the energy of another added system. I do not accept that wording because it would open the way for you to continue to play more specious word games.Chjoaygame (talk) 06:43, 14 April 2013 (UTC)


 * Ok, that ties down exactly where the problem begins. However, not accepting the wording because it would allow me to play specious word games is an ad hominem objection, not a rational objection. Do you have a rational objection? By using the term "loaded" I assume you mean that the question carries implicit assumptions which are questionable or invalid. If that is correct, what assumptions are these? The question does indeed talk about an increase in the energy of a system of interest and of the energy of another added system. What is wrong with that? PAR (talk) 15:32, 14 April 2013 (UTC)


 * It was not that you personally could play word games, but that anyone could play specious word games with an acceptance of that way of posing the question. It was not just anyone who posed the question in that loaded way; it was you who did so, and, ignoring my previous answers that were constructed for a properly worded version of the question, again directed it to me personally, for the $III$th time, a sort of badgering cross-questioning, suggesting an argumentum ad baculinum.Chjoaygame (talk) 20:03, 14 April 2013 (UTC)

LOL - and I am not trying to force you to accept Smith's paper by beating you with a stick, but by reasoned discussion. In the Socratic method, nobody gets "cut to ribbons". Hopefully the one who has been shown to be wrong or self-contradictory simply amends his position, and the discourse is ended or moves on to a modified discussion. Thanks to your argumentation, I have amended my position regarding $$\delta R=\mu dN$$ to $$\delta R=u' dN$$, as reflected in my amended edit.

Speaking of which, I have to amend my position on Callen.

Callen is saying that, for an open system, if TdS is the energy added quasistatically as heat, without change in mass or volume, and -PdV is the energy added quasistatically as work, without change in mass or entropy, then µdM is the "quasistatic chemical work" which accounts for the energy deficit due to the addition of mass. It's the energy that is added by the addition of mass, without change in entropy or volume.

The problem is that for a real situation, you cannot add mass without change in entropy and volume, because µ is very often negative. You cannot add mass and subtract energy at the same time. Callen's description is accurate, but not measurable or "sensible". This is the same mistake I made in my original edit, which you correctly objected to, but apparently for the wrong reason.

This is where Smith comes in - he basically says that if you are adding mass reversibly, it must be at the same temperature and pressure as the system you are adding it to, and that you must also, unavoidably, add entropy and volume. Therefore, in Smith's scenario, TdS does not represent the energy added as heat. The energy added as heat is $$\delta Q=T(dS-dS_m)$$ where $$dS_m$$ is the entropy of the added mass. The energy added as work is $$\delta W=-P(dV-dV_m)$$ where $$dV_m$$ is the volume of the added mass. The energy of the added mass is $$\delta R=dU_m$$. If the total energy change is dU, then


 * $$dU=\delta Q+\delta W+\delta R=T(dS-dS_m)-P(dV-dV_m)+dU_m$$

If you separate terms,


 * $$dU=TdS-PdV-(TdS_m-PdV_m-U_m)$$

But the Euler integral for the small system states that:


 * $$dU_m=TdS_m-PdV_m+\mu dM$$

substituting,


 * $$dU=TdS-PdV+\mu dM$$

which is consistent with Callen. Its just that Callen's supposition that TdS is heat and -PdV is work is not supposed by Smith, because Callen's supposition is not generally realizable in practice, and Smith's scenario is. I fault Callen for not explaining what Smith has undertaken to explain.[This unsigned comment was posted by Editor PAR at 05:20, 18 April 2013]


 * You write: "I am not trying to force you to accept Smith's paper by beating you with a stick, but by reasoned discussion." Well, at least that looks as if you are saying that you are trying to force me to accept Smith's paper; that is an improvement in clarity on much of your other commentary.


 * The question here is as to appropriateness for the article on conservation of energy. I do not offer a complete assessment of Smith's paper, though mostly I think it is a useless and misleading word game, which has misled you. But what counts here is that I assert that Smith's paper, as cited by the edit under challenge, does not supply material or support relevant or useful or adequate for the article on conservation of energy. I have here given plenty of reason for this assertion, reason to which you have not responded except evasively.


 * I have nearly reached the end of my tether. You claim to be trying to force me to accept Smith's paper "by reasoned discussion". I think you are not engaging in reasoned discussion, because you mostly ignore what I write, as I have complained here many times. For example, you are here replying under the heading of an old post but not replying to my most recent one, in which I spent time responding in some detail to your arguments and summarizing the argumentative situation.


 * Your present comment persists in your repeated error of supposing, in contradiction to reliable sources, that transfer of internal energy as heat is defined for an open system, when it is not. Though I agree that Callen is faulty here, the flaws in your present comment are numerous and repetitive of your previous muddles. I have already dealt with them so much here, that I am no longer willing to try to list them and refute them yet again. I now have to say that it seems a waste of time to try to continue this discussion.Chjoaygame (talk) 10:31, 18 April 2013 (UTC)


 * Ok. I am still awaiting Munster and Tisza, and after reading them carefully, I will respond again. Could you specify what work of Caratheodory you refer to?


 * I did read what you wrote. The dissection of the term "chemical work" is not helpful, it's Callen who uses it as a series of words for µdM, and I don't care to discuss whether it is a good choice or not.


 * Smith has two steps argument: 1) adding mass by "removing the partition" between the large and the infinitesimal systems, both of which have the same intensive parameters. 2) add heat and work to the resulting composite (and closed) system. (addition of heat is, of course, not reversible).


 * He concludes that this constitutes a definition of heat and work, for an open system (under the restrictions that the mass addition be reversible), with the initial system defined as the large system prior the two steps, and final state defined as the composite system after the two steps. Since the steps are infinitesimal, they can be performed in any order is implicit in Smith's development.


 * Your unreasoned (but not necessarily invalid) objections basically boil down to the fact that you can find no support or justification or duplication of this procedure in any of the literature, and that a number of references contend that it cannot be done. I cannot respond to these unreasoned objections except to first read the literature you refer to which I will do as soon as they arrive.


 * Your reasoned objections amount to the claim that the infinitesimal steps cannot be carried out in any order, which I strongly doubt and would be happy to discuss. The claim that Smith is essentially working with a closed system would be false if these steps can indeed be carried out in any order.


 * If I have missed any other reasoned objections, I apologize. PAR (talk) 11:10, 19 April 2013 (UTC)


 * A mostly reliable translation is to be found at Kestin, J. (1976). The Second Law of Thermodynamics, Dowden, Hutchinson & Ross, Stroudsburg PA. Carathéodory does not talk about pushing his subsystems till they perish, or letting them appear from nowhere; his processes are finite in that respect.


 * I am sorry you couldn't find Münster or Tisza in a borrowing library. Münster is a good book, very careful, but says little if any more than I have already quoted from it about the present question. Münster's two-volume work on statistical thermodynamics is perhaps a certificate that he is no fool. As for Tisza, it is general and the only specifically relevant thing here I think is the distinction between operations and processes, which I think is uncontroversial enough. Well, unless it needs to be explicitly established that Gibbs' work was a radical step forward.


 * I think Münster's example of surrounding pressure increase acting on a system in a rigid but permeable container needs to be addressed if you want to say that in general work and heat can be defined in terms of the accepted Wikipedia (and Münster and Haase and others) definition. Perhaps you will say "Oh, that's just a special and trivial case, of zero work and zero heat transfer, with all the internal energy transfer belonging to the matter." Others would say that it is typical of processes for open systems. What if there is also a shaft-driven agitator that is mixing the contents of the system. That would affect how the matter transfer occurred, and the amount of energy that accompanied it. I don't think the article on conservation of energy is the place for such puzzles.


 * If the system is closed, it is well accepted that the infinitesimal steps can be carried out in any order. For example, chasing an ordinary quasi-static process around a PV curve can be done by going alternately in infinitesimal steps along adiabats and isotherms. This is because the operations from step to step might also be fairly represented simply as infinitesimal changes in the intensive variables of the surrounds, leaving the amount of substance in the system unchanged; not the more radical and rarely charted operations of changing the amount of substance of the system. A physical partition can be permeable to both work and heat and does not need to be changed at the steps. The reason for flagging the operations that separate the stages of the running of a Carnot engine is just that one wants to keep separate tracks of the transfers for the hot and cold reservoirs and for the work reservoir.


 * But changes in the substance of the system are not like that. From the perspective of the usual treatments of the first law for closed systems, they are new and radical operations. What goes for ordinary processes in infinitesimal steps does not necessarily go for infinitesimal steps that involve system-and-partition-changing operations. The infinitesimal increments of matter would be expected to come from a finite reservoir. Something has to happen to that reservoir when the system boundary is changed so that internal energy can be transferred with separate tracking of heat and work. Smith says nothing about what happens to that reservoir. The partitions have to change at the steps.


 * You posted your edit originally right off the top of your head, without any attempt at sourcing, but embarked on a rescue operation when it was challenged, and wouldn't take it down, but instead insulted the intelligence of the challenger while appealing to your own authority. Now you are taking time to look at sources, which I don't think will much advance things. It would have been better if you had done things in the other order.


 * If you can establish all that you want, I still say it would be original research. It is hardly reasonable to expect a Wikipedia editor to act as peer reviewer for a piece of original research that should be published with peer review, on the grounds that the researcher is Socrates. A sketchy assertion like Smith's in a rarely cited paper is still primary source material and should be noted as such. And the Smith story is not about such general processes as would be appropriate for a general article such as this, about conservation of energy, not about special cases in thermodynamics. The edit airbrushes away the radical advance made by Gibbs, which should not be airbrushed away. It has given pause to the best minds, and is often dealt with just by postulative fiat.


 * My objection is not just about quasi-static conceptual constructs. Restriction to infinitesimal alternating reversible steps is radically restricting the permitted kinds of process. A general process likely involves finite steps of change in the surrounds, such as a jump of pressure. It is one thing to calculate the difference between the initial and final state by use of quasi-static conceptual constructs that describe conceptual limit-processes that could be approached by physical ones; it is another to describe non-quasi-static irreversible physical processes, which are the general kind of physical process, and are a main reason why work and heat are of interest.Chjoaygame (talk) 16:34, 19 April 2013 (UTC)


 * Thank you for the Caratheodory reference. Let's continue this after I get the references and ponder them, and your response. Should be about a week. Is that ok? PAR (talk) 17:33, 19 April 2013 (UTC)


 * My claim includes that Smith is not working with an ordinary open system, not that he is working only with an ordinary closed system, nor exactly just that he is essentially working with a closed system.


 * More importantly, my assertion is that neither your edit nor Smith uses the ordinary Wikipedia definition of transfer of internal energy as heat because that is for closed systems. You may wish to prove and rely upon a proposal that they use an equivalent definition by some ad hoc definition of equivalence that you propose, but I say that such reliance on such an equivalence would be original research. Smith himself is clear about this, as I have previously pointed out. He writes: "... a convention is established that the heat flow into an open system is zero when the system, its supply tank and discharge tank are all surrounded by an adiabatic enclosure. This convention is partly a consequence of conventional notions of heat and partly an arbitrary device." Above you wrote, and not retracted: "With regard to ″supply″ and ″discharge″ tanks, I am not sure what he means." It means that he is not using an ordinary open system, but is using a composite system that overall is closed. And you want to reverse the burden on proof on this. For example, you write above: "Can we agree that IF this convention can be justified to your satisfaction, you would agree that heat and work CAN be distinguished for an open system? I'm not asking this because I think I can justify it to your satisfaction, I ask it only to clarify the nature of our disagreement." You were there trying to put the burden of proof on my satisfaction with Smith's proposed convention.Chjoaygame (talk) 23:40, 19 April 2013 (UTC)Chjoaygame (talk) 01:33, 20 April 2013 (UTC)Chjoaygame (talk) 01:54, 20 April 2013 (UTC)

"More importantly, my assertion is that neither your edit nor Smith uses the ordinary Wikipedia definition of transfer of internal energy as heat because that is for closed systems."


 * This is not a reasoned argument - it amounts to "one cannot extend the concept because the concept has not been extended"

"You may wish to prove and rely upon a proposal that they use an equivalent definition by some ad hoc definition of equivalence that you propose, but I say that such reliance on such an equivalence would be original research."


 * Again, not a reasoned argument - it amounts to "Since the concept has not been extended, any extension is ad hoc and original research". Original research by whom? Not me, by Smith. But then Gibbs, Planck, Einstein, etc. are all gave "ad hoc" extensions to existing theory which constituted original research. The point is not whether Smith is equivalent to Gibbs et. al., its whether his extension is valid and consistent.

He (Smith) writes: "... a convention is established that the heat flow into an open system is zero when the system, its supply tank and discharge tank are all surrounded by an adiabatic enclosure. This convention is partly a consequence of conventional notions of heat and partly an arbitrary device."


 * Again, not a reasoned argument. Who knows what he means by "arbitrary"? Who cares? If his extension is valid and consistent, it doesn't matter.

"It (discharge and supply tanks) means that he is not using an ordinary open system, but is using a composite system that overall is closed."


 * It is only closed after the first step. Before that, it is open. I am still not sure what he means by supply and discharge tanks. Probably the small system is the supply tank, the large system the discharge tank. Does it matter? The essence is in the mathematics and that makes sense.

"You were there trying to put the burden of proof on my satisfaction with Smith's proposed convention."


 * No, I was asking a hypothetical question. If you answered with a simple "yes" then I would have known that the basic problem was with the convention, and would have concentrated my attention on justifying that. If you had answered with a simple "no", then I would have known that the basic problem was elsewhere, and would have asked futher questions to determine where the basic problem lay. I was not putting any burden on you except to help me clarify what your basic objection is. It is difficult to address a problem that is not well defined. You, on the other hand, have written "I am entitled to observe that your argumentation is muddled without detailing exactly why." Sure, and I am entitled to edit the article, with a supporting reference to a peer-reviewed journal. That doesn't mean either one of us is doing the right thing. PAR (talk) 05:14, 20 April 2013 (UTC)

recent comments
I note that Buchdahl (section 66, page 121 "A single inert phase as open system") discusses exactly the same scenario for an open multi-component system as does Smith. Both use systems that are not redefined on the fly, so to speak, so that will not be an issue. Buchdahl arrives at a different conclusion, however, which I think is wrong, namely that the work done by compressing one of the pistons, forcing $$dN_i$$ particles across the permeable membrane into the large system is equal to $$\mu_i dN_i$$. The simplest way to see that it is wrong is to note that the process is carried out at constant volume and temperature, while the chemical potential is the increase in energy at constant volume and entropy. Also, again, the chemical potential can be negative, in which case energy is extracted by the addition of mass, which is impossible. Buchdahl seems to agree with Callen, but describes the process in much more detail. It worries me that these two well-known references seem to contradict Smith. Neither of the two justify their claims, while the development of Smith is even more detailed than Buchdahl and gives results that seem reasonable to me. I will have to go thru Buchdahl very carefully to see if I have missed something in his discussion. PAR (talk) 20:59, 21 April 2013 (UTC)

I have received my copies of Munster and Tisza. Both very good books, thanks for the recommendation. From what I can see, Tisza does not address the definition of heat or work for open systems. Munster, beginning on page 45 does, and he gets it wrong. He discusses two examples, (a), and (b). Example (b) discusses multi-component systems and so does not address what we are discussing. Example (a) discusses one-component systems and this is where he gets it wrong.

He is discussing a composite system ("surroundings" and "the system"), where the system is surrounded by a mass-permeable wall. He states that if the surroundings are "compressed", there is work done, mass and energy transferred to the system, while its volume is unchanged, and since its volume is unchanged, no work is done, and this is a contradiction. What he misses is that the work is done on the surroundings, not the system, and the volume of the surroundings must change in order for there to be "compression". This is the volume change associated with the work. The volume of the system does not change, so no work is done on the system.

This can be cast into the same problem considered by Callen, Buchdahl, and Smith, with Smith being the only one that gets it right. Suppose you have a closed composite system, composed of two subsystems separated by a mass-permeable wall which conducts no energy save that of the mass transferred. (Say system 1 on the left, system 2 on the right). Both systems contain the same single component gas. The composite system is in equilibrium, so the intensive parameters of each system are the same. If you now do an infinitesimal amount of reversible work $$\delta W=-P_1 dV_1$$ on system 1, an infinitesimal amount of mass dN, energy dU and entropy dS will be transferred from 1 to 2. Since the volume of system 2 does not change, no work is done on it. Callen and Buchdahl seem to be saying that the energy transferred is $$\mu dN$$ which is incorrect. The amount of energy transferred is clearly $$u dN$$ where u is the internal energy density of system 1 (which is the same as system 2). This is what Smith says, and he is right.

The question remains, what is heat? There is no work done on system 2, yet its internal energy is increased. Shall we defined the heat as simply that increase, or is there a reasonable breakdown of that added energy into two other parts, heat $$\delta Q$$ and something else $$\delta R$$? Smith says yes, and admits that the division is "arbitrary" to some extent.

Smith proposes that the added energy is not heat, $$\delta Q=0$$ since the semi-permeable membrane only transmits energy via the energy of the transmitted mass. This is, in a sense arbitrary, but then one might say the separation of dU into $$\delta Q$$ and $$\delta W$$ for a closed system is arbitrary. The thing that recommends this "arbitrary" separation is that work is directly measurable by non-thermodynamic means, heat is not. The statement by the first law that U is a state variable, and the ability to perform adiabatic work allows you to measure the function U(P,V,N), which then allows you to define heat.

The division of the energy added to system 2 into heat $$\delta Q=0$$ and $$\delta R$$ has a number of strong recommendations:


 * Like work, the amount of added energy due to mass transfer is measurable, and heat is then defined as the amount of energy remaining, in a more general case in which heat is added. In this specific case the heat added is zero.


 * The heat so defined corresponds to all other definitions of heat for single component systems (i.e. the Boltzmann equation, de Groot & Mazur's definition, hydrodynamic definition, etc. etc.)

In short, the more I study this, the more I realize that Smith is correct. PAR (talk) 18:44, 26 April 2013 (UTC)

response 0 to recent comments
With no further comment based on Editor PAR's going "thru Buchdahl very carefully", it seems I should now respond to the above recent comments by Editor PAR. My aim here is to show that the edit is not adequately supported and is inappropriate for its place in this article.Chjoaygame (talk) 00:27, 29 April 2013 (UTC)

response 1 to recent commments
Editor PAR comments:
 * "I note that Buchdahl (section 66, page 121 "A single inert phase as open system") discusses exactly the same scenario for an open multi-component system as does Smith. Both use systems that are not redefined on the fly, so to speak, so that will not be an issue. Buchdahl arrives at a different conclusion, however, which I think is wrong, namely that the work done by compressing one of the pistons, forcing particles across the permeable membrane into the large system is equal to . The simplest way to see that it is wrong is to note that the process is carried out at constant volume and temperature, while the chemical potential is the increase in energy at constant volume and entropy. Also, again, the chemical potential can be negative, in which case energy is extracted by the addition of mass, which is impossible. Buchdahl seems to agree with Callen, but describes the process in much more detail. It worries me that these two well-known references seem to contradict Smith. Neither of the two justify their claims, while the development of Smith is even more detailed than Buchdahl and gives results that seem reasonable to me. I will have to go thru Buchdahl very carefully to see if I have missed something in his discussion."

I respond to this as follows.Chjoaygame (talk) 00:27, 29 April 2013 (UTC)

response 1a
That comment is inaccurate in saying that Buchdahl discusses exactly the same scenario as does Smith, and that both systems are not redefined on the fly, so to speak.

Smith's scenario redefines the system on the fly. The addition of mass in Smith's scenario is workless and heatless. This is because the addition of mass is not a physical process. It is a conceptual operation, of redefining the system of interest. Before the addition of mass there were two systems, separated by a wall of unspecified nature, the system initially of interest, and the incremental infinitesimal system; and no mention of surroundings for either of these two systems. The addition of the mass is brought about by "removal of the wall". After the addition of mass, there is a new system, the one finally of interest, created by "removal of the wall". Smith gives it surroundings, from which it is separated by a wall permeable to energy but not to matter. This redefinition of the system of interest is followed in Smith by a physical process. In contrast to what Buchdahl writes, there is no suggestion in Smith of trying to describe this as a physical process; it just this that justifies Smith's calling the addition workless and heatless.

Buchdahl adds mass by a physical process. I agree with Editor PAR that Buchdahl does this in faulty way, but that is just because we fault the way that Buchdahl describes the physical process; I not agree with Editor PAR's reason for finding fault with Buchdahl, as I will detail below. But as to the basic scenario, Buchdahl has two systems, $n$ and $K$, separated by a semipermeable membrane which permits the passage of component $K_{i}$ alone. Initially for Buchdahl's process, the pressure of $C_{i}$ is just such that $K_{i}$ will will not pass through the membrane. I think it fair to say that the system $C_{i}$ is the system of interest and that the system $K$ is its surroundings. The physical process that Buchdahl contemplates is a transfer of matter and energy, from the surroundings, to the system of interest, through the semipermeable membrane, which is not removed to bring that transfer about. This is a difference in scenario.

Moreover, the "work" to which Buchdahl refers is radically different in description and in purport from the "work" referred to by Smith. Buchdahl's "work" is done during the process of transfer of matter and energy from system $K_{i}$ to system $K_{i}$, primarily on the system $K$, and derivatively or indirectly on the system of interest $K_{i}$. Smith's "work" is done on the new system finally of interest, after the end of the addition of matter. This is a further difference in scenario.

Editor PAR wishes to deny the importance of these differences in scenario. Perhaps his reason is that he thinks that "The essence is in the mathematics and that makes sense." My view is that the physics is not fully expressed in the mathematical formulas, but needs also the words that give them physical meaning, and that those words differ importantly here.Chjoaygame (talk) 00:27, 29 April 2013 (UTC)


 * Please see response 3 PAR (talk) 13:14, 2 May 2013 (UTC)

response 1b
In one respect here, Editor PAR and I more or less agree, I think. Considering Buchdahl's presentation, we find fault in Buchdahl's writing: "The work done on $K$ may be looked on as work done on $K_{i}$ in the process ..." I find this loose and vague and imprecise and thus inadequate, Editor PAR finds it wrong.

How is Buchdahl faulty? Editor PAR and I seem to agree that Buchdahl is faulty, but we differ as to how. I say that Buchdahl is faulty because he is not aware of the problems of defining "work" for an open system. Editor PAR thinks that Buchdahl is faulty because he gives a wrong amount of "work".

The problems of defining "work" for an open system are not discussed in every textbook. Only some do it.

For example, Denbigh, K.G. (1951), The Thermodynamics of the Steady State, Methuen, London, Wiley, New York.p. 56. Denbigh states in a footnote that he is indebted to correspondence with Professor E.A. Guggenheim and with Professor N.K. Adam. From this, Denbigh concludes "It seems, however, that when a system is able to exchange both heat and matter with its environment, it is impossible to make an unambiguous distinction between energy transported as heat and by the migration of matter, without already assuming the existence of the 'heat of transport'." Professor Denbigh is aware of the problem and feels a need to consult an authority on it. The authority is Guggenheim, but Guggenheim himself in his texts that I have detected, prefers to say nothing about the problem, I guess because he feels he has no answer to it, and doesn't want to burden the reader with chatter about something he does not intend to discuss. Another text is that of Fitts, D.D. (1962), ''Nonequilibrium Thermodynamics. A Phenomenological Theory of Irreversible Processes in Fluid Systems'', McGraw-Hill, New York, p. 28. Fitts writes there: "There exists an arbitrariness in the definition of heat flow for open systems, so that it is impossible to separate internal energy flux $K$ into a diffusive and a purely conductive term by any unique method."

I say that Buchdahl did not seem to be aware of, and failed by not dealing explicitly with, this problem when he wrote on his page 121 about the "work done on $j_{E}$ in the process of introducing the amount $K$ of $dn_{i}$ into it."

Editor PAR finds a different fault in Buchdahl here. Editor PAR writes:
 * "Buchdahl arrives at a different conclusion, however, which I think is wrong, namely that the work done by compressing one of the pistons, forcing $$dN_i$$ particles across the permeable membrane into the large system is equal to $$\mu_i dN_i$$. The simplest way to see that it is wrong is to note that the process is carried out at constant volume and temperature, while the chemical potential is the increase in energy at constant volume and entropy."

Well, perhaps, but perhaps Buchdahl was thinking in terms of "work" defined by the so-called 'Helmholtz free energy' or the 'Helmholtz potential' or the 'Helmholtz function' or the 'work function'. If one works with the independent variables of the Helmholtz function, $C_{i}$, then the chemical potential, $F = F(T, V, N_{1}, N_{2}, ...)$, in these independent variables, is as Buchdahl I guess intends, also equal to the partial derivative of $μ_{i}$ with respect to $F = F(T, V, N_{1}, N_{2}, ...)$ at constant $N_{1}$ and $T$.

Perhaps Buchdahl might be partly defended by a statement that Buchdahl is not tackling the same problem as Smith. Buchdahl's aim is perhaps to provide a maieutic derivation of the Gibbs formula "$V$" for an open system; it is not to provide a definition of heat and work for an open system. Smith's aim is to provide a definition of heat and work for an open system.

Whatever, we seem to agree that Buchdahl is not satisfactory here.Chjoaygame (talk) 00:27, 29 April 2013 (UTC)


 * This section is irrelevant to the present discussion. It deals with a multicomponent system, and we are discussing a single-component system.

response 1c
Editor PAR writes:
 * "Buchdahl seems to agree with Callen, but describes the process in much more detail. It worries me that these two well-known references seem to contradict Smith. Neither of the two justify their claims, while the development of Smith is even more detailed than Buchdahl and gives results that seem reasonable to me."

I agree with Editor PAR's revised view, that Callen, p. 36, is faulty; I think this need no further comment here. I, however, think that the aims and scenarios of Callen and of Buchdahl are not the same as those of Smith.Chjoaygame (talk) 00:27, 29 April 2013 (UTC)

response 2 to recent comments
Editor PAR writes:


 * "I have received my copies of Munster and Tisza. Both very good books, thanks for the recommendation. From what I can see, Tisza does not address the definition of heat or work for open systems. Munster, beginning on page 45 does, and he gets it wrong. He discusses two examples, (a), and (b). Example (b) discusses multi-component systems and so does not address what we are discussing. Example (a) discusses one-component systems and this is where he gets it wrong.


 * He is discussing a composite system ("surroundings" and "the system"), where the system is surrounded by a mass-permeable wall. He states that if the surroundings are "compressed", there is work done, mass and energy transferred to the system, while its volume is unchanged, and since its volume is unchanged, no work is done, and this is a contradiction. What he misses is that the work is done on the surroundings, not the system, and the volume of the surroundings must change in order for there to be "compression". This is the volume change associated with the work. The volume of the system does not change, so no work is done on the system."

My response to this is as follows. I will conclude that Münster does not get it wrong as alleged by Editor PAR.Chjoaygame (talk) 00:27, 29 April 2013 (UTC)

response 2a
As for Tisza. The relevance of citing Tisza is


 * 1. that Tisza makes a clear and thoroughly considered axiomatic distinction between what he calls 'Clausius-Kelvin-Carathéodory' thermodynamics, and what he calls the 'macroscopic theory of equilibrium', which is more or less the thermodynamics of Gibbs.


 * I contend that this is important because the usual textbook rigorous and Wikipedia definition of heat is for closed systems, such as those of 'Clausius-Kelvin-Carathéodory' thermodynamics, not for open systems, such as for the Gibbsian 'macroscopic theory of equilibrium'.


 * 2. that Tisza points out Carathéodory's introduction of the composite "simple system", as a methodological device. I contend that this is important because it is a systematic and very well accepted way of dealing with composite systems for the definition of heat and work.


 * 3. that Tisza clarifies the distinction between a thermodynamic process and a thermodynamic operation. I contend that this is important because it makes clear what is appropriate for reasoning that changes the system of interest in midstream, as I contend Smith's does.Chjoaygame (talk) 00:27, 29 April 2013 (UTC)

Please see response 3. PAR (talk) 13:14, 2 May 2013 (UTC)

response 2b
As for Münster. I agree with Editor PAR that Münster's example (b) does not apply to the present problem, and that his example (a) does apply. I disagree with Editor PAR's view that "Münster ... gets it wrong".

Editor PAR writes:


 * "What he [Münster] misses is that the work is done on the surroundings, not the system, and the volume of the surroundings must change in order for there to be "compression". This is the volume change associated with the work. The volume of the system does not change, so no work is done on the system."

I contend that Editor PAR has read Münster partially and mistakenly. Münster discusses the formulation of the first law for an open system. He writes on page 50: "As explained in §14 the classical point of view (equivalence of heat and work) as well as Carathéodory's point of view (definition of heat) are meaningless for open systems. The usual formulation can be saved by an independent and new definition of the heat absorbed. This device is of no interest in connection with the present discussion." We here in our Wikipedia articles from the physical viewpoint usually use what Münster refers to as the Carathéodory point of view for defining heat. It relies on processes of pure adiabatic work, which is impossible in an open system, by definition. On page 46 Münster writes: "It is, therefore, not generally possible to define clearly the 'volume work' done on an open phase." He also writes: "... adiabatic work as required by §8 cannot, by definition, be done on an open phase."

In view of these remarks by Münster it is implausible to read him as does Editor PAR, as open to the criticism that Münster "misses that work is done on the surroundings, not on the system, and the volume of the surroundings must change in order for there to be "compression". This is the volume change associated with the work. The volume of the system does not change, so no work is done on the system." Münster's relevant statement here is in his example (a): "Work is obviously done due to compression but the volume remains constant."

Editor PAR made his partial and mistaken reading, I suppose, partly by misinterpreting Münster's word "obviously". Münster does not mean that he is too lazy to say exactly why work is done on the system; he means that to a casual and uncritical reader, for example, Buchdahl, it might speciously appear that work is done in a defined way on the system, but that such a reader would be mistaken.

To go into perhaps otiose detail, risking being too chatty, I would make some pictorial remarks about "work on the system" when its volume does not change. Isochoric work is work done on a system when its volume does not change. Examples of isochoric work recognized in closed system thermodynamics are friction on the wall of the system, such as in Rumford's work, and stirring by shaft work, such as in Joule's experiments. In the case of the present problem of an open system, one might riskily and probably wrongly propose that isochoric work is done on the system when new matter is forced into it through its rigid but permeable walls. The new matter may be loosely thought of as compressing the initially present matter, before they mix and become indistinguishable in the final state of internal thermodynamic equilibrium. Such compression might be regarded as being done by the surroundings as it drives the new matter in, and might be thought of as isochoric. Münster perhaps thinks that someone might think along those lines as "obvious", but he rejects its possible claim to be precise and well defined physics.

Münster knows that others, perhaps such as Guggenheim, have considered the problem that he is considering, the question of the meaning, if any, of work in general for an open system, and have long ago reached the same conclusion that he reaches, as just quoted above. He is willing to mention the problem, but not to dwell too much on it, and not to try to evade it by an arbitrary device, that he knows would be just a word game with no real physical content. Smith, on the other hand, announces that he intends to try to deal with it by an admittedly "arbitrary device"; I contend that Smith's arbitrary device is just a word game with no real physical content. Here, what matters is that Editor PAR wants to put Smith's "arbitrary device" into the article on conservation of energy, as in the edit under discussion. I agree with Münster explicitly and Guggenheim tacitly and by hearsay, that such an arbitrary device is not notable for basic discussions of thermodynamics, let alone of the more general topic of conservation of energy, the subject of this article.Chjoaygame (talk) 01:23, 29 April 2013 (UTC)

Please see response 3. PAR (talk) 13:14, 2 May 2013 (UTC)

response 3 to recent comments
Editor PAR writes:


 * "Munster, beginning on page 45 does, and he gets it wrong. He discusses two examples, (a), and (b). Example (b) discusses multi-component systems and so does not address what we are discussing. Example (a) discusses one-component systems and this is where he gets it wrong.


 * He is discussing a composite system ("surroundings" and "the system"), where the system is surrounded by a mass-permeable wall. He states that if the surroundings are "compressed", there is work done, mass and energy transferred to the system, while its volume is unchanged, and since its volume is unchanged, no work is done, and this is a contradiction. What he misses is that the work is done on the surroundings, not the system, and the volume of the surroundings must change in order for there to be "compression". This is the volume change associated with the work. The volume of the system does not change, so no work is done on the system.


 * "This can be cast into the same problem considered by Callen, Buchdahl, and Smith, with Smith being the only one that gets it right. Suppose you have a closed composite system, composed of two subsystems separated by a mass-permeable wall which conducts no energy save that of the mass transferred. (Say system 1 on the left, system 2 on the right). Both systems contain the same single component gas. The composite system is in equilibrium, so the intensive parameters of each system are the same. If you now do an infinitesimal amount of reversible work $$\delta W=-P_1 dV_1$$ on system 1, an infinitesimal amount of mass dN, energy dU and entropy dS will be transferred from 1 to 2. Since the volume of system 2 does not change, no work is done on it. Callen and Buchdahl seem to be saying that the energy transferred is $$\mu dN$$ which is incorrect. The amount of energy transferred is clearly $$u dN$$ where u is the internal energy density of system 1 (which is the same as system 2). This is what Smith says, and he is right."

The topic of this section of the talk page is the new edit, posted by Editor PAR. I continue to contend that it should be deleted because it is inappropriate for its place in the article on conservation of energy. The edit is about a fine point of thermodynamics, proposing a statement of the first law for an open system in terms of heat and work. I am contending that such a statement should not be made here, relying on the view that heat and work are not defined (according to the Bryan-Carathéodory-Born definition of heat and work that is accepted in the present Wikipedia thermodynamics articles), stated by several sources which I consider to be reliable. I contend that such a fine point of thermodynamics is not appropriate for such a place in the article on conservation of energy, because that is a far more general topic than a fine point of thermodynamics. I also contend that the edit is misleading or not notable. Editor PAR's recent comments do not explicitly address this question directly, but instead they defend the source Smith cited by the edit. Nevertheless, Editor PAR's recent comments I suppose are intended as indirect defence of the edit.

I contend that those recent comments are not an effective defence of the edit. They distract attention, away from the edit, to a general question, of the rightness or otherwise of Smith's 1980 paper. I suppose that Editor PAR intends that if Smith is right, then the edit is justified and should stand. I contend that the problem with the edit is that it purports to indicate that heat and work are defined for open systems, at least for one-component open systems. That this risks being seriously misleading is exemplified by the behaviour of Editor PAR himself, as I will now show. Editor PAR might be regarded as a fair enough reasonable sample reader of the article. I now propose that Editor PAR's initial version of his edit exemplifies a way of reading this question that might be the initial prejudice of a reasonable reader. Editor PAR's initial version of the edit read as follows:


 * "For a simple open system (in which the particles may be exchanged with the environment) containing a single type of particle, the first law is written:
 * $$\mathrm{d}U = \delta Q - \delta W+\mu dN,\,$$


 * where $$dN$$ is the change in the number of particles and $$\mu$$ is the chemical potential per particle, the energy per added particle required to maintain an unchanged volume and entropy."

On this talk page, Editor PAR proposed that this was mainstream thinking. It was unsourced in the article, but on challenge on the talk page he cited, amongst other sources, Callen's page 36 equation 2.6, $dG = V dP − S dT + Σ μ_{i} dn_{i}$. I think it would be fair to say that Editor PAR was at that time interpreting that formula with the idea in mind that $dU = T dS - P dV + μ_{1} dN_{1} + ... + μ_{r} dN_{r}$ represented the heat and that $T dS = δQ$ represented the work. I contend that this is a likely enough interpretive presupposition which a new reader of edit might start with. The point here is that a reasonable reader might read the edit as implying that heat and work are defined in general in a physically important way for an open system, and that this makes the edit seriously misleading. I contend that heat and work are not defined in general in a physically important way for an open system, with support in reliable sources. For an open system, the safe statement of the first law is simply in terms of the internal energy transferred in a process, as is also insisted upon by many, though not all, careful and reliable sources for a closed system.

Editor PAR's revised version of the edit, now standing in the article, reads:


 * "For a simple open system (in which mass may be exchanged with the environment), containing a single type of particle, the first law is written:
 * $$\mathrm{d}U = \delta Q - \delta W + u'\,dM,\,$$


 * where $$dM$$ is the added mass and $$u'$$ is the internal energy per unit mass of the added mass. The addition of mass may be accompanied by a volume change which is not associated with work (e.g. for a liquid-vapor system, the volume of the vapor system may increase due to volume lost by the evaporating liquid). In the reversible case, the work will be given by $$\delta W=-P(dV-v\,dM)$$ where v is the specific volume of the added mass."

I continue to contend that this is misleading or not notable and should be deleted. I contend that, for this article, a defence of Smith does not form an adequate defence of this version of the edit. What Smith proposes is not notable for this article on conservation of energy as it stands, and the report of it in the article is not an adequate representation of what Smith proposes.Chjoaygame (talk) 21:39, 30 April 2013 (UTC)

Editor PAR's recent comment as above does not argue that Smith's device is appropriate for this article, as would be needed for a defence of the edit. Instead, Editor PAR's recent comment argues that Münster gets it wrong while Smith gets it right, an interesting proposition, though not a sound defence of the edit. This proposition in Editor PAR's recent comment is self-contradictory. Rather than one being right and the other wrong, Münster and Smith largely agree in important respects. They agree that an arbitrary device is needed in order to make an ad hoc definition of work and heat for an open system. Smith knows this and cites Münster in this connection. Smith explicitly says that he is providing an arbitrary device. Münster is concerned to state the first law for an open system, and says that for such a general statement of a major principle of physics, an arbitrary device is not of interest. I agree with Münster on this. Most texts do not explicitly say that they are not stating the first law for an open system; they just state it for a closed system and say nothing about it for an open system. They do often state a combination of the first and second laws in the form of Gibb's formula, for example in Callen, equation 2.6, on page 36 cited above, $P dV = δW$. Only some few texts are explicit as is Münster in stating the first law for open systems simply in terms of the internal energies, without heat and work; many others are silent on the point. Smith, Münster, and Editor PAR agree that the statement of the first law for an open system, in terms simply of the internal energies, without heat and work, is valid. It is just that the edit in question goes further, into a place where angels fear to tread, a place where I contend the general article on conservation of energy should not go.

Editor PAR's recent comment here is faulty. He writes:


 * "This can be cast into the same problem considered by Callen, Buchdahl, and Smith, with Smith being the only one that gets it right. Suppose you have a closed composite system, composed of two subsystems separated by a mass-permeable wall which conducts no energy save that of the mass transferred. (Say system 1 on the left, system 2 on the right). Both systems contain the same single component gas. The composite system is in equilibrium, so the intensive parameters of each system are the same. If you now do an infinitesimal amount of reversible work $$\delta W=-P_1 dV_1$$ on system 1, an infinitesimal amount of mass dN, energy dU and entropy dS will be transferred from 1 to 2. Since the volume of system 2 does not change, no work is done on it. Callen and Buchdahl seem to be saying that the energy transferred is $$\mu dN$$ which is incorrect. The amount of energy transferred is clearly $$u dN$$ where u is the internal energy density of system 1 (which is the same as system 2). This is what Smith says, and he is right."

Editor PAR is rightly aware that to justify his edit, he needs to attack Münster. He writes: "This can be cast into the same problem considered by Callen, Buchdahl, and Smith." Too long a cast, I would say. Münster is considering a statement of the first law of thermodynamics for open systems. He reaches the conclusion, now in my words and formulation, that a safe statement is that if two adiabatically isolated systems, not in relative motion, and with no relative gross potential energy, and with no external force fields present, with respective internal energies $dU = T dS - P dV + μ_{1} dN_{1} + ... + μ_{r} dN_{r}$ and $U_{1}$, are placed beside each other, still separated by a common adiabatic wall, and then that wall is removed, then the new system so created will have an internal energy $U_{2}$. This proposition of Münster is agreed, I think, between all participants, Callen, Buchdahl, Smith, Editor PAR, and me. It is important. It is discussed by Landsberg P.T. (1961), Thermodynamics, with Quantum Statistical Illustrations, Interscience, New York, on page 135 et seq.. Landsberg points out that here we are introducing the notion of an extensive variable. He considers it so important as a new axiom of thermodynamics, extending from classical closed system theory to open system theory, that he wants to call it the "fourth law of thermodynamics". We do not have to accept this label, but it is not right to try to airbrush its importance out of our account. We are not dealing, as Münster seems to suggest, with a thermodynamic process here. We are looking at the thermodynamic operation of conversion of a "compound system", with two component systems with respective internal energies separated by an adiabatic wall, into a "simple system" with only one internal energy. (This term "simple system" is not defined as is that of Carathéodory.) There is here no question of heat or work because there is no process. Tisza 1966 is needed to provide articulation of this idea. It is a pity Münster did not cite Tisza on this point, although Münster does recomment Tisza in general. If Editor PAR wants to mark this as a fault in Münster, I will agree, but I will point out that Münster is not too far from the mark here, when he emphasizes the conceptual step involved in stating the first law for open systems, a step beyond the conceptual structure of closed system thermodynamics. But it does not impugn Münster's message, which he states briefly because he knows it is not new, that heat and work are not properly defined for processes of an open system.

There is a likeness between the Münster proposition and the first stage of Smith's scenario. They refer to a thermodynamic operation, not just a thermodynamic process, because of the removal of the partition, which in effect amounts to a re-definition of the system of interest. But Editor PAR wants to have Smith's operation considered as a process, a heatless workless process. There is physics here, not just the addition of some mathematical terms. This is implicitly recognized by Smith when he points out that his scenario is an arbitrary device.Chjoaygame (talk) 01:18, 1 May 2013 (UTC)

Continuing.

Editor PAR knows that to defend his edit he needs to attack Münster. I think his attack fails. There is too much support for Münster for him to succumb to Editor PAR's efforts at attack. One can cite Denbigh quoting Guggenheim, and Fitts, and Haase, and indeed Smith, who does not attack Münster. The difference between Smith and Münster is not that Smith contradicts what Münster says about physics. The difference is that Smith makes a choice that Münster does not make. Smith rushes in where Münster, Guggenheim, Fitts, and Haase fear to tread. In agreement with these writers, Münster judges that for a general statement of the first law for open systems, it is not good to try to talk in general about heat and work because to do so must rest on some arbitrary device, not an appropriately general way to go. But Smith judges otherwise, and Editor PAR says that this makes Smith "correct" and "right" and Münster "wrong".

The usual way of talking about thermodynamic processes for a system is to talk about the system and its surroundings. The system has only its states of internal thermodynamic equilibrium; in classical thermodynamics, one does not describe the system during transfers that take it out of thermodynamic equilibrium. The surroundings are allowed a much wider range of adventures. Thus there is an important asymmetry between system and surroundings.

The concept of the quasi-static process allows calculations of the changes of the state variables between the initial and the final state of an arbitrary possible process. The calculation relies on a fictive pathway through the state space. The pathway is a smooth curve, along which integration can be calculated from knowledge of the equations of state of the system, combined with the laws of thermodynamics. It is not a physical process, but can be regarded as a limit of a set of physical processes. All of the states on the pathway are states of internal thermodynamic equilibrium of the system.

The surroundings can contain thermodynamically describable systems and it can contain other devices and objects. All of these can be supposed to initiate changes which affect the system through the walls that connect the system and its surroundings. For example, the surroundings can be supposed to contain a heat reservoir, from which internal energy can be transferred to the system through a wall permeable only to heat. Usually, account is kept of the amount of internal energy so transferred, and the temperature of the reservoir during the transfer. Internal energy is a state variable of a system. Also it is allowed that such a transfer includes transfer of entropy, and account is kept of the transferred amount of entropy and the temperature of the reservoir during the transfer. Entropy is not a conserved quantity in general, but is it a state variable of a system, and for this transfer, if the temperature of the system and of the reservoir are infinitesimally close, the transfer of entropy is balanced, the entropy lost by the reservoir is equal to the entropy gained by the system. If the temperatures are not infinitesimally close, then the entropy transfer is unbalanced, entropy not being a conserved quantity in general.

For a general transfer to the system from a thermodynamically defined reservoir in the surroundings, a conserved quantity is transferred. In the case of a transfer as heat, the conserved quantity transferred is a quantity of internal energy, transferred in a certain manner, namely a manner other than as adiabatic work. Heat is a process quantity, not a state variable that measures a conserved quantity. Thus it is only loose speech to say that "heat is transferred"; properly speaking, internal energy is transferred in a prescribed way, namely in a way other than as adiabatic work. To speak of "heat flux" is a commonly allowed abuse of language, yes, commonly allowed, but still an abuse of language. Properly speaking there is no such thing as "heat flux".

Other transfers of energy to the system than from a thermodynamically defined reservoir are allowed. The energy may start in the surroundings as mechanical energy, transferred as work, but be registered in the system as internal energy. Isochoric work is an example. For example, the surroundings may contain an engine that creates a changing magnetic field which moves a magnetic stirrer inside the system. Thermodynamic systems in internal thermodynamic equilibrium do not contain such engines. In a sense they can be described as black boxes. The price of this is that they are not as adventurous as are the surroundings. Thus the asymmetry between system and surroundings. Shaft work such as in Joule's measurements is another example. The energy is transferred by some carrier of force, such as a field or a shaft, and does not travel by magic carpet.

For an open system, the transfer of matter is usually considered to take place between the system and a reservoir in the surroundings, through a definite wall between them. The name van't Hoff comes to mind, and one thinks of selectively semi-permeable membranes. Like energy, matter is not transferred by magic carpet. In this sense, the removal of the partition by Smith and others does not describe a process of transfer of matter to the system from a reservoir in the surroundings. The removal of the partition describes a thermodynamic operation, often called "addition" of systems. It re-defines the system.

With a re-definition of the system, one re-defines the problem; one stops considering the old problem and starts considering a new one. New state functions are defined, and so forth. Talking about infinitesimal systems rests on ideas of passing to the limit from finite systems, with continuous functions of state, differentiable at the point of interest. Changing from one system with its state functions to another system with its state functions is not the natural home of continuous functions of state of a system, differentiable at the point of interest. It cannot be supposed that simple and convenient ideas of passing to the limit, and consequent talk of infinitesimal step, are mathematically well founded. Such suppositions are not the ordinary stuff of rigorous thermodynamic thinking.

Thus I contend that it is misleading to say that "This [Münster's account] can be cast into the same problem considered by Callen, Buchdahl, and Smith." We can forget Callen and Buchdahl for this purpose since it is agreed that they are faulty. Münster's account cannot validly be cast into the same problem considered by Smith, however much Editor PAR would like that. Smith is not talking about a transfer of matter from the surroundings to the system; he is talking about re-defining his system. He says no more about the old surroundings' reservoir from which the matter was transferred. He will set up a new surroundings, separated from the new system by a wall impermeable to matter, but permeable to energy as heat and work. He has been upfront about this. Like Editor PAR, he wants us to allow him to re-define an adiabatic wall, a re-definition that he calls an arbitrary device, recalling the words of Münster for this very situation. For adventurers such as Smith, it is a convenient thing to forget the importance of the usual definition of an adiabatic process, such as is referred to by Landsberg, P.T. (1961), ''Thermodynamics. With quantum statistical illustrations'', Interscience, New York, page 120: "One may also ask why adiabatic processes play such an important part in the development of thermodynamics." Adventurer Smith wants the kudos of the word 'adiabatic', but not the weight that it carries for others. Editor PAR here does not mind altering definitions for his needs.

Smith is re-defining an "open system". His new "open system" is a hybrid between an open system and a closed system. It is open when he wants matter to transfer, and closed when he wants energy to transfer as heat and work. However interesting and valid his newly chosen scenario, it is not an account of an open system as ordinarily defined. It is as Smith says, an arbitrary device.

Having seen Smith re-define 'adiabatic' and 'open system', we now find that we are being asked also to re-define 'heat'. Editor PAR writes above:
 * "The question remains, what is heat? There is no work done on system 2, yet its internal energy is increased. Shall we defined the heat as simply that increase, or is there a reasonable breakdown of that added energy into two other parts, heat $$\delta Q$$ and something else $$\delta R$$? Smith says yes, and admits that the division is "arbitrary" to some extent.


 * "Smith proposes that the added energy is not heat, $$\delta Q=0$$ since the semi-permeable membrane only transmits energy via the energy of the transmitted mass. This is, in a sense arbitrary, but then one might say the separation of dU into $$\delta Q$$ and $$\delta W$$ for a closed system is arbitrary. The thing that recommends this "arbitrary" separation is that work is directly measurable by non-thermodynamic means, heat is not. The statement by the first law that U is a state variable, and the ability to perform adiabatic work allows you to measure the function U(P,V,N), which then allows you to define heat.


 * "The division of the energy added to system 2 into heat $$\delta Q=0$$ and $$\delta R$$ has a number of strong recommendations:


 * "Like work, the amount of added energy due to mass transfer is measurable, and heat is then defined as the amount of energy remaining, in a more general case in which heat is added. In this specific case the heat added is zero.


 * "The heat so defined corresponds to all other definitions of heat for single component systems (i.e. the Boltzmann equation, de Groot & Mazur's definition, hydrodynamic definition, etc. etc.)"

In Editor PAR's way of proceeding, are we playing a word-game, or what?

Strong recommendations they may be, but they are still recommendations to re-define heat.

Editor PAR argues hard. He wrote above:


 * "″More importantly, my assertion is that neither your edit nor Smith uses the ordinary Wikipedia definition of transfer of internal energy as heat because that is for closed systems.″


 * This is not a reasoned argument - it amounts to ″one cannot extend the concept because the concept has not been extended″"

As he re-defines heat, when I assert that he is doing so, he complains that what I called "my assertion" is not a reasoned argument. In context, with me advertising it as an assertion, it was not intended as a reasoned argument: it was intended as a correction to what Editor PAR had just tried to put into my mouth, and now he offers new words that he wants to put into my mouth, words that I don't intend in general, though I do intend them in the present editing context. But Editor PAR agrees that my assertion is true. He wants to re-define heat. In the article on conservation of energy.

Editor PAR also wrote above:


 * "It is only closed after the first step. Before that, it is open. I am still not sure what he means by supply and discharge tanks. Probably the small system is the supply tank, the large system the discharge tank. Does it matter?"

Editor PAR seems to have said that it doesn't matter what Smith means. As it happens I disagree with Editor PAR's guess about what Smith means. Moreover, I think it does matter what Smith means.

Looking again at what Editor PAR writes above:


 * "The heat so defined corresponds to all other definitions of heat for single component systems (i.e. the Boltzmann equation, de Groot & Mazur's definition, hydrodynamic definition, etc. etc.)"

As a matter of precision, the word heat is being used in two senses here. The word heat in macroscopic thermodynamics has a particular meaning, but the equations of non-equilibrium thermodynamics to which Editor PAR points, are, as I have detailed above, using the word heat in a different sense. They are really referring to transfer of internal energy by mechanisms other than bulk transport. This is the same kind of abuse of language that has us talking about latent heat of fusion and so forth; accepted but still not a rigorously supportable usage. As I have noted above, there is, properly speaking, no such thing as "heat flux". It is well known that the definition of "heat flux" in local-thermodynamic-equilibrium non-equilibrium thermodynamics often, as in the cases he cites, and in the kinetic theory, refers to transfer of internal energy by mechanisms other than bulk transport. Editor PAR is not only trying to re-define heat for macroscopic thermodynamics, he is also trying to make it agree with an abuse of language that is often accepted in other theories.

Editor PAR writes above:


 * "This is, in a sense arbitrary, but then one might say the separation of dU into $$\delta Q$$ and $$\delta W$$ for a closed system is arbitrary."

Here Editor PAR wants to minimize the notion of arbitrariness, that Münster and Smith agree on. Editor PAR wants us to accept that the distinction between heat and work for a closed system is arbitrary in the same sense that Smith's device is arbitrary. What is he smoking? Does he really dismiss classical thermodynamics as an arbitrary word game?

Editor PAR writes above:


 * "In short, the more I study this, the more I realize that Smith is correct."

The question here is not whether Smith is "correct"; it is whether the edit is appropriate. Smith is playing a word-game. There is no new physics and no new concept of transfer of energy in Smith's paper. Humpty Dumpty comes to mind. When one claims to set up an arbitrary convention, as Smith does, the notion of "correctness" doesn't arise, because one intends only a word game.

Editor PAR is playing a word game here, re-defining basic concepts, but the edit that I am challenging does not warn the reader about that. This article is no place to play word games like that, and this is a reason to delete the edit.Chjoaygame (talk) 03:19, 3 May 2013 (UTC)

reply to response 3 to recent comments

 * The problem with redefining systems "on the fly" can be disposed of by an equivalent two-step process, in which no systems are so redefined: The small system and the large system (containing the same single component) are separated by a mass-permeable membrane. Both systems have the same intensive parameters (T, P, etc.). The small system is subject to reversible compression until its volume is zero and its contents have been entirely forced into the large system. The work done on the small system is $$-P \Delta V$$ and the increase in internal energy of the large system is $$dU=\hat{U}\Delta M+P\Delta V$$ where $$\hat{U}$$ is the internal energy per mole common to both systems, and $$\Delta V$$ is the volume of the small system before compression. Reversible work is now extracted from the large system until it recovers the volume lost in the compression. This work is $$ -P\Delta V$$ and the increase in internal energy of the large system is $$dU=\hat{U}\Delta V+P\Delta V-P\Delta V$$. The large system is now in the same state as the "on the fly" scenario in which the large system was expanded to include the small system.


 * The crucial point is now that at no point has heat energy been added to the system, and the net work is zero: $$(P\Delta V-P\Delta V)$$ in the above energy balance equation. Smith's "arbitrary device" is just this: If mass is added to a single-component system by the above described process, no heat has been transferred to the large system. This is totally justified, since the process yields the same results as simply removing the mass permeable wall on the original composite system, which clearly involves no heat transfer. The problem of the large system being redefined "on the fly" is avoided. Again, this "arbitrary" expansion of the concept of heat, when applied to the continuum case, yields the same heat flux vector found in the Boltzmann transport equation, de Groot and Mazur's heat flux vector, etc. etc. This is a fundamental and strong point - to deny the concept of work or heat transfer in open single-component systems is to deny the existence of a heat flux vector for such systems, yet this heat flux vector is ubiquitous in the literature. Again, this does not apply to multi-component systems with diffusion.


 * If reversible work $$\delta W=-P dV_w$$ and heating $$\delta Q$$ are now done on the system, the energy balance equation for the system is:


 * $$dU=\hat{U}\Delta V+P\Delta V-P\Delta V-PdV_w+\delta Q$$


 * The net volume change in the large system is $$dV=dV_w+\Delta V$$ so the energy balance equation can be rewritten $$dU=\hat{U}\Delta V+P\Delta V-PdV+\delta Q$$ or equivalently, $$dU-\hat{U}dM=\delta Q-P(dV-\Delta V)$$ where the work is $$\delta W=-PdV_w=-P(dV-\Delta V)$$ (Smith's equation 6 where $$\Delta V=\hat{V}dM$$) so that $$dU-\hat{U}dM=\delta Q+\delta W$$ (Smith's equation 3) which can also be written in the form $$dU=\delta Q+\delta W+\delta R$$ with $$\delta R=\hat{U}dM$$.


 * I think this explanation deals most the points you have made. It is not a word game with no physical content. During the initial compression of the small system, work has been done (on the small system) yet the volume (of the large system) remains the same. Munster's statement of the above (without parentheses) implies a conundrum where there is none. Isochoric work has not been done on the large system, but rather reversible volume-work has been done on the small system. Mass has been reversibly transferred to the large system during this process. The volume of the large system has remained constant, and only reversible volume-work has been done, so clearly, no work, isochoric or otherwise, has been done on the large system. Munster is muddying the waters with vague statements. PAR (talk) 13:09, 2 May 2013 (UTC)


 * Round and round in circles are we led by Editor PAR. There is nothing new in the above reply of his. I have in archived sections of this page and in the above already dealt with what he writes here. In order to drive the matter from the samll system into the large system at constant volume of the large system, one must increase the pressure in the small system above the value $$P$$, mistakenly proposed by Editor PAR as fixed constant during the process. Editor PAR does not in the above take the calculation the next step that Smith takes, of re-defining the system as closed and then letting it suffer heat and work exchange. Though Editor PAR is now accepting that there is a problem with re-defining systems on the fly, he does not here avoid doing so. He just does it in a slightly different way, leaving it unstated in the above reply. Münster is not muddying the waters, he is pointing out that they are muddy, by stating a fact which Editor PAR has previously accepted and now still accepts, namely that the transfer of matter is accompanied by transfer of internal energy that cannot in general be uniquely split into heat and work; Editor PAR transfers the matter accompanied by an unsplit amount of internal energy $$\hat{U}\Delta V$$. Münster (in agreement with other authorities that I have already cited) judges that to go beyond this by use of an arbitrary device is of no use for the present purpose, a valid and well judged message that Editor PAR doesn't want to hear, so he resorts to shooting the messenger.


 * I have reached the end of my tether. If Editor PAR wants to leave his edit there, he does not have my consensus. I see no payoff in my spending more time on this.Chjoaygame (talk) 13:00, 3 May 2013 (UTC)


 * Fine. You cannot have possibly dealt with what I wrote, because this is the first time I wrote it. One does not increase the pressure of the small system above that of the large system, that would be irreversible work, and I specifically stated that the process was reversible. The scenario in which there is no on-the-fly redefinition of systems is in fact equivalent to Smith's on-the-fly redefinition. I do not accept that on-the-fly redefinitions have a problem, I only proposed this equivalent scenario to demonstrate that there is no problem. For about the third or fourth time, you make the mistake of assuming that the aim of Smith is to divide the energy added by mass transfer into work and heat, and for the third or fourth time I have to explain that it is a transfer of energy by a process that is neither work or heat, that is, the $$\delta R$$ term in Smith. Munster on page 46 invokes a scenario in which the surroundings are compressed in order to force mass into a fixed volume enclosed by a mass-permeable membrane. He states that volume work has been done, yet the volume of the system remains constant while its energy has increased, and that this is a conundrum which means that heat cannot be defined for an open single-component system. I say he is wrong, because the volume work was done on the surroundings, not the system. The volume of the surroundings must have decreased in order for there to be compression, the volume of the system remains the same and there is no conundrum. This is the same scenario I have proposed, except the small system takes the place of "surroundings" and the analysis is in terms of infinitesimals. You have failed to address this except to essentially say that Munster disagrees. PAR (talk) 13:49, 3 May 2013 (UTC)


 * The edit is misleading and not notable for this article, and should be deleted. No more.Chjoaygame (talk) 01:05, 4 May 2013 (UTC)

where the problem lies
Yes, indeed the posing of the question does carry implicit assumptions which are invalid. The problem is in the use of the terms 'increase in the energy of a system of interest' and 'added system' in the same sentence. The term 'system of interest' is intended merely to make it explicit that the surroundings might also be considered as a system but are not meant, while your question was in your context of no surroundings to be considered; so the phrase 'of interest' is redundant, and that makes it potentially misleading. The 'increase of energy' looks as if it might refer to a process of transfer between a system and its surroundings, while what is meant by 'adding' is an operation, not a process. 'Adding' a system as you propose, without reference to surroundings, does not fit with the term 'system of interest'. The 'adding' is a commutative operation, but the phrase 'of interest' is explicitly ruling out commutation. The mixing of these unfitting terms invites muddle. That invitation is the loading in your wording, accepting which would open the way for anyone, not just you who constructed the wording, to play specious word games. That is what is wrong with your wording.Chjoaygame (talk) 20:03, 14 April 2013 (UTC)


 * argumentum ad baculinum? No, wrong, we are (I hope) engaging in the Socratic method of argument. When have I ever used any form of threat?


 * Regarding my wording - I was trying to explain a valid concept in my own words. Wishing to use more standard terminology, I see Callen speaks of much the same thing.


 * Under "1.7 Measurability of the Energy" (p18 in my book) please read the paragraph beginning with: "The only remining limitation to the measurability of the energy difference of any two states is the requirement that the states must have equal mole numbers..."


 * Note the conclusion: "by employing adiabatic walls and by measuring only mechanical work, the energy of any thermodynamic system relative to an appropirate reference state can be measured." "Any" clearly means open systems as well. Smith is merely carrying out Callen's prescription in detail.


 * Callen then goes on to define heat for constant mole numbers. Under "1.9 The basic problem of thermodynamics" (p25 in my book) please read the paragraph beginning with: "Before formulating the postulate ...."


 * Note the mention of two simple systems and the composite subsystem, before and after "removing the constraint" (i.e. changing the properties of the boundary between them, or, in the present case, removing it). Note that this includes removing walls restrictive of mass. Again, Smith is merely carrying out Callen's prescription in detail. What I have been calling the system of interest should be called one of the simple systems (the large one) before the removal of constraint, and the composite system after removal of constraint, so, to use this terminology, my question simply amounts to asking if you agree that the internal energy of the isolated composite system is equal to the sum of the internal energies of the individual unclosed systems. I expect you will agree to this statement.


 * What Smith is doing is simply expressing the work done on the composite system in terms of the parameters of the three systems, with the addition of matter constituting a third term in the expression for dU, which Smith calls $$dR$$ which I call $$\delta R$$ and which Callen calls $$dW_c$$ (Eq 2.10, p37). Calls this term "chemical work" and the expression $$\delta R=\mu dN$$ for a simple single component system is the "quasistatic chemical work". This is fully consistent with Smith's exposition, except that he expresses things in terms involving all three systems. For example, for the simple system $$\delta W=-P(dV-\Delta V)$$ where dV is the volume of the composite system after removal of the partition and performance of work minus the volume of the large system beforehand. You can continue Smith's line of reasoning to show that his $$dR$$ is just the quasistatic chemical work $$\mu \Delta N$$, as stated in Callen (Eq 2.9). PAR (talk) 14:20, 15 April 2013 (UTC)


 * Socrates didn't, so far as I recall, try to force his interlocutors to accept Smith's 1980 paper. I vaguely recall, however, that he always sliced them to ribbons. So I am to prepare myself to be sliced to ribbons, not beaten with a baculum? I will try to avoid that fate. At least now you are revealing where your questioning is trying to drive me. Just as I anticipated. Sad to say, you are leading us round in circles. We have discussed all this before.


 * Your comment is a bundle of ideas, not easy to deal with succinctly. But it seems to fall to me to show how it goes wrong. So here goes.


 * You conclude: "You can continue Smith's line of reasoning to show that his $$dR$$ is just the quasistatic chemical work $$\mu \Delta N$$, as stated in Callen (Eq 2.9)."


 * Do you mean that $U = U_{1} + U_{2}$ is a work component of the transferred energy? That would seem to mean that after all, the energy transfer has been split completely into heat and work. I think it is agreed that such a split is impossible. So I suppose you mean that $dR$ is a form of transferred internal energy but is not work sensu strictu.


 * You airily invite me to continue Smith's line of reasoning to reach the conclusion that you propose here. If that were a natural thing to do, it would be strange that Smith himself did not go that way. In any case, it is not up to me to continue Smith's line of reasoning.


 * I do not accept your assertion that Smith's line of reasoning can be continued in general to show that his $$dR$$ is just the quasistatic chemical work $$\mu \Delta N$$.


 * On page 36, in section 2-1, Callen writes: "This type of energy flux, although intuitively meaningful, is not frequently discussed outside thermodynamics and does not have a familiar distinctive name. We shall call $dR$ the quasi-static chemical work." Callen speaks on this occasion of "quasi-static chemical work" but you have above told us "An increment of work is a clearly defined concept, it is force times the increment of distance." Callen's "quasi-static chemical work" of section 2-1 is not work sensu strictu. But Callen's discussion in sections 1-5 to 1-9 is only about work sensu strictu. The key to those sections is that internal energy can be measured by purely mechanical means. "Quasi-static chemical work" is Callen's one-off shorthand for a formulaic term such as $Σ_{j} μ_{j} dN_{j}$ but does not denote a quantity of work measured by purely mechanical means, as specified by your "An increment of work is a clearly defined concept, it is force times the increment of distance," nor as intended by the method of sections 1-5 to 1-9. In those sections there is no mention of "quasi-static chemical work". True, Callen's index on page 493 indicates page 36 for "chemical work", but that term as such, pure and simple, does not appear there; what appears there is "quasi-static chemical work", a term that Callen tells us he has invented for his present purpose, but is not a customary term.


 * You order me: "Note the conclusion: ″by employing adiabatic walls and by measuring only mechanical work, the energy of any thermodynamic system relative to an appropirate reference state can be measured.″ ″Any″ clearly means open systems as well."


 * If you had read what I have written for you, you would know that I have long ago pointed out that this is so.


 * You add "Smith is merely carrying out Callen's prescription in detail."


 * Not so. Smith is doing something different from Callen. In section 1-7, Callen is defining internal energy. Callen in section 1-8 goes on to define heat for closed systems; he does not mention open systems in this section, because his reasoning there, about heat and work for closed systems, does not apply to open systems. Smith is re-writing the first law of thermodynamics ostensibly so as to apply it to heat and work for open systems. You claim that he is nevertheless "carrying out Callen's prescription in detail".


 * Callen is following Carathéodory's method, to which I have repeatedly adverted here. I will here use Carathéodory's account because it is more complete and explicit than Callen's. Work is defined for a composite system that Carathéodory labels "simple" because he requires it to have only one non-deformation variable for its full specification, beyond its deformation variables. It has internal partitions which define subsystems such as are referred to by Callen when he writes on page 18 "Consider two simple subsystems ..." (he uses "simple" here to refer to what Carathéodory calls a "phase"). The Carathéodory simple system (with its subsystems) has internal transfers of matter and energy, but for those internal transfers of energy, only internal energy is defined, not heat or work. It is only for the overall "simple" system that Carathéodory defines work. The overall "simple" system is closed. Whatever Smith might like you to believe, and whatever you might like to believe, Smith succeeds in defining heat and work only for a closed system, just as does Callen, while Carathéodory defines only work for it. True, within his closed system, Smith has subsystems, which, like Carathéodory's, are allowed to transfer matter between each other, but work and heat are not defined for them. Such transfers are not transfers between open systems proper; they are transfers between subsystems of a closed system; this is because there is only one non-deformation variable that must be shared amongst the several subsystems of the "simple" closed system proper, while an open system proper has a private non-deformation variable (which might be its temperature, for example) all of its own. There is a slight problem here. Carathéodory has his subsystems undergoing real processes. He does not go as Smith goes, with allowing a subsystem to be completely abolished by total absorption into another subsystem. Carathéodory's subsystems undergo real finite processes, not driven to complete obliteration of one of them as Smith drives his infinitesimal subsytem.


 * There is nothing new to our discussion here, but perhaps this collected summary may make the whole structure of the thinking clearer.


 * You write: "What Smith is doing is simply expressing the work done on the composite system in terms of the parameters of the three systems, with the addition of matter constituting a third term in the expression for dU, which Smith calls $$dR$$ which I call $$\delta R$$ and which Callen calls $$dW_c$$ (Eq 2.10, p37)."


 * That is an admission that Smith is not describing a simple thermodynamic process. Work is defined for a simple thermodynamic process for a system and its surroundings, two systems, not for three systems as used by Smith, who is in effect trying to set up a new and private definition of work. As I have noted above, Smith makes this clear: "... a convention is established that the heat flow into an open system is zero when the system, its supply tank and discharge tank are all surrounded by an adiabatic enclosure". The heat and work account is not for the system, it is for the system together with its supply and discharge tanks. The game is over at this point. Smith more or less admits this in his next sentence: "This convention is partly a consequence of conventional notions of heat and partly an arbitrary device." The edit is naturally read as referring not to an ad hoc device such as Smith's. The edit is naturally read as referring to a simple thermodynamic process. I would oppose further efforts to patch this up.Chjoaygame (talk) 19:59, 15 April 2013 (UTC)