User:Chjoaygame/sandbox

User:Chjoaygame/sandbox/archive 1

common


Xxx〈bra|ket〉 xxX


 * $$\langle \mathrm{bra}|\mathrm{ket}\rangle$$.

$|$p$\rangle$

text in blue font
 * $$\mathrm {latex \, minus \, sign}\, - $$

$ν = c⁄λ$

Rendering math

Properties of water

Gibbs' mixing paradox
Gibb's mixing paradox concerns mixing of two distinct chemical species that scarcely differ, in comparison with what happens when two bodies of identical material are put in direct contact without a separating wall. In the case of the distinct species, a significantly large entropy change may occur. But none in the case of identical material. The question arises, of what happens as the difference of species decreases continuously to zero. One physical answer to this question is that no such continuous decrease to zero is possible, because chemical species are defined quantally. That is the quantum theory, and is generally accepted as correct.

Second law
The second law of thermodynamics states that when a thermodynamically defined process of transfers of matter and energy occurs, the sum of the entropies of the participating bodies must increase. In an idealized limiting case, that of a reversible process, this sum remains unchanged.

In a thermodynamically defined process of transfers between bodies of matter and radiation, each participating body is initially in its own state of internal thermodynamic equilibrium. The bodies are initially separated from one another by walls that obstruct the passage of matter and energy between them. The transfers are initiated by a thermodynamic operation: some external agency makes one or more of the walls less obstructive. This establishes new equilibrium states in the bodies. If, instead of making the walls less obstructive, the thermodynamic operation makes them more obstructive, there is no effect on an established thermodynamic equilibrium.

The law expresses the irreversibility of the process. The transfers invariably bring about spread,  dispersal, or dissipation of matter or energy, or both, amongst the bodies. They occur because more kinds of transfer through the walls have become possible. Irreversibility in thermodynamic processes is a consequence of the asymmetric character of thermodynamic operations, and not of any internally irreversible microscopic properties of the bodies. Thermodynamic operations are macroscopic external interventions imposed on the participating bodies, not derived from their internal properties.

The second law is an empirical finding that has been accepted as an axiom of thermodynamic theory. Of course, thermodynamics relies on presuppositions, for example the existence of perfect thermodynamic equilibrium, that are not exactly fulfilled by nature. Statistical thermodynamics, classical or quantum, explains the microscopic origin of the law. The second law has been expressed in many ways. Its first formulation is credited to the French scientist Sadi Carnot in 1824 (see Timeline of thermodynamics).

reasons for Planck's statement
To comply with Editor User:'s concern about convoluted wording quoted from a translation of Planck, I am posting a re-worded version of the Planck statement, as follows: "The second law of thermodynamics states that in every natural thermodynamic process the sum of the entropies of all participating bodies is increased. In the limiting case, for reversible processes this sum remains unchanged."

reasons
There are several reasons why Planck's statement of the law is excellent.


 * It is explicitly positive for natural processes. It ignores the trivial exception, of a "process" in which nothing happens. In non-trivial processes, the entropy sum increases. It does not leave the reader to puzzle about whether the entropy sum does indeed increase.
 * It makes explicit that several systems participate and contribute to the entropy sum, leaving implicit that there occur transfers between them.
 * It expresses the law in terms of entropy, implicitly both for initial and for final states of thermodynamic equilibrium.
 * It avoids unnecessary talk of evolution which might be read as referring to gradual non-equilibrium progression, for which entropy is undefined.
 * It explicitly mentions the limiting case of a mathematically idealized reversible process.

There are some background considerations, as follows.

internal adiabatic enclosure
Here Editor Ppithermo, with concurrence here from Editor PAR, considers an isolated system with an internal adiabatic wall, for example a piston that allows transfer as work, but not of energy as heat, or of matter, that creates internal adiabatic enclosures. He refers to problem 2.7–3 in the second edition of Callen. He had brought up the discussion of this problem in the first edition of Callen, in Appendix C, headed Equilibrium with internal adiabatic constraints.

Callen further indicates this point by his use of the proviso "in the absence of an internal constraint" in his statement of his


 * Postulate $II$.  There exists a function (called the entropy $S$) of the extensive parameters of any composite system, defined for all equilibrium states and having the following property: The values assumed by the extensive parameters in the absence of an internal constraint are those that maximize the entropy over the manifold of constrained equilibrium states.

Bailyn is less explicit, but observes the same point in what he calls the "superstrong entropy" version of the law:


 * The entropy of an isolated system will spontaneously increase until equilibrium is reached, unless prevented from doing so.

Landsberg discusses a distinction between "simple" and "compound systems". Compound systems contain, for example, simple systems separated by adiabatic walls. Landsberg writes about equilibria of compound systems: "... This can occur if certain partitions separate the systems, or certain constraints are part of the arrangement, which are capable of preventing a thermodynamic process which would otherwise be possible." Landsberg sets a student exercise: "5.11. Decide the following finer points of thermodynamics, giving reasons: ... (b) How good a statement is 'The entropy of an isolated system cannot decrease with time'?

These items are why it is not part of the usual statements of the second law to claim that "... isolated systems always evolve toward thermodynamic equilibrium, the state with maximum entropy." True, those just quoted words are rather vague, and they can be pressed to read so as to make them not strictly false. But they have a strong potential to mislead, and express an idea that is not explicit in the standard statements of the second law. They should not be in the first sentence of the lead, that is more or less a definition.

the form of a thermodynamic process
In the background of the Planck version, there is the following thinking.

The process starts with a state of thermodynamic equilibrium between several systems, each obeying the minus oneth law of thermodynamics, separated by walls of specific permeabilities. Then a thermodynamic operation occurs, marking the transition from initial to final states, changing the permeabilities, and allowing initially prohibited transfers. There follows a final state of thermodynamic equilibrium. Entropy sums are defined and compared for the initial and final states.

The Planck version avoids talk about some idea of "progressive advance towards equilibrium". This is desirable because an equilibrium state is of practically infinite duration and is subject to recurrence. A transient "initial disequilibrium" can be ignored for a state of infinite duration. Entropy is defined for states of thermodynamic equilibrium.

Properties of entropy
The second law is conveniently stated in terms of a quantity called 'entropy'. The present section of this article intends to explain how this is so.

The concept of entropy rests on some presuppositions:
 * 1) entropy is defined as a quantity that describes a system that is in its own state of internal thermodynamic equilibrium, that is adequately described by extensive macroscopic thermodynamic variables, thus having the nature of a thermodynamic system.
 * 2) the zeroth and first laws of thermodynamics are presupposed.
 * 3) It is desired that the entropy of a thermodynamic system should be an extensive property. This means that entropy should have the scaling property: if, by a thermodynamic operation, a wall is put into place so as to partition a given thermodynamic system into two completely separate systems without otherwise disturbing them, and the ratio of their volumes $V_{1}$ and $V_{2}$ of the two systems is $λ:(1−λ)$, then the ratio of their entropies, $S_{1}:S_{2}$, is also $λ:(1−λ)$.
 * 4) It is desired that the entropy of a thermodynamic system should be an additive property. This means that entropy of a compound system consisting of two completely separate systems is the sum of their separate entropies.
 * 5) It is desired, as a convention, that entropy should obey the second law of thermodynamics. A quantity the satisfies the foregoing requirements could mathematically or logically either obey the second law, or else it could obey a putative law that entirely negated the second law, decreasing upon the occurrence of a thermodynamic process; such a putative possibility is ruled out by the present conventional requirement.

Removal of a partition
One may consider two isolating enclosures separated by an impermeable wall. Initially, one contains a gas in its own internal state of thermodynamic equilibrium, the other a vacuum. The entropy of the one may be denoted $S_{1}$. From the scaling and additive properties, the other has entropy $0$. The entropy of the initially compartmented compound system, from the additive property, is $S_{+} = S_{1} + 0 = S_{1}$. Now a thermodynamic operation may remove the partition. In the consequent new equilibrium, according to the second law, the entropy $S_{u}$ of the new unpartitioned system obeys $S_{u} > S_{+} = S_{1}$.

Replacement of the partition
By a second thermodynamic operation, the partition may then be replaced. By the scaling property, the entropy of each new half-system is $S_{1/2} = S_{u}/2$. The entropy of the compound of the two separated half-systems is $S_{c} = 2S_{1/2} = S_{u}$, unchanged by the operation.

Restoration by adiabatic compression followed by heat transfer
The original two-compartment compound system can be restored by adiabatic compression by a force in the surroundings, acting on the expanded compound system, followed by heat transfer to or from the surroundings. A force in the surroundings can compress the gas only in accord with the second law, increasing the entropy sum of the compound system and the surroundings. Also the work transfer increases the internal energy of the comppund system. It is conventional to suppose that the adiabatic work is suppplied by a source that does not thereby increase its own entropy. Then the entropy of the adiabatically compressed system, before heat transfer, has an entropy that satisfies $S_{a} > S_{c} = S_{u} > S_{1}$. It is as if the work transfer was associated with the "creation" of some entropy inside the compound system. The transfer of heat must by the first law be from the compound system to the surroundings, so as to restore the original internal energy. It is as if the heat transfer is accompanied by a "transfer of entropy", as if entropy were some kind of material, that could be transferred; rigorously considered, this does not really make sense, but it is, for the present, a harmless metaphor.

Temperature
"The starting point is undoubtedly the qualitative connection between the temperature concept and our crude physiological sensations of hot and cold."


 * I find something incongruous. We have editors who like to be careful to emphasize the mathematical distinction between an inner product and the action of a linear functional, and use the term 'inner product', over-ruling such physicists as Dirac, Gottfried, Cohen-Tannoudji, and Weinberg in the context, who write of the scalar product. On the other hand, now we are discussing the difference between state vectors and wave functions, the latter being scalars relative to the state vectors. Yet we prefer to speak of a component rather than use the Wikipedia terms scalar projection, scalar resolute or scalar component'''.

PAR's table
δQ is heat, δWx is irreversible work, so TdS=δQ+δWx. If both are zero, then dS=0. For the 3 possible walls, "T ins" means thermally insulated, and "No IW" means no irreversible work. "External intensive variable" specifies the region external to the system.

Einstein vis à vis Whitehead
Einstein (1936, Physics and Reality:


 * ... Andererseits aber haben jene Begriffe und Relationen, insbesondere die Setzung realer Objekte, überhaupt einer "realen Welt," nur insoweit Berechtigung, als sie mit Sinneserlebnissen verknüpft sind, zwischen welchen sie gedankliche Verknüpfungen schaffen.


 * Dass die Gesamtheit der Sinneserlebnisse so beschaffen ist, dass sie durch das Denken (Operieren mit Begriffen und Schaffung und Anwendung bestimmter funktioneller Verknüpfungen zwischen diesen sowie Zuordnung der Sinneserlebnisse zu den Begriffen) geordnet werden können, ist eine Tatsache, über die wir nur staunen, die wir aber niemals werden begreifen können.


 * ... On the other hand, these concepts and relations, and indeed the status of real objects and, generally speaking, the existence of "the real world," have justification only in so far as they are connected with sense impressions between which they form a mental connection.


 * The very fact that the totality of our sense experiences is such that it can be put in order by means of thinking (operations with concepts, and the creation and use of definite functional relations between them, and the coördination of sense experiences to these concepts) — this fact is one which leaves us in awe, but which we shall never understand.

This is very close to Whitehead's ontological principle. Translation touched up by me.


 * ... However, the fixation will never be final. It will have validity only for a special field of application (i.e. there are no final categories in the sense of Kant).

Agrees with Whitehead.

London and Newcastle Tea Company
Established in 1875, the London and Newcastle Tea Company's offices were in Charlotte Square, Newcastle. Early branches were in New Bridge Street, Sandhill, Scotswood Road, Shields Road, Westgate Road and Clayton Street but the firm later expanded to more outlying parts of the city. It went out of business between 1959 and 1962.

According to James B. Jefferys, the London and Newcastle Tea Company was one of the first five firms in Britain in the grocery and provisions trade to operate in a multiple branch scale. In 1875, it ran between 10 and 20 branches; in 1880, it was the second biggest grocery chain in Britain, with between 40 and 50 branches, just ahead of the rapidly expanding Thomas Lipton.

The firm had a loyalty scheme in operation as early as 1875. The network of groceries, which sold the company’s tea, gave a brass check with each purchase. Customers were invited to save the checks until they had acquired enough to claim a prize such as a toy, an item of crockery or a household gadget. The checks are now collectors’ items. By 1928, the shop at 212 Chillingham Road, Heaton, had been acquired by the London and Newcastle Tea Company.

dispersal
Guggenheim writes


 * "To the question what in one word does entropy really mean, the author would have no hesitation in replying 'Accessibility' or 'Spread'. When this picture of entropy is adopted, all mystery concerning the increasing property of entropy vanishes. The question whether, how and to what extent the entropy of a system can decrease finds an immediate answer." Guggenheim, E.A. (1949), Statistical basis of thermodynamics, Research: A Journal of Science and its Applications, 2, pp. 450–454, Butterworths, London, pp. 450–454, page 452.

E.T. Jaynes has expressed opinion on this topic.


 * "We have seen the mathematical expression $p log (p)$ appearing incidentally in several previous chapters, generally in connection with the multinomial distribution; now it has acquired a new meaning as a fundamental measure of how uniform a probability distribution is." Jaynes, E.T. (2003), Probability Theory: The Logic of Science, edited by G. Larry Bretthorst, Cambridge University Press, Cambridge UK, page 351, ISBN 978-0-521-59271-0.

Also


 * "We have made no use of the notions of order and disorder. Indeed, as Maxwell noted in the article on diffusion, those terms are only expressions of human aesthetic judgments. But in a well-known work on statistical mechanics (Penrose, 1970) it is stated that "... the letters of the alphabet can be arranged in 26! ways, of which only one is the perfectly ordered arrangement ABC ... XYZ, all the rest having varying degrees of disorder." To suppose that Nature is influenced by what you or I consider "orderly" is an egregious case of the Mind Projection Fallacy.
 * "As a more pertinent example, Nature has decreed that water vapour has a higher entropy than liquid water, although most of us would consider the vapour far more "orderly" in both structure and behavior. The vapour has a higher entropy than the liquid, not because it is less "orderly", but because the microstates compatible with the vapour macrostate occupy a larger phase volume. Thus we cannot understand the second law, in either biology or physics, in terms of intuitive notions of order and disorder." Jaynes, E.T. (1989), Clearing up Mysteries: the Original Goal, in Maximum Entropy and Bayesian Methods, J. Skilling, Editor, Kluwer Academic Publishers, Dordrecht, Holland, pp. 11–27.

Denbigh writes


 * "Another common interpretation of entropy is in terms of order and disorder, but this is not entirely satisfactory. A counter-example to the idea that an entropy increase implies an increase of 'disorder' is due to Bridgman. This is concerned with the spontaneous crystallization of a supercooled liquid; if this takes place under adiabatic conditions the entropy of the resulting crystal will be greater than that of the supercooled liquid, but it would be difficult to claim that there has been an increase in 'disorder'.
 * "Perhaps one of the most useful verbalisms is 'spread', as used by Guggenheim; an increase of entropy corresponds to a 'spreading' of the system over a larger number of possible quantum states.
 * "Similarly, the increase in the entropy of a body when it takes in heat is essentially an increased spread over the energy states." Denbigh K.G. (1981/1997), The Principles of Chemical Equilibrium: with Applications in Chemistry and Chemical Engineering, 4th edition, Cambridge University Press, Cambridge UK, pp. 55–56.
 * "Similarly, the increase in the entropy of a body when it takes in heat is essentially an increased spread over the energy states." Denbigh K.G. (1981/1997), The Principles of Chemical Equilibrium: with Applications in Chemistry and Chemical Engineering, 4th edition, Cambridge University Press, Cambridge UK, pp. 55–56.
 * "Similarly, the increase in the entropy of a body when it takes in heat is essentially an increased spread over the energy states." Denbigh K.G. (1981/1997), The Principles of Chemical Equilibrium: with Applications in Chemistry and Chemical Engineering, 4th edition, Cambridge University Press, Cambridge UK, pp. 55–56.

impartial
Anderson writes


 * "The central fact about entropy as used in science is that it involves the distribution of energy in a system. Energy tends to become “spread out,” or delocalized, if not prevented from doing so. The “configurational entropy” much used by mineralogists in discussing the various arrangements of atoms on a crystal lattice (Chapter 14) is fundamentally different fom the arrangement of checkers on a board because energy is transferred when atomic arrangements are changed – the heat capacity of each arrangement is different.


 * "If you “really” want to understand entropy, you need to learn more than just equilibrium thermodynamics. In this book, we take the simple view that entropy is a parameter, having a clearly defined method of measurement, which enables us to define thermodynamic potentials in chemical systems. It is simply related to “disorder” in many simple situations, which is an intuitive aid, but this aid doesn’t extend very far. Because of this resemblance to probability and disorder, entropy has been related to everything from shuffled cards to the fall of empires, but these connections for the most part have nothing to do with the second law of thermodynamics." Anderson, G.M. (2005), Thermodynamics of Natural Systems, 2nd edition, Cambridge University Press, Cambridge UK, ISBN 978 0 521 84772 8, page 106.

Atkins & de Paula write


 * "The concept of the number of microstates makes quantitative the ill-deﬁned qualitative concepts of ‘disorder’ and ‘the dispersal of matter and energy’ that are used widely to introduce the concept of entropy: a more ‘disorderly’ distribution of energy and matter corresponds to a greater number of microstates associated with the same total energy." Atkins, P., de Paula, J. (2006), Physical Chemistry, 8th edition, W.H. Freeman, New York NY, ISBN 9780716787594, page 5.

Bridgman writes


 * "There is a fuzziness about the common-sense notion of "disorder" which makes it not always altogether suited as an intuitive tool in discussing the second law." Bridgman, P.W. (1943), The Nature of Thermodynamics, Harvard University Press, Cambridge MA, page 176.

disorder
Adkins writes


 * "In seeking the most probable configuration of a system we are, in fact, seeking the configuration of the greatest disorder permitted by the constraints to which the system is subjected." Adkins, C.J (1983), Equilibrium Thermodynamics, 3rd edition, Cambridge University Press, Cambridge UK, page 78.

Attard writes


 * "In physical terms, entropy is often interpreted as a measure of the disorder of a system. If one compares two macrostates, then the one with the greater number of microstates (or greater weight of microstates if they are not equally likely) is the one with greater entropy. But in the sense that ordered means predictable and disordered means unpredictable, the more microstates there are the less one is able to predict the speciﬁc microstate that the system is in. As another example, if one could place a few objects on a large grid, then the number of regular or ordered arrangements is very much less than the number of irregular arrangements, and since the logarithm of the number can be identiﬁed with the entropy, one sees that greater entropy corresponds to greater disorder." Attard, P. (2012), Non-Equilibrium Thermodynamics and Statistical Mechanics: Foundations and Applications, Oxford University Press, Oxford UK, ISBN 978 0 19 966276 0, page 18.

Baierlein writes


 * "There is usually nothing wrong with referring to entropy as "a measure of disorder." The phrase, however, doesn't take one very far. To gain precision and something quantitative, one needs to connect "disorder" with "absence of correlations" and then with multiplicity. It is multiplicity that has sufficient precision to be calculated and to serve as the basis for a physical theory." Baierlein, R. (1999/2005), Thermal Physics, Cambridge University Press, Cambridge UK, ISBN 978-0-521-59082-2, page 45.

Brush writes


 * "This explanation suggested to Boltzmann that entropy — previously a rather mysterious quantity — should be interpreted as a measure of disorder; the tendency toward increasing entropy is simply a tendency toward increasing disorder." Brush, S.G. (1976/1986), The Kind of Motion We Call Heat: A History of the Kinetic Theory of Gases in the 19th Century. Book 1, Physics and the Atomists, North Holland, Amsterdam, page 83.

Callen writes


 * "Thus we recognize that the physical interpretation of the entropy is that the entropy is the quantitative measure of the disorder in the relevant distribution of the system over its permissible microstates." Callen, (1985), page 381.

Causality
Multiple causes

Any event may have several causes. This possibility is not excluded by my definition (given explicitly on p. 9), though I speak there of A being 'the' cause of the effect B. Actually the 'number' of causes, i.e. of conditions on which an effect B depends, seems to me a rather meaningless notion. One often finds the idea of a 'causal chain' A1, A2, •••, where B depends directly on A1, A1 on A2, etc., so that B depends indirectly on any of the An. As the series may never end — where is a 'first cause' to be found ? — the number of causes may be, and will be in general, infinite. But there seems to be not the slightest reason to assume only one such chain, or even a number of chains; for the causes may be interlocked in a complicated way, and a 'network' of causes (even in a multi-dimensional space} seems to be a more appropriate picture. Born, Max (1949), Natural Philosophy of Cause and Chance, Oxford University Press, London UK, page 129.

efficacy

heat transfer by convective circulation
Editor Incnis Mrsi has made an edit here.

The present article is about the thermodynamic concept of heat transfer, which is carefully defined in thermodynamics. This should be made clear in the article, which for a general readership should start from elementary considerations. So defined, heat transfer by convection must be through a process with a mechanism that results in no net transfer of matter: the convection must be circulatory. Though implicit in them, this is not explicitly emphasized in the articles Convective heat transfer and Natural convection. Also important here is that convective circulation is spontaneous only beyond some suitably specified threshold.

The thermodynamic definition of heat refers to a process of transfer of energy that causes a change of a body from one state of its own internal thermodynamic equilibrium to another. In the early days of thermodynamics, this was expressed in terms of cyclic processes. The notion of thermodynamic equilibrium requires zero macroscopic flows. The articles about Convective heat transfer and about Natural convection are mainly about flows, and are specialized developments beyond elementary thermodynamics.

A thermodynamic process is initiated and terminated by thermodynamic operations. In the present context, one may envisage three bodies, a source body, a fluid intermediary, and a destination body. The heat is transferred from source to destination, eventually making no change to the fluid intermediary. This may be arranged through thermodynamic operations by which the walls separating the three bodies are changed from adiabatic to diathermal (initiating) and back from diathermal to adiabatic (terminating). The source body starts at a higher temperature than does the destination body. Such a temperature difference is conceptually proper to elementary thermodynamics, which does not deal with the dynamics of the flows by which the heat is transferred. For the thermodynamic definition of heat transfer, such a temperature difference is suitable as a threshold parameter. Temperature gradients entail flow, and do not belong to the thermodynamic definition of heat transfer.

The edit by Incnis Mrsi is concerned with dynamic flow variables internal to the fluid intermediary of the process of convective circulation, not with the respective initial and final temperatures of the source and destination bodies. It is conceptually specialized beyond an elementary or fundamental approach to thermodynamics. The edit belongs to topics such as fluid dynamics, which deal with the dynamic stability of flows, beyond the scope of the four laws of thermodynamics. For example, chapter 2 of Hydrodynamic and Hydromagnetic Stability, the monumental 1961 textbook by Chandrasekhar, treats the onset of convective circulation in a special case. That chapter mentions neither of the touchstones of thermodynamics, entropy and the second law of thermodynamics, because it is not about thermodynamics, the domain of the present article.

For a Wikipedia article, it is valuable to present material with clarity of principle, because Wikipedia is partly pedagogic. Consequently, it is worth distinguishing between the respective scopes of thermodynamics and fluid mechanics because of Einstein's dictum that, within its domain of applicability, thermodynamics is the one area of physics that will never be overthrown. A factor of the permanent reliability of thermodynamics is that its domain of applicability is strictly defined and confined.

Placed in the lead of the present article, the edit will confuse the thinking of ordinary readers.

reply
The previous entry was "Though spontaneous, convective circulation does not necessarily and immediately occur merely because of temperature difference; for it to occur in a given arrangement of systems, there is a threshold temperature difference that needs to be exceeded."

The new edit reads "Natural convection, though spontaneous, does not occur merely because of temperature difference but due to Rayleigh instability caused by combination of gravity and thermal expansion in supplement to sufficient temperature gradient."

Non-convective heat transfer
Non-convective transfer of energy as heat has two kinds: passive, as in, for example, conduction and radiation; and active, as in, for example, Joule's original mechanical-shaft-and-paddle experiment, magnetic stirring, and Joule heating.

In passive non-convective heat transfer between two thermodynamic systems, source and destination transfers are of the same character. Each thermodynamic system, starting from an initial state of homogeneous internal thermodynamic equilibrium, can export or import energy as heat in this way. Transfer is governed merely by temperature difference between source and destination bodies, and is spontaneous, immediate in onset, and necessary, whenever there is a suitable pathway for transfer.

In active non-convective heat transfer between two thermodynamic systems, source and destination transfers are of different characters. The source energy transfer is as work done by forces originating in energy-exporting system, and the destination energy transfer is as heating of the energy-importing system. A thermodynamic system, starting from an initial state of internal thermodynamic equilibrium, cannot export energy as heat in this way. Active non-convective heat transfer is not governed by temperature difference between source and destination bodies. For active non-convective heat transfer, the source system must be in an inhomogeneous internal equilibrium. A system in a homogeneous internal equilibrium cannot actively export energy as heat.

Neither of these two kinds of non-convective heat transfer has a temperature threshold that needs to be exceeded.

Convective heat transfer
Also, convective circulatory heat transfer has two kinds: spontaneous, and driven.

As defined in thermodynamics, spontaneous circulatory convective heat transfer has a feature different from non-convective heat transfer: in a given arrangement of systems and surroundings, it occurs only when a threshold difference in the temperatures of the source and destination bodies is exceeded.

In driven heat spreading by circulatory convection, the driving work is done by agencies in the intermediary surroundings of the source and destination bodies, at least one of which should exhibit passive heat transfer. It may be a fine point to require that passive heat transfer occur at both source and destination. One could allow that, at just one of source or destination, energy transfer between convective fluid and body of interest involve transfers of matter that preclude a proper and unique definition of transfer as heat. For an example in nature, in the transfer of energy from working muscles to the surroundings through the skin, carried by the blood stream, driven by the work of the heart, the transfer from skin to surroundings by radiation is passive heat transfer, while the transfer of energy from muscles to blood will in general involve matter transfers so that heat transfer cannot be uniquely separated or defined. Unlike the spontaneous kind of circulatory convective heat transfer, driven circulatory convective heat transfer is not necessarily subject to a threshold difference in the temperatures of the source and destination bodies.

The thermodynamic definition of heat transfer is by exclusion of thermodynamic work and matter transfer. Quantitatively, it is expressed in terms of thermodynamic variables such as temperature and entropy, which are defined for source and destination bodies initially and finally in their own states of internal thermodynamic equilibrium, which by definition requires zero macroscopic flows. For spontaneous circulatory convection in a given arrangement of systems, calculations of the temperature difference threshold are not directly based on the laws of thermodynamics. Such calculations require non-thermodynamic variables, in particular, those of fluid dynamics, beyond the scope of this present article.

logic
An edit has replaced the entry


 * "When such externally applied macroscopic mechanical work, described by macroscopic mechanical variables in the surroundings, is done isochorically, it is not thermodynamic work done on the thermodynamic system, as defined here, because it is not pressure–volume work. The external system mixes, and generates friction on and in, the thermodynamic system."

with the entry


 * "When such externally applied macroscopic mechanical work, described by macroscopic mechanical variables in the surroundings, is done isochorically, it is not thermodynamic work done on the thermodynamic system, as defined here, because it depends on a non-equilibrium process—namely, kinetic friction—and cannot be described with state variables."

The edit cover note reads “because it is not pressure–volume work” was an exemplary poor logic, wasn’t it?.

The logic of the former entry seems fine to me. What is wrong with it? The only kind of thermodynamic work that is relevant here is pressure–volume work. The relevant externally applied macroscopic mechanical work is not pressure–volume work. Therefore it is not the kind of thermodynamic work that is relevant here.

The new phrase "non-equilibrium process" is likely to confuse or even mislead the ordinary reader of Wikipedia. At a glance, the new phrase may seem to be a customary term of art in thermodynamics, but it is not so. A thermodynamic process is a change in a thermodynamic system from one state of thermodynamic equilibrium to another. Consequently, every thermodynamic process involves a departure from, and an entry into, some thermodynamic equilibrium or other, and in that sense might be called 'non-equilibrium', so that it would make no sense to speak of an 'equilibrium process'; then the phrase 'non-equilibrium process' appears as an uninformative tautology, unhelpful for the reader. The term 'reversible process' is used often enough, and perhaps the term "non-equilibrium process" is intended refer to a process that is not reversible. The term 'reversible process', however, is itself suggestive of misconception, unless it is accompanied by a reminder that every actually occurring thermodynamic process is irreversible, and that the term refers to a fictive, conceptual, or mathematical idealization. In short, the phrase "non-equilibrium process" is unfit for the present Wikipedia purpose.

In context, pressure and volume are the relevant state variables or state functions. That the work "cannot be described with state variables" evidently means just that it is not pressure–volume work.

The new entry is not as suitable as the one it replaces, and may be misleading.

Adkins, 3rd edition (1983)
This book uses the word 'matter' as ordinary language, but, in near, though not exact, agreement with the poster of the edit, it once uses the phrase 'transfer of mass'. It writes neither 'mass transfer', nor 'transfer of matter'.

Page 222:
 * Then the only displacements accessible to the system are those involving the transfer of mass from one phase to another.

Page 30:
 * According to the molecular motion theory, heat was associated with rapid vibrations of the molecules of which matter was composed.

Page 121:
 * However, if both these were absent, there would be no condensed state of matter, and the perfect gas laws would be true at all temperatures and pressures.

Page 131:
 * ... as the film is expanded the proportion of matter close to the surface increases and the average density increases.

Page 157:
 * Classical thermodynamics is primarily concerned with describing the behaviour of matter in terms of macroscopic variables.

Page 270:
 * When the universe was small and hot, matter and radiation evolved with a common temperature.

Callen, 2nd edition (1985)
This book uses the word 'matter' as ordinary language. It uses the phrases 'matter transfer' and 'transfer of matter', but does not use the phrase 'mass transfer'.

Page 5:
 * Perhaps the most striking feature of macroscopic matter is the incredible simplicity with which it can be characterized.

Page 17:
 * This definition of closure differs from a usage common in chemistry, in which closure implies only a wall restrictive with respect to transfer of matter.

Page 26:
 * Assume that the cylinder walls and the piston are rigid, impermeable to matter, and adiabatic and that the position of the piston is firmly fixed.

Page 58:
 * ... the chemical potential plays a role in matter transfer or chemical reactions fully analogous to the role of temperature in heat transfer or pressure in volume transfer.

Denbigh, 4th edition (1981)
This book uses the word 'matter' as ordinary language. It uses the phrases 'transfer of matter', and 'transfer of material', but not the phrase 'mass transfer'.

Page 5:
 * In particular, there is no possibility of the transfer either of energy or of matter across the boundaries of the system.


 * ... but there is no transfer of matter across the boundaries.

Page 6:
 * ... boundaries across which there is the possibility of transfer of energy and matter.

Page 77:
 * If there is a transfer of matter between two systems ...

Page 81:
 * ... due to transfer of material into the system.


 * For whenever there is a simultaneous transfer of matter as well as of energy the notion of heat becomes ambiguous.

Guggenheim, 5th edition (1967)
This book does not use the phrase 'mass transfer' where the poster of the edits would expect it. This book uses the word 'matter' as in ordinary language, and the phrase 'flow of matter' in a place where the poster of the edit would expect 'mass transfer'.

Page 51:
 * According to elementary statics the mechanical equilibrium of the matter enclosed by AA'BB' ...

Page 59:
 * It is in fact possible to derive these principles from our knowledge of the structure of matter including the elements of quantum theory together with a single statistical assumption of a very general form.

Page 157:
 * The general laws formulated in the preceding sections concerning the behaviour of matter extrapolated to T = 0 are equivalent to the following theorem.

Page 327:
 * The modification of the gravitational field by the presence of matter in amounts dealt with in ordinary chemical and physical processes ...


 * ... and regard the gravitational potential at each point as independent of the presence or state of any matter there.


 * Since a phase was defined as completely homogeneous in its properties and state, two portions of matter of identical temperature and composition will be considered as different phases if they are differently situated with respect to a gravitational field.


 * The characteristic property of the gravitational potential is that the work w required to bring a quantity of matter of mass m from a place where ...

Page 328:
 * ... thus depending on the mass but not on the chemical nature of the matter.

Page 338:
 * It is therefore desirable, if not essential, to start from formulae which are not restricted to the assumption that the permeability of each piece of matter is invariant.

Page 341:
 * ... then in the absence of any matter between the plates the electric field is uniform, ...

Page 342:
 * When the space between the plates of the capacitor is filled with uniform matter, this matter becomes electrically polarized as a result of the field due to the charges on the plates.

Page 343:
 * Its value in general depends on the composition of the matter, the temperature, the pressure, and the field strength.

Page 345:
 * We turn now to a magnetic system consisting of current circuits and magnetic matter, concerning which our only restrictive assumption is the absence of hysteresis.

Page 348:
 * The experimenter is more interested in the behaviour of a specimen of matter introduced into a magnetic field which was uniform before the introduction of the specimen.

Page 366:
 * There is a consequent interplay between the flow of matter and the flow of electric charge.

Buchdahl 1966
This book does not use the phrase 'mass transfer' where the poster of the edits would expect it. This book uses the word 'matter' as in ordinary language, and the phrases or clauses 'passage of matter', 'exchange of matter', 'matter exchange', 'it cannot exchange matter', 'no matter could be transferred', 'addition of matter to the phase from without', 'flow of matter', and 'transfer of matter', in places where the poster of the edit would expect 'mass transfer'.

Page 7:
 * ... granted of course that the total amount of matter within K is kept fixed …

Page 9:
 * Such a view must in any case be adopted as soon as the discontinuous structure of matter is taken at least qualitatively into account.

Page 13:
 * Let a system K in equilibrium be contained entirely within an enclosure which need not be rigid but shall be supposed to be impermeable to matter.

Page 16:
 * As far as phenomenological theory is concerned the question whether the constitution of matter is continuous or discrete does not arise.

Page 18:
 * … it was laid down at the end of Section 3 that the total amount of matter constituting any particular system was to be kept fixed.

Page 51:
 * … the impossibility of distinguishing by means of local experiments the effects of the acceleration of a local frame of reference from the gravitational effects of matter in its neighbourhood …

Page 108:
 * … so long as the total amount of matter in the system remains constant.

Page 117:
 * That the system is 'given' is intended to imply that its generic structure is fixed, in particular that it is closed: meaning that it cannot exchange matter with its surroundings.

Page 119:
 * One is therefore now admitting the possibility of the passage of matter across such a boundary: in the case of the standard system of Section 10c, on the other hand, no matter could be transferred from a phase contained in one enclosure to a phase contained in any other, since the boundary between them was material and impermeable.


 * A phase, temporarily regarded as a subsystem, is 'open', i.e. the amount of matter in it is not fixed, as distinct from the situation which obtains with regard to proper subsystems.

Page 121:
 * As the external state is varied, the redistribution of matter amongst the various phases will take care of itself, whether by chemical reaction or passage from one phase to another, so that under these conditions the internal state is already determined by the external state.


 * … in an enclosure impermeable to matter.

Page 129:
 * … but also addition of matter to the phase from without …

Page 145:
 * … if any matter added to K is taken to have come from some standard position in the gravitational field …

Page 155:
 * … if two separate enclosures of equal volume which initially contain different amounts of a certain gas are joined together by a tube permitting the flow of matter …

Page 203:
 * The stability of a general system with respect to transfer of matter between phases may, in principle, be investigated without difficulty.

Cardinal functions
The enthalpy, $H(S[P],P,{N_{i}})$, expresses the thermodynamics of a system in the energy-language, or in the energy representation. As a function of state, its arguments include both one intensive ($P$) and several extensive ($S[P],{N_{i}}$) state variables. The state variables $S[P]$, $P$, and ${N_{i}}$ are said to be the natural state variables in this representation. They are suitable for describing processes in which they are experimentally controlled.

Initially, it will simplify the present account to rule that ${N_{i}}$ be permanently fixed, so that one is considering a closed system, for which $H = H(S[P],P)$ is the natural description of state. Such a system admits transfer of energy only as thermodynamic work and as heat, but not transfer of matter. This is the usual form of system considered in initial pedagogic accounts of thermodynamic work and heat.

Nonsense to be fixed
For some problems, it is especially convenient to use enthalpy as the cardinal energy variable of the system.

This is so when the processes for the system are required to occur due only to thermodynamic operations of change of pressure in the surroundings, without heat transfer and without matter transfer. Matter transfer is prevented by enclosing the system with walls that are impermeable to matter, or by defining the moving boundary of the system so that no matter transfer occurs; such a system is said to be closed; its processes are transfers only of energy, as work and as heat. To consider a conceptual and idealized process in which there is negligible energy transfer into the system through friction within the system, so that heat transfer is entirely prevented, the processes of interest are conceptually further restricted to being infinitely slow (thus 'quasi-static', also called 'quasi-equilibrium'). Then the system can change volume only through thermodynamic work. The pressure, volume, and temperature of the system can then change. Changes of system volume and temperature are determined by the pressure changes.

It is then convenient to describe the system with enthalpy as the cardinal energy variable. Then one writes
 * $$H=H(S[P],P)$$

In this way, the values of $S[P]$ and $P$ define the state of the system.

When it is convenient to consider that heat transfer shall occur at constant pressure $P$ has been chosen as an independent variable becuais made when it is convenient to consider that thermodynamic work shall occur at constant (time-invariant) pressure, set by devices in the surroundings of the system. Then then thermodynamic work can occur only with changes of $"V"$, the system volume. The system does thermodynamic work $W = P ΔV$ on its surroundings when, in a thermodynamic operation, the pressure applied by the surroundings is changed by $ΔP$. In the sign convention used in physics (the contrary convention is used in chemistry) when $ΔP < 0$, then $W > 0$, and when $ΔP > 0$, then $W < 0$. In these circumstances, in a turn of language, it may be said that the piston is "permeable" to volume transfer under controlled pressure (transfer of $V$, the relevant extensive variable, with $P$ as its conjugate intensive variable). The thermodynamic operation has imposed a change in pressure, the driver $ΔP$, causing a response $ΔV$, the volume that has been "transferred". End of nonsense.} This is the basis of the so-called adiabatic approximation that is used in meteorology.

Alongside the enthalpy, with these arguments, the other cardinal function of state of a thermodynamic system is its entropy, as a function, $S[p](H,p,{N_{i}})$, of the same list of variables of state, except that the entropy, $S[p]$, is replaced in the list by the enthalpy, $H$. It expresses the entropy representation. The state variables $H$, $p$, and ${N_{i}}$ are said to be the natural state variables in this representation. They are suitable for describing processes in which they are experimentally controlled. For example, $H$ and $p$ can be controlled by allowing heat transfer, and by varying only the external pressure on the piston that sets the volume of the system.

Temperature lead
A temperature expresses hot and cold, as measured with a thermometer. There are various temperature scales that nearly or approximately agree with one another, but differ slightly because of the various characteristics of particular thermometric substances. The most commonly used scales are the Celsius scale (formerly called centigrade) (denoted °C), Fahrenheit scale (denoted °F), and Kelvin scale (denoted K). The kelvin (the word is spelled with a lower-case k) is the unit of temperature in the International System of Units (SI).

In physics, hotness is a body's ability to impart energy as heat to another body that is colder. In a body in which there are processes of chemical reaction and flow of matter, temperature may vary over its parts, and over time, as measured by a suitably small and rapidly responding thermometer, and may depend also on the match of the processes to the characteristics of the thermometer.

When a body has no macroscopic chemical reactions or flows of matter or energy, it is said to be in its own internal state of thermodynamic equilibrium. Its temperature is uniform in space and unchanging in time. Then, referring to the Boltzmann constant, a temperature scale is defined and said to be absolute because it is independent of the characteristics of particular thermometric substances and thermometer mechanisms. This is the Kelvin or thermodynamic scale, widely used in science and technology. The thermodynamic temperature is always positive, relative to an absolute zero.

For some conditions other than thermodynamic equilbrium, a suitable thermometer calibrated on the thermodynamic scale, including absolute zero, can register a negative temperature; such conditions are hotter than absolute zero.

Temperature is important in all fields of natural science, including physics, chemistry, Earth science, medicine, and biology, as well as most aspects of daily life.

revision
A new revision of the lead has been posted here. The edit summary reads "The language here has been deteriorating; where is hotness defined like this? the temperature scales paragraph makes no accessible sense by its verbiage.)" No attempt was made to talk about this on the article's talk page.

I will content myself with a couple of observations. The first sentence of the revision, "Temperature is a physical quantity that expresses the subjective sensations of hot and cold", verges on nonsense. Subjective sensations are no so expressible. That is why they are called subjective. That is why temperature is defined as a physical quantity, not as a subjective sensation. There are plenty of textbook physical definitions of hotness, that have been cited in these pages, perhaps removed by other editors, apparently unnoticed by the reviser.

Second law versions
There are various statements of principle that are, by various writers, each respectively described as an expression of the second law of thermodynamics. They may be assembled under several headings. Several terms are useful for this purpose. A simple thermodynamic system is a body contained by walls of respective specified permeabilities, defined by its own internal state of thermodynamic equilibrium. A compound thermodynamic system is a collection of bodies separated by walls of respective specified permeabilities, defined by their mutual state of thermodynamic equilibrium. The surroundings of thermkdynamic system are not required to be thermodynamic systems, but may include one or more of them.

One working body subject to cycles of thermodynamic operations from its surroundings that include thermodynamic systems
The statements by Carnot, Clausius, Kelvin, Planck.

One thermodynamic system or body subject to a single process acting from its surroundings that are not thermodynamic systems
Planck

One thermodynamic system or body subject to an "adiabatic" process acting from its surroundings that are not thermodynamic systems
Carathéodory

Several thermodynamic systems interacting through their walls, but otherwise isolated
Planck

Kelvin details
In theory, there is a unique absolute extreme of coldness, in which a body has only zero-point energy; according to the Third Law of Thermodynamics, its temperature, known as absolute zero, is approachable but unattainable through any actual physical process. It is denoted as $0 K$ on the Kelvin scale. In an ideal gas, and in other theoretically understood bodies, the thermodynamic temperature is proportional to the average kinetic energy of microscopic particles, which can be measured by suitable techniques. The proportionality constant is the Boltzmann constant; its value is defined by international convention; this defines the magnitude of the kelvin, the unit of the thermodynamic temperature scale.

Theoretically-based
Theoretically-based temperature scales are based directly on theoretical arguments, especially those of kinetic theory, thermodynamics, and quantum mechanics. They are more or less ideally realised in practically feasible physical devices and materials. Theoretically based temperature scales are used to provide calibrating standards for practical empirically based thermometers.

In physics, the internationally agreed conventional temperature scale is called the Kelvin scale. It is calibrated through the internationally agreed and prescribed value of the Boltzmann constant, referring to motions of microscopic particles, such as atoms, molecules, and electrons, constituent in the body whose temperature is to be measured. In contrast with the thermodynamic temperature scale invented by Kelvin, the presently conventional Kelvin temperature is not defined through comparison with the temperature of a reference state of a standard body, nor in terms of macroscopic thermodynamics.

In theory, there is a unique absolute extreme of coldness, in which a body has only zero-point energy. According to the third law of thermodynamics, its temperature, known as absolute zero, is closely approachable but eventually unattainable through any actual physical process. It is used as a zero reference for the Kelvin scale, denoted as $0 K$.

Apart from the absolute zero of temperature, Kelvin temperature of a body in a state of internal thermodynamic equilibrium is defined by measurements of suitably chosen of its physical properties, such as have precisely known theoretical explanations in terms of the Boltzmann constant. That constant refers to chosen kinds of motion of microscopic particles in the constitution of the body. In those kinds of motion, the particles move individually, without mutual interaction. Such motions are typically interrupted by inter-particle collisions, but for temperature measurement, the motions are chosen so that, between collisions, the non-interactive segments of their trajectories are known to be accessible to accurate measurement.

In an ideal gas, and in other theoretically understood bodies, the Kelvin temperature is defined to be proportional to the average kinetic energy of non-interactively moving microscopic particles, which can be measured by suitable techniques. The proportionality constant is a simple multiple of the Boltzmann constant. If molecules, atoms, or electrons, are emitted from a material and their velocities are measured, the spectrum of their velocities often nearly obeys a theoretical law called the Maxwell–Boltzmann distribution, which gives a well-founded measurement of temperatures for which the law holds. There have not yet been successful experiments of this same kind that directly use the Fermi–Dirac distribution for thermometry, but perhaps that will be achieved in future.

The speed of sound in a gas can be calculated theoretically from the molecular character of the gas, from its temperature and pressure, and from the value of Boltzmann's constant. For a gas of known molecular character and pressure, this provides a relation between temperature and Boltzmann's constant. Those quantities can be known or measured more precisely than can the thermodynamic variables that define the state of a sample of water at its triple point. Consequently, taking the value of Boltzmann's constant as a primarily defined reference of exactly defined value, a measurement of the speed of sound can provide a more precise measurement of the temperature of the gas.

Measurement of the spectrum of electromagnetic radiation from an ideal three-dimensional black body can provide an accurate temperature measurement because the frequency of maximum spectral radiance of black-body radiation is directly proportional to the temperature of the black body; this is known as Wien's displacement law and has a theoretical explanation in Planck's law and the Bose–Einstein law.

Measurement of the spectrum of noise-power produced by an electrical resistor can also provide an accurate temperature measurement. The resistor has two terminals and is in effect a one-dimensional body. The Bose-Einstein law for this case indicates that the noise-power is directly proportional to the temperature of the resistor and to the value of its resistance and to the noise band-width. In a given frequency band, the noise-power has equal contributions from every frequency and is called Johnson noise. If the value of the resistance is known then the temperature can be found.

Historically, till May 2019, the definition of the Kelvin scale was that invented by Kelvin, based on a ratio of quantities of energy in processes in an ideal Carnot engine, entirely in terms of macroscopic thermodynamkcs. That Carnot engine was to work between two temperatures, that of the body whose temperature was to be measured, and a reference, that of a body at the temperature of the triple point of water. Then the reference temperature, that of the triple point, was defined to be exactly $273.16 K$. Since May 2019, that value has not been fixed by definition, but is to be measured through microscopic phenomena, involving the Boltzmann constant, as described above. The new definition does not have a reference temperature.

An ideal material on which a macroscopically defined temperature scale might be based is the ideal gas. The pressure exerted by a fixed volume and mass of an ideal gas is directly proportional to its temperature. Some natural gases show so nearly ideal properties over suitable temperature ranges that they can be used for thermometry; this was important during the development of thermodynamics and is still of practical importance today. The ideal gas thermometer is, however, not theoretically perfect for thermodynamics. This is because the entropy of an ideal gas at its absolute zero of temperature is not a positive semi-definite quantity, which puts the gas in violation of the third law of thermodynamics. The physical reason is that the ideal gas law, exactly read, refers to the limit of infinitely high temperature and zero pressure; these conditions guarantee non-interactive motions of the constituent molecules.

Kinds of transfer of energy as heat
In this article, the definition of quantity of energy transferred as heat is not the only definition used by reliable sources, but it is a distillation of what Wikipedia editors have found most consistent or widely agreed amongst an array of many different reliable sources. An attempt to state word-for-word all the definitions found in reliable sources would be like an attempt to state all possible views about the length of a piece of string, and is not undertaken in this article.

Working with the definition of quantity of energy transferred as heat in this article, one may observe that several kind of transfer are admitted. The primary definition in this article refers just to the energy received as heat by the thermodynamic system of interest, and does not specify how the energy leaves the surroundings of the system. The present definition admits two kinds of heat reception.


 * 1) from body or system, in the surroundings of the system of interest, that supplies energy as heat from itself to the body or system of interest. According to the present definition, such a system in the surroundings might regard, as its own surroundings, the system of interest. Then by the present definition, heat transfer from the source to the destination is bilateral, one transfer having simply the negative sign of the other. For example, two bodies in direct contact, but such as to exchange no matter, may transfer energy as heat by conduction and radiation, in such a way that the heat into one has the same magnitude but opposite sign as heat out from the other. This kind of transfer is widely described, for example in the Wikipedia article Heat transfer. In these transfers, the energy leaves the source and reaches the destination in one and the same mode, as heat.
 * 2) from the body or system, in the surroundings of the system of interest, that supplies, to the body or system of interest, energy as work assessed in the surroundings of the system or body of interest (but not as thermodynamic work specified by changes in the system's state variables; concomitant changes in the system's state variables, other than temperature or entropy, must be accounted for as work done by the system on its surroundings, or as matter transfer). The mechanisms of this kind of transfer are various kinds of friction on the surface of and within the system of interest. An example is heating by shaft work (an example of isochoric work), as in Joule's original experiments that established the first law of thermodynamics for closed systems. Another example is in Joule heating. It might imaginably be said that the friction transduces work into heat, but the term 'transduce' usually intends not to refer to transfer as heat. In these transfers, the energy leaves the source in one mode, as work, and reaches the destination in another mode, as heat.

Some reliable sources speak of "conversion of work into heat" or "into heat energy" or "into thermal energy". Such locutions refer to energy in transfer, not to energy in a static state of either system or surroundings by themselves considered separately. A few, especially older, reliable sources speak of "heat production" in these circumstances, but the term 'conversion' is more compatible with the present definition of transfer of energy as heat. Also, some reliable sources speak of "conversion of heat into work", or "thermal energy to mechanical energy"; the present definition of transfer of energy as heat does not use such locutions. This is because, even fictively, reversal of friction to provide work is not only physically utterly impossible, but is almost inconceivable. Planck regarded this fact as a prime example of the second law of thermodynamics.

These considerations may be expressed in mathematical terms for a closed system under controlled pressure, described in the energy language by $H = H(S[P],P)$. One may observe that work done by factors or agencies in the surroundings of the system is not explicitly described in this formulation. That is to say, for example, that some pressure–volume work $A_{P–V}$ might be done on the system, and also that some isochoric work $A_{isoch}$ might be done on it, defined within the surroundings. The present sign convention (that used in physics, opposite to that used in chemistry) counts thermodynamic work done by the system on its surroundings as positive, and thermodynamic work done by the surroundings on the system as negative. Isochoric work includes work that is simply measurable in the surroundings, such as for example shaft work. It also includes other kinds of frictional work, that are not easily, or even not at all, assessable in the surroundings. For example, when a body is compressed, its volume change incurs friction internally in its substance, depending on the speed, and perhaps the oscillatory character, of the compression. Such frictional work cannot be directly assessed in the surroundings. It has to be inferred, by use of the First Law, and from knowledge of the thermodynamic work done in the complete process. That relies on knowledge, acquired in extensive experiment, of the thermodynamic properties of the substance of the body or thermodynamic system of interest. For example, one may consider a process in which initial and final volumes differ by $ΔV = V_{final} − V_{initial} < 0$, while the initial and final pressures are equal, $P$. Then the thermodynamic work done by the system is $W = P ΔV < 0$.

Then, as defined in the surroundings, the work done on the system is
 * $$A=A_{\mathrm{P-V}}+A_{\mathrm{isoch}},\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(\mathrm{i})$$

so that
 * $$A_{\mathrm{P-V}}=A-A_{\mathrm{isoch}}.\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(\mathrm{ii})$$

As defined for the thermodynamic system of interest, the thermodynamic work done by it is then
 * $$W=-A_{\mathrm{P-V}}=-(A-A_{\mathrm{isoch}}).\,\,\,\,\,\,\,\,\,\,\,\,\,(\mathrm{iii})$$

Then, in this language, in the present sign convention, as usual, the first law of thermodynamics will be written


 * $$ \Delta H = Q-W.\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(\mathrm{iv})$$

From this, by substitution, one gets


 * $$ \Delta H = Q-(-A_{\mathrm{P-V}})\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(\mathrm{v})$$
 * $$ \Delta H = Q+A_{\mathrm{P-V}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(\mathrm{vi})$$
 * $$ \Delta H = Q+A-A_{\mathrm{isoch}}.\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(\mathrm{vii})$$

If one wishes to write these formulas in terms of the work $A$, as defined in the surroundings, done by the surroundings on the system, and the quantity $Q$ of energy transferred to the system by mechanisms other than thermodynamic work and transfer of matter, and in terms of the quantity $Q_{con-rad}$ of energy transferred by conduction and radiation to the system from the surroundings, one will write
 * $$ \Delta H = Q_{\mathrm{con-rad}}+A.\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(\mathrm{viii})$$

Then, continuing to write with the term $A$ for the work done by the surroundings on the system, and eliminating $ΔH$, from (vii) and (viii), one has
 * $$ Q_{\mathrm{con-rad}}+A = Q+A-A_{\mathrm{isoch}}.\,\,\,\,\,\,\,\,\,\,\,\,\,\,(\mathrm{ix})$$

Thence
 * $$ Q_{con-rad} = Q-A_{isoch}.\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(\mathrm{x})$$

so that, with the present definition of heat as quantity of energy transferred to the system by mechanisms other than thermodynamic work and transfer of matter, one has
 * $$Q = Q_{\mathrm{con-rad}}+A_{\mathrm{isoch}}.\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(\mathrm{xi})$$

Third law
Taking up the admirable comment that it is not easy to find reliable sources for our presentation of the four laws.

At the risk of being seen as excessively garrulous, I first note that we had a lot of rain here last night and that the river is running very high. I am commenting for information only, no action intended.

Moreover, I have had another look at the thoughts of Callen, who does not present the laws in precisely the terms 0, I, II, and III. He offers his own system of postulates, which are nearly or practically the same as the usual four laws.

I am wishing particularly to chat about his Postulate IV. He writes


 * Postulate IV. The entropy of any system vanishes in the state for which
 * $$\frac{\partial U}{\partial {S_{V,N_i,...N_r}}}=0$$    (that is, at the zero of temperature)
 * This postulate is an extension, due to Planck, of the so-called Nernst postulate or third law of thermodynamics.
 * This postulate is an extension, due to Planck, of the so-called Nernst postulate or third law of thermodynamics.

In a much later chapter of his book, he writes


 * The postulate as first formulated by Walther Nernst in 1907 was somewhat weaker than our postulate IV, stating only that the entropy change in any isothermal process  approaches zero as the temperature approaches zero. The statement that we have adopted emerged several decades later through the work of Francis Simon and the formulation of Max Planck; it is nevertheless referred to as the Nernst postulate. It is also frequently called the "third law" of thermodynamics.


 * … The Nernst statement that the change in entropy $$\Delta H$$ vanishes in any reversible isothermal process at zero temperature, can be restated: ''The $$T=0$$ isotherm is also an isentrope (or "adiabat"). …
 * The Planck restatement assigns a particular value to the entropy: The $$T=0$$ isotherm coincides with the $$T=0$$ adiabat.


 * … In the thermodynamic context there is no a priori meaning to the absolute value of the entropy. The Planck restatement has significance only in its statistical mechanical interpretation, to which we shall turn in Part II. We have, in fact, chosen the Planck form of the postulate rather than the Nernst form because of the pithiness of its statement rather than because of any additional thermodynamic content.

As I read this, it means that in a simple thermodynamic context, the Planck form relies on statistical mechanical notions, beyond classical thermodynamics per se.

Guggenheim is circumspect in stating the third law. He concludes


 * … and instead choose as our third law the following statement.


 * By the standard methods of statistical thermodynamics is it possible to derive for certain entropy changes general formulae which cannot be derived from the zeroth, first, or second laws of classical thermodynamics. In particular one can obtain formulae for entropy changes in highly disperse system (i.e. gases), for those in very cold systems (i.e. when $$T \to 0$$), and for those associated with the mixing of very similar substances (e.g. isotopes).

I will not pursue his view further here.

Adkins writes


 * 12.2. The third law
 * The third law is concerned with the limiting behaviour of systems as the temperature approaches absolute zero. The statement of the law in the form due to Simon reads:


 * ▻ The contribution to the entropy of a system by which each aspect is in internal thermodynamic equilibrium tends to zero as the temperature tends to zero.

He then proceeds to derive


 * ... all heat capacities tend to zero as the temperature approaches absolute zero. This result emphasizes the connection between the third law and quantum theory, for classical heat capacities do not vary with temperature (equipartition of energy). It is therefore impossible to derive a classical interpretation of the third law.

For information only, no action intended.

Enthalpy
I like Callen's account of the Legendre transforms of system energy and of system entropy. An example that comes to mind is enthalpy. The only source that I know that uses the term 'cardinal function of state' is Tschoegl. He uses it to qualify internal energy and its corresponding entropy. One might say that the one-source character makes the term idiosyncratic. I like the term, to signify that the internal energy and its corresponding entropy describe an isolated state if the extensive variables are held fixed, with no transfers permitted. A transfer is specified by a change in an extensive variable.

I like to think of enthalpy as a function of its natural state variables, such as {entropy, pressure} for a closed system. Then it would have a reference state defined by a distinguished {entropy, pressure} value. A problem is to relate such a quantity to internal energy, which has a reference state defined by a distinguished {entropy, volume} value. To define enthalpy, IUPAC proposes the Euler relation $$H=U+PV$$. Presumably that means that one defines a common reference state as for internal energy, with a reference {entropy, volume} value, and measures the pressure at that reference state, and uses that pressure to define the reference state for enthalpy.

Starting at that reference state and using adiabatic walls to prevent heat transfer, if then, slowly enough to annul the kinetic energy imparted by the system to the surroundings, one reduces the pressure of the surroundings, to get a new state, then the system will expand, doing work on the surroundings, and reaching a new volume $$V + \Delta V$$, where $$\Delta V > 0$$, and a new pressure, $$P + \Delta P$$, that of the new surroundings, where $$\Delta P < 0$$. I think this guarantees an adiabatic process. The entropy will not change. The energy will increase by $$\int_P^{P+\Delta P} V(P) \mathrm d P <0 $$.

In a second process, one may then make a system wall diathermic, and slowly enough heat the system by conduction, till its temperature reaches that of the reference state.

Let us define


 * $$H=H(S^H,V)$$ and


 * $$U=U(S^U,V)$$.

These can be solved to give us


 * $$S^H=S^H(H,V)$$ and


 * $$S^U=S^U(U,V)$$.

Let us stipulate a common reference state in which the body has temperature $$T_0$$, pressure $$P_0$$, and volume $$V_0$$, which we can measure without knowing the energy or entropy.

We are free to define for the common reference state the values $$H_0$$ and $$U_0$$.

We are free to stipulate

that $$S_0^H=S^H(H_0,V_0)$$, with $$H_0=H(S_0^H,V_0)$$, and

that $$S_0^U=S^U(U_0,V_0)$$,  with  $$U_0=U(S_0^U,V_0)$$.

We are still free to stipulate the common reference state values $$S_0^H = S_0^U$$.

Consequently, we are stipulating that


 * $$\,\,\,\,\,\,\,\,\,\,\,H_0 \,\,\,\,\,\,\,\,\,=\,\,\,\,\,\,\,\,\,\, U_0 \,\,\,\,\,\,\,\,\,+ P_0 V_0$$, so that
 * $$H(S_0^H,V_0) = U(S_0^U,V_0) + P_0 V_0$$.

We also have


 * $$\mathrm d H = T \, \mathrm d S^H + V \, \mathrm d P$$ and


 * $$\mathrm d U = T \, \mathrm d S^U \, + P \,\mathrm d V$$.

Enthalpy of reaction


\Delta H_{reaction}^\ominus = \sum_p \nu_p\Delta H_{\mathrm f \,(products)}^{\ominus} - \sum_r \nu_r\Delta H_{\mathrm f \,(reactants)}^{\ominus} $



\textstyle\Delta H_{reaction}^\ominus = \sum_p \nu_p\Delta H_{\mathrm f \,(products)}^{\ominus} - \sum_r \nu_r\Delta H_{\mathrm f \,(reactants)}^{\ominus} $$


 * $$\nu_{\text {A}} \text {A} + \nu_{\text {B}} \text {B} ~+ ... \rightarrow \nu_{\text {P}} \text {P} + \nu_{\text {Q}} \text {Q} ~+ ...$$

Intrinsic energy
It can be convenient for purposes of exposition to use the term 'intrinsic energy of the system'. The term covers state functions such as internal energy, enthalpy, Helmholtz free energy, Gibbs free energy, as well as others. Here it is convenient to use the symbol $$M(.)$$ to denote an intrinsic energy. As a function of state, that symbol is incomplete, lacking definition of the dummy argument (.).

This notation may be exemplified by writing


 * $$U(S,V,N)\equiv M(S,V,N)$$,

where now $$U(.)$$ is the customary notation for the customarily named state function 'internal energy', with all its arguments being extensive state variables.

Another example is


 * $$H(S,P,N)\equiv M(S,P,N)$$,

where now the intrinsic energy is the customarily named state function 'enthalpy', with its arguments as shown, just one of them, $$P$$, being an intensive state variable.

Another example is


 * $$F(T,V,N)\equiv M(T,V,N)$$,

where now the intrinsic energy is the customarily named state function 'Helmholtz free energy', with its arguments as shown, just one of them, $$T$$, being an intensive state variable.

A further example is


 * $$G(T,P,N)\equiv M(T,P,N)$$,

where now the intrinsic energy is the customarily named state function 'Gibbs free energy', with its arguments as shown, just two of them, $$T$$ and $$P$$, being intensive state variables.

At this stage of this account, the list of customary names is running short, but in principle there are more possible versions of intrinsic energy. In order for the intrinsic energy to be a characteristic function of state, at least one of the argument state variables must be extensive.

An example of an intrinsic energy, lacking a conventional name, is


 * $$M(S,V,\mu)$$,

where now just one of its arguments, $$\mu$$, is an intensive state variable.

Callen offers another convenient systematic notation for the present topic. It distinguishes the intensive state variable arguments, leaving unmentioned the remaining extensive state variables.

For example, where the foregoing $$M$$ notation writes


 * $$H(S,P,N) \equiv M(S,P,N)$$,

Callen writes


 * $$H(S,P,N) \equiv U[P]$$.

enthalpy physical interpretation
Enthalpy is a mathematical abstraction that keeps account of transfers of energy that befall a body of radiation and matter that has a chemical composition defined by a suitable list of chemical constituents. To understand this, some background knowledge of thermodynamics is necessary. The present account covers only a simplified range of thermodynamic variables and processes, for a simple system.

With two exceptions that epitomise thermodynamics, variables and functions of thermodynamic state are directly determined by respective single concrete measurements, for example temperature and mass. The thermodynamic state of a body is always fully specified by the values of several pairs of such measurements, along with temperature. For example, the volume and pressure, and the mole numbers and chemical potentials of the chemical constituents, along with the temperature. It is remarkable and notable, and a most basic fact of nature, and a foundational postulate of thermodynamics, that bodies in such states of matter and radiation exist, and persist or endure over time if the body is isolated. It is sometimes called the minus-one-th law of thermodynamics. They are called states of thermodynamic equilibrium.

Taking into account full knowledge of the specific properties of the chemical constituents, and observing that it refers to a state of thermodynamic equilibrium, such a specification uses one more single-measurement quantity than is necessary. A prime example is that temperature can be omitted from the list, while taking into account the specific properties of the chemical constituents.

Thermodynamics works by using mathematical abstractions that summarise the specific properties of the chemical constituents. In general terms, these abstractions are (intrinsic) energy and entropy. These are the two exceptions mentioned just above. They can be specified in what are known as 'characteristic functions', and in what are known as 'fundamental equations', to be formulated below. As summaries of much detailed information, they can be determined only by a range of several or many concrete measurements, and are defined with respect to particular kinds of thermodynamic process. They are called 'characteristic' because they summarise the particular physical and chemical properties that uniquely characterise the listed chemical constituents, and 'fundamental' because they provide a full summary of all relevant thermodynamic information. The fundamental equations or characteristic functions provide information that is not fully present in any single equation of state, but they can be used to construct several various equations of state.

Of the characteristic function pairs, two are distinguished, and may be called the cardinal functions. They are functions only of extensive variables of state, not including intensive variables of state. They are called internal energy and entropy; for clarity and brevity in this section of this article, the latter will be called cardinal entropy. Enthalpy is a characteristic function that is convenient for describing certain kinds of thermodynamic process that are not conveniently described by internal energy and cardinal entropy.

To understand enthalpy, it is convenient to think initially about the cardinal pair of what are known as the Euler relations. They presuppose knowledge of internal energy and cardinal entropy, and are formulated with respect to a chosen reference state of the body of interest, that fixes certain reference constants:
 * $$~U~ = TS^U - PV ~+ ~\mu_1 N_1 + \mu_2N_2 ~+ ... + \mu_k N_k ~$$, and
 * $$S^U = \frac{1}{T}U + \frac{P}{T}V + \frac{\mu_1}{T} N_1 + \frac{\mu_2}{T} N_2 + ... + \frac{\mu_k}{F} N_k ~$$.

Beyond observing that the Euler relations express much about the fundamental concepts of thermodynamics, explaining their logic and source is beyond the scope of the present account.

As functions of state, internal energy and cardinal entropy refer to processes defined by transfers of prescribed amounts (including zero amounts) of extensive variables, such as cardinal entropy, volume, and mole number.

For describing processes defined in the same way except that, instead of an amount of volume transferred, a pressure imposed from the surrounding is prescribed, a particularly convenient formulation is provided by enthalpy, $$H$$. The corresponding formulas are
 * $$~H~ = ~U ~+~ PV = ~TS^H + ~\mu_1 N_1 + \mu_2N_2 ~+ ... + \mu_k N_k ~$$, and
 * $$S^H = S^U + \frac{P}{T} V = \frac{1}{T}H ~ + \frac{\mu_1}{T} N_1 + \frac{\mu_2}{T} N_2 + ... + \frac{\mu_k}{F} N_k ~$$.

Ideally, the processes that define them are, for internal energy, transfers of energy, as thermodynamic work, and of matter, and for cardinal entropy, transfers, of energy, as heat, and of matter. In terms of mathematical symbols, this may be written:
 * $$~U~ = U(S^U,V,\{N_j\})~$$ and
 * $$S^U = S^U(U,V,\{N_j\})~$$,

where $$U$$ denotes internal energy, $$S^U$$ denotes cardinal entropy, $$V$$ denotes system volume, and $$\{N_j\}$$ denotes the set of mole numbers that constitute the system. The pairing of internal energy with cardinal entropy indicates that each of them is a monotonic function of its arguments, and that each can be obtained by solving the other.

For closed systems, in which matter transfers are prevented, the thermodynamic processes of interest may be formulated:
 * $$~\Delta U~ = U(S^U + \Delta S^U,V + \Delta V,\{N_j\}) - ~ U(S^U,V, \{N_j\}) = Q - W$$ and
 * $$\Delta S^U = ~ S^U(U + \Delta U,V + \Delta V,\{N_j\}) ~ - ~ S^U(U,V,\{N_j\})~$$,

where $$\Delta U$$ denotes the increment in internal energy due to the system's having done thermodynamic work, <>W, by a prescribed expansion $$\Delta V$$ against a resisting pressure in the surroundings, and having gained energy as heat $$Q$$ from the surroundings, and $$\Delta S^U$$ denotes the increment in cardinal entropy due to those transfers.

Instead of choosing that work done by the system be determined by a prescribed change of volume, it may be convenient to let the work done be determined by holding the surrounding resisting pressure at a prescribed value. For such processes, another special pair of characteristic functions are necessary. Instead of 'internal energy', the intrinsic energy is then called enthalpy. There is no customary special name for the corresponding entropy, but for clarity in this section of this article, it will be called enthalpic entropy.

The state variables and functions are then reformulated:


 * $$~H~ = H(S^H,P,\{N_j\})~$$ and
 * $$S^H = S^H(H,P,\{N_j\})~$$,

where $$H$$ denotes enthalpy, $$S^H$$ denotes enthalpic entropy, $$P$$ denotes system pressure, and $$\{N_j\}$$ denotes the set of mole numbers that constitute the system.

For closed systems, in which matter transfers are prevented, the thermodynamic processes of interest may be formulated:
 * $$~ \Delta H~ = Q - W~$$ and
 * $$\Delta S^H = S^H(H + \Delta H,P,\{N_j\}) - S^H(H,P,\{N_j\})~$$,

where $$\Delta H$$ denotes the increment in enthalpy due to the system's having done thermodynamic work, by some measured expansion $$\Delta V$$ against the prescribed resisting pressure $$P$$ in the surroundings, and having gained energy as heat $$Q$$ from the surroundings, and $$\Delta S^H$$ denotes the increment in enthalpic entropy due to that gain $$\Delta H$$ of enthalpy.

trajectories
Boltzmann defined two kinds of monode, the ergodes and the holodes.

heat
The 1980 article by Smith has occurred to my drifting mind.

I have become slightly less ignorant since I last considered that article. I now have, I think, a clearer view, in the light of Born's comments on the topic.

My current view is that heat and work can be uniquely distinguished primarily for processes in closed systems (matter transfer not permitted), but for open systems only when the heat transfer path and the work transfer mechanism/path are between the system and its surroundings and are distinct from every matter transfer path.

It is conceptually key that the system and surroundings, and transfers between them, be uneqivocally distinguished and defined.

For uniqueness, it is practically necessary to restrict attention to spontaneous or natural processes. In practice, this means letting the system do thermodynamic work on its surroundings while keeping the heat and matter transfers separate from the work transfer. Then the heat and matter energy transfers can also be uniquely defined. The thermodynamic work transfer can in principle be measured as gain in internal energy of an otherwise isolated compartment in the surroundings, provided that the work be done monotonically. For example, the system can be allowed to expand against pressure exerted on it from the surroundings through a piston, during the process the surroundings pressure being kept only a little less than the system pressure. During the work transfer, heat and matter transfers are also permitted, through their separate pathways. If there is matter transfer, then the energy transferred in it must be uniquely defined, between the system and a compartment of the surroundings that is otherwise isolated; in other words, that compartment is permitted to transfer neither energy nor matter to or from any other part of the surroundings.

Entropy history
[https://en.wikipedia.org/w/index.php?title=Entropy&diff=next&oldid=84833493 This edit, dated 31 October 2006, and still standing, added the following paragraph.


 * In the 1850s and 60s, German physicist Rudolf Clausius gravely objected to this latter suppostion, i.e. that no change occurs in the working body, and gave this "change" a mathematical interpretation by questioning the nature of the inherent loss of usable heat when work is done, e.g., heat produced by friction. This was in contrast to earlier views, based on the theories of Isaac Newton, that heat was an indestructible particle that had mass.

Sad to say, I can't work out what first sentence of this means.Chjoaygame (talk) 10:53, 11 March 2021 (UTC)

Thermodynamics
The characteristic extensive thermodynamic functions of state are energy and entropy, specified in various particular ways. For convenience of exposition, considered first here are the various energy functions, which are Legendre transforms of one another, known as thermodynamic potentials, several of which have well known names, such as 'the Gibbs free energy'. Further along below, the various entropy functions are considered; they are known as Massieu functions.

The cardinal energy state function is the internal energy, specified as a function of the entropy and of suitable ordinary physical variables, such as volume. For example, a Legendre transformation converts the internal energy into another energy function or thermodynamic potential (called enthalpy) of entropy and pressure, where the pressure is the conjugate state variable of the volume. A different Legendre transform converts the internal energy into another energy function, called the Helmholtz free energy, switching the argument entropy to the argument temperature, which is the state variable conjugate to the entropy. One of a conjugate pair is extensive, the other intensive.

du Châtelet
Newton, in 1721, in his Opticks, in a long discussion of bodies and motions, elastic and inelastic, on pages 350 and 373, wrote:


 * Qu. 31. Have not the small Particles of Bodies certain Powers, Virtues or Forces, by which they act at a distance, not only upon the Rays of Light for reflecting, refracting and inflecting them, but also upon one another for producing a great part of the Phænomena of Nature? For it's well known that Bodies act one upon another by the Attractions of Gravity, Magnetism and Electricity; and these Instances shew the Tenor and Course of Nature, and make it not improbable but that there may be more attractive Powers than these.




 * ... For from the various Composition of two Motions, 'tis very certain that there is not always the same quantity of Motion in the World. For if two Globes joined by a slender Rod, revolve about their common Center of Gravity with an uniform Motion, while that Center moves on uniformly in a right Line drawn in the Plane of their circular Motion ; the Sum of the Motions of the two Globes, as often as the Globes are in the right Line described by their common Center of Gravity, will be bigger than the Sum of their Motions, when they are in a Line perpendicular to that right Line. By this Instance it appears that Motion may be got or lost. But by reason of the Tenacity of Fluids, and Attrition of their Parts, and the Weakness of Elasticity in Solids, Motion is much more apt to be lost than got, and is always upon the Decay. For Bodies which are either absolutely hard, or so soft as to be void of Elasticity, will not rebound from one another.

We are looking at writings in several languages, from several historical epochs. A glossary may help.


 * "The marquise brought energy, intelligence, and excitement." Quote from Emilie du Châtelet, Daring Genius of the Enlightenment, by Judith Zinsser.


 * vis viva. Latin for a quantity belonging to a material body, originated by Leibniz, and scarcely recognised by Newton.


 * force vive. Du Châtelet’s translation into French of Leibniz's vis viva.

It is no simple thing to say how vis viva is to be seen as 'belonging' to a 'body'. It needs to be said how a 'body' is constituted, and how it can have intrinsic and relational properties. It was not initially clear whether to regard such a quantity as $$mv^2$$ as intrinsic or relational. Leibniz regarded space as relational.

Over a collision between two bodies $$\text {a}$$ and $$\text {b}$$, if the collision is elastic, then the sum $$m_{\text {a}} v_{\text {a}}^2 + m_{\text {b}} v_{\text {b}}^2$$ is unchanged. If the collision is inelastic, it is not. But perhaps the missing quantity of vis viva has passed into microscopic components, Newton's "small Particles" of the bodies. This needs to be precisely articulated, and was controversial. According to Alejandro Jenkins "Leibniz argued that in an inelastic collision the missing vis viva is transferred to the imperceptible motion of the bodies’ microscopic components. This is consistent with our current understanding of dissipation, but at the time it was an untestable speculation." Loemker writes of Leibniz's expression of "the principle of the conservation of force (motive action)—that in any system of moving bodies the sum of $$mv^2$$ is a constant." Also Leibniz knew of conservation of 'quantity of progress', our 'momentum'. Loemker seems to say that Leibniz used the terms conatus, momentum, and vis viva, for $$ma$$, $$mv$$, and $$mv^2$$ respectively, but examination of the text seems to refute this, at least in part. It seems that Loemker's thinking may be muddled?

Newton knew that over a right line collision between bodies, elastic or not, the sum $$m_{\text {a}} v_{\text {a}} + m_{\text {b}} v_{\text {b}}$$ is unchanged. Momentum is conserved even in an inelastic collision.


 * quantity of motion

The following, with direct quotes, is from Alejandro Jenkins (https://arxiv.org/abs/1301.3097v2).

In 1644, Descartes proposed that a positive scalar quantity $$\sum_{i} m_i v_i$$ is conserved, where the $$v_i$$ are the positive speeds of the bodies. This was proposed as a law of conservation of 'quantity of motion'. Obviously, it is a law of conservation neither of vector momentum, nor of scalar energy.

"In papers presented before the Royal Society in 1668, John Wallis and Christopher Wren showed that the quantity conserved upon a collision was" the vectorial sum $$\sum_{i} m_i \boldsymbol v_i$$.

"Shortly afterwards, Christiaan Huygens published a result that he had already derived in the 1650s: that elastic collisions conserve another quantity as well, corresponding to twice the modern kinetic energy, $$2E = \sum_{i} m_i v_i^2$$."

Mittelstrass & Aiton:


 * ... the force of a body in motion is measured by the product of the mass and the height to which the body could rise (the effect of the force). Using the laws of Galileo, this height was shown by Leibniz to be proportional to the square of the velocity, so that the force (vis viva) could be expressed as $$mv^2$$. Since vis viva was regarded by Leibniz as the ultimate physical reality,[14] it had to be conserved throughout all transformations. Huygens had shown that, in elastic collision, vis viva is not diminished. The vis viva apparently lost in inelastic collision Leibniz held to be in fact simply distributed among the small parts of the bodies.[15]

Bertrand Russell:


 * Leibniz discovered the conservation of momentum, and believed himself to have discovered another law, the conservation of Vis Viva, both of which were unknown to Des Cartes (D. 88; L. 327; G. iv. 497)

Daniel Garber (lots here):


 * Leibniz, of course, also thinks that what we call momentum (and what he called ‘‘common progress’’) is also conserved. (He also argued for the conservation of a vector quantity he called ‘‘respective speed.’’) For a discussion of Leibniz’s different conservation laws, see Garber (1995), 316–19.

Du Châtelet’s book Foundations of Physics was published in 1740. Besides her analysis of the physics of heat, light, and fire, and her translation of Newton, it expresses her main contributions to rational mechanics.

In §579, du Châtelet states that Leibniz was the inventor of the concept of "forces vives" [in Leibniz's Latin vires vivae]. The vis viva of a body of mass $$m$$ moving with a speed $$v$$ is measured by $$mv^2$$. This is distinct from that body's "force morte", measured by $$mv$$, also called by Leibniz "quantity of motion".

Leibniz had discovered the law of conservation of momentum. Du Châtelet observes that Leibniz was the first to distinguish between "force vive" and "force morte".) Leibniz is translated (Ariew & Garber p. 157) as writing in "On nature itself" (1698):


 * The foundation of the laws of nature, among other things, provides a notable indication of this. That foundation should not be sought in the conservation of the same quantity of motion, as it has seemed to most, but rather in the fact that it is necessary that the same quantity of active power be preserved, indeed (something I discovered happens for a most beautiful reason) that the same quantity of motive action also be conserved, a quantity whose measure is far different from that which the Cartesians understand as quantity of motion. [Need to find Leibniz's original Latin: what is the difference between "active power" and "motive action"?]

Leibniz (A & G p. 50) proposes a distinction between "force" and "quantity of motion" as follows. "Force" in this sense is measured as directly proportional to $$m_ih_i~$$, where $$m_i$$ denotes the mass of a body lifted through a height $$h_i~$$. Assuming a conservation law, Leibniz lets the bodies of masses $$m_1~$$, $$m_2$$ fall back through heights $$h_1$$ and $$h_2~$$, reaching speeds $$v_1$$ and $$v_2$$. They attain quantities of motion $$m_1v_1$$ and $$m_2v_2$$. Leibniz proposes that though the "forces" $$m_1h_1$$ and $$m_2h_2$$ be made equal, the "quantities of motion" $$m_1v_1$$ and $$m_2v_2$$ will in general be unequal, thus distinguishing "force" from "quantity of motion". At this point in this letter, he does not mention the quantities $$m_1v_1^2$$ and $$m_2v_2^2$$.

Elsewhere, (Loemker p. 299) Leibniz writes "the living forces of equal bodies are not proportional to their velocities but to the squares oftheir velocities." Also (A & G p. 111): "the powers of unequal bodies are jointly proportional to the size of the bodies and the square of the velocities."

According to Ducheyne, the Leiden physicist 's Gravesande was a respected expositor of Newtonian physics (natural philosophy). For example, Voltaire went to Leiden to discuss it with him.

Quote from Brush: "The term potential energy was introduced by Rankine around this time and immediately adopted by Thomson. W. J. M. Rankine, Proc. Glasgow Phil. Soc. 3, 276 (1853); Papers, p. 203; footnote on p. 554 of Thomson's Papers 1."

Talk: Standard enthalpy of reaction

 * Thank you for your care in this.


 * I would like to clarify some thoughts.


 * Enthalpy is suitable as an index for energy of reaction because enthalpy is a function of state, with standard values for standard states, independent of how they are reached. Enthalpy is chosen as the index energy because of historical tradition that heat of reaction was measured by calorimetry under atmospheric pressure. An alternative index energy, sometimes used, is the 'free enthalpy' or Gibbs energy.


 * The standard entropy of reaction is a calculated composite, not a simple single measured quantity for a simple thermodynamic process. The calculation does not refer directly to the actual reaction process. The actual conditions, for example, in solution, of the process itself are not immediately relevant. Instead, the logical ingredients of the calculation are stoichiometric quantities for the respective separate unmixed reactants and products in their respective separate unmixed standard states. The standard enthalpy of reaction is calculated as a balance of those quantities.


 * How would you feel about changing


 * In chemistry, the standard enthalpy of reaction is the enthalpy change when reactants in their standard states (p = 1 bar, T = 298 K) change to products in their standard states. This quantity is the standard heat of reaction at constant pression and temperature, but it can be measured by calorimetric methods in which the temperature does vary, provided that the initial and final pressure and temperature correspond to the standard state, since enthalpy is a state function.


 * to


 * In chemistry, the Standard enthalpy of reaction or 'standard heat of reaction' is the enthalpy difference, between separate unmixed reactants in their respective standard states (p = 1 bar, T = 298 K), and separate unmixed products in their respective standard states.

fourth law
Editor ReyHahn, thank you for your care in citing texts. I much respect that.

Editor Kbrose, thank you for your comment.

I will try to reply with two wings. One will be a more direct reply to the comments of Editor ReyHahn, the other to those of both Editors just mentioned, in a more general approach.

Looking at the sources listed by Editor ReyHahn:

Some of them are not standard texts on thermodynamics.

Deffner & Campbell. I regret that still don't have access to this. I would point out that it is not primarily about thermodynamics as such.

Nag. I have access to the 2002 reprinting of the first edition and to the second edition (2010), not the 2008 14th reprinting of the first edition that you link to. For the second edition, the author removed the chapters that cover the Onsager relations. One might say that this counts against the Onsager relations being regarded as belonging to thermodynamics as such.

Tiwari has a sense of humour that I like. On page 542 he writes:


 * Onsager relationships are fundamental and significant enough that many call their statement as the 4th law of thermodynamics. Nernst, who formulated the 3rd law, and called that law my "law", would have been unhappy about the appearance of a 4th one. His claim would be that there were three people (Rudolf Clausius, William Rankine and Germain Hess) associated with the first law, two people (Sadi Carnot and Rudolf Clausius) with the second, and only one—him, Walther Hermann Nernst—with the third. Ipso facto, there could be no more thermodynamic laws.

I don't accept the idea that Tiwari attributes to Nernst, that Rankine should not appear in a short list of originators of the second law.

I think Tiwari's book isn't primarily about thermodynamics as such, and doesn't justify suggesting in our article that the Onsager relations might be a fourth law of thermodynamics.

Srivastava & Saha & Jain write on page 214:


 * The thermodynamics discussed so far is based on the concept of equilibrium and hence should be called equilibrium thermodynamics. As already discussed in Chapter 2, equilibrium is an idealized concept and can be attained only in infinite time. The other concept, which the equilibrium thermodynamics heavily relies upon is the concept of reversibility; reversible operations. Since every point on a reversible path is an equilibrium point, moving along a reversible path is moving from one equilibrium point to another and so on. The perfectly reversible path is nothing more than a concept and resides only in our imagination. Thus equilibrium thermodynamics is not the thermodynamics of real systems or real situations. Further, the equilibrium thermodynamics deals either with isolated systems or closed systems. Since the systems which nature has created, e.g. living system – plants or animals – are open systems, the equilibrium thermodynamics is incompetent to deal with them, because attainment of equilibrium is out of question in open systems. The time invariant situation attained in open systems is steady state and not equilibrium (refer to Chapter 2), thermodynamics having competence to deal with open systems can be given either of the following names: (i) thermodynamics of open system (ii) thermodynamics of steady state (iii) thermodynamics of irreversible processes (iv) non-equilibrium thermodynamics. Since the emergence of this new thermodynamics owes its origin to the reciprocal relations discovered by Onsager it is sometimes also called Onsager's thermodynamics. Onsager's reciprocal relations which in fact are at the very foundations of this new thermodynamics have been given the status of fourth law of the Thermodynamics.

These authors feel that so-called "non-equilibrium thermodynamics" makes classical thermodynamics obsolete. With respect, judging from your having cited them without critical comment, I guess that you might agree with them. Please tell me that my guess is mistaken.

My opinion is that the paragraph from Srivastava et al. that I have copied just above is riven with nonsense. The authors are misled in precisely the way that gives me reason to oppose putting in material that suggests that the Onsager relations might be laws of thermodynamics. I guess that you might think I am misled in this.

The nearest that I can offer in reply is to refer to Phil Attard's concept of many-time entropies. I wrote to him, asking how to measure them. He replied that he didn't know. To me, this implies that they do not belong to thermodynamics in the ordinary sense of the word. In a nutshell, Srivastava et al. is not a Wikipedia reliable source on this point.

I am not persuaded by the Nobel Prize speech.

Now looking more generally.

My reason is respect for clarity of thought. Thermodynamics is a monumentally clear and straightforward theory, for which Einstein gave a celebrated distinction. It is essentially macroscopic, and builds upon the distinction between heat and work, to construct its key quantity, entropy. So-called 'non-equilibrium thermodynamics' is a radically different topic, resting on a direct contradiction of the foundations of thermodynamics. Wikipedia should not erase that. To erase it would be to mislead newcomer readers, likely incurably.

The heart of it is that entropy is well defined only for a thermodynamic system in its state of internal thermodynamic equilibrium. That is why it makes sense of Boltzmann's formula, which expresses a symmetry, with all 'states' equally weighted. This sets up the possibility of a logically sound statistical mechanical explanation of the second law.

It is regrettable to read a suggestion that 'non-equilibrium thermodynamics' is a more advanced topic. Yes, it is a more difficult topic. That is because it deals with more difficult problems. But it hasn't yet established an adequate generalization of the concept of entropy. That would make it truly advanced.

I have repeatedly said that the Onsager relations are important. But my main point is that they do not belong to thermodynamics as such. My above list of standard texts, that discuss them but do not say that they are called the fourth law of thermodynamics, is not a sample of thermodynamics texts in general. It is a sample of a smaller set, those that discuss the relations. Many standard texts on thermodynamics do not mention them, for example, Bailyn, M. (1994), A Survey of Thermodynamics, American Institute of Physics, New York, ISBN 0-88318-797-3. I think this counts against the Onsager relations being regarded as belonging to thermodynamics as such.

I think that 'non-equilibrium thermodynamics' is a misnomer, or clang word-association. It is about transport theory; it does not belong to thermodynamics. Yes, it uses the term 'entropy production', but it doesn't actually use the concept to calculate entropy because it can't. Alternatively, one might regard 'non-equilibrium thermodynamics' as an approximation, though without clearly specified scope, not thermodynamics as such. The calculation of time rate of entropy production is interesting, but it is generally observed that it does not contribute to transport calculations, which are based on transport coefficients that do not use the concept entropy. These facts are not emphasised by many texts on so-called 'non-equilibrium thermodynamics'. When it came out, I was thrilled to read Glansdorff & Prigogine's Thermodynamic Theory of Structure, Stability, and Fluctuations (1971), Wiley–Interscience, London. But that did not make it belong to thermodynamics as such; though it discusses them, it does not suggest that the Onsager relations should be called a fourth law of thermodynamics, so that it could be added to my list. Though I recognise that I may not persuade you about it, I think that putting the Onsager relations in this article would detract from the quality of Wikipedia.

transfer

 * Open systems have walls that allow transfer of both energy and matter to and from the system.


 * A physical process in which matter is exchanged is called a matter transfer or mass transfer. When a heat transfer takes place through a matter transfer, it is called a heat transfer by convection.


 * If matter can be transferred through the boundary between the system and its surroundings the system is classifed as open.


 * In the case of a control surface that is closed to mass ﬂow, so that no mass can escape or enter the control volume, it is called a control mass containing the same amount of matter at all times.


 * The stability of a general system with respect to transfer of matter between phases may, in principle, be investigated without difficulty.


 * This definition of closure differs from a usage common in chemistry, in which closure implies only a wall restrictive with respect to the transfer of matter.


 * Open systems are those which can exchange both energy and matter with their environment.


 * ... open systems, which may exchange matter with their surroundings.


 * If a system is so described that matter crosses its boundaries in the course of a change of state, it is called an open system.

Page 230:


 * If the system experiences a change of state, matter may transfer from one phase to another.

Page 400:


 * ... a variation consisting of a transfer of mass at constant energy ...


 * Engineers use principles drawn from thermodynamics and other engineering sciences, including fluid mechanics and heat and mass transfer ...

Page 151:


 * For control volumes entropy also is transferred in and out by streams of matter.

Page P-1


 * A control volume is a system that ... allows a transfer of matter across its boundary.


 * An isolated system can exchange neither matter nor energy with its surroundings.


 * The closed system (Fig.1.2) is a system of fixed mass. There is no mass transfer across the system boundary.

Page 2:


 * If a system is defined as a certain quantity of matter, then the system contains the same matter and there can be no transfer of mass across its boundary. However, if a system is defined as a region of space within a prescribed boundary, then matter can cross the system boundary.

Page 3:


 * If there is no chemical reaction or transfer of matter from one part of the system to another, such as diffusion or solution, the system is said to exist in a state of chemical equilibrium.

Page 302:


 * When equilibrium has been reached, there is no transport of matter from one phase to another.


 * Closed system
 * No matter (particle) exchange with the surroundings.


 * ... we can think of conducted heat as energy transferred by means of microscopic atomic or molecular collisions in processes that occur without the transfer of matter and without changing the macroscopic physical boundaries of the system under consideration.


 * In contrast, open systems, which exchange both matter and energy with their surroundings, can reach equilibrium only after the flow of matter and energy has stopped.


 * When a system in mechanical equilibrium does not tend to undergo a spontaneous change of internal structure, such as a chemical reaction, or a transfer of matter from one part of the system to another, such as diffusion or solution, however slow, then it is said to be in a state of chemical equilibrium.

article on heat
The article on heat was wrecked on the impetus of a quote from Steven Weinberg's 2021 book Foundations of Modern Physics, which was treated as a reliable source. Weinberg may be an expert on modern physics, especially on quantum physics, but he is careless and slipshod on the topic of heat in thermodynamics, disqualifying himself as a reliable source on it. Weinberg is inconsistent in slipping between 'heat' as in ordinary language and as a technical term in thermodynamics. This is partly due to Weinberg's slipping between statistical mechanics and thermodynamics, which will tend to confuse a reader who is new to the topics.

Weinberg's book's section 2.1, 'Heat and Energy', derives a law of conservation of kinetic energy in a wrong way. It examines a collision on the basis that the colliding bodies interact only when they are in contact, forgetting that the proper basis is that the collision should be elastic. An inelastic collision converts kinetic energy into heat imparted to the inelastic body, not by virtue of a temperature difference.

Section 2.2, 'Absolute Temperature', carelessly says that the first law of thermodynamics is the conservation of energy, without mentioning heat and work. The section goes on to say that the 1850 paper by Clausius shows that it is possible to ﬁnd a deﬁnition of temperature $$T$$ with absolute signiﬁcance by the study of thermodynamic engines known as Carnot cycles. The section then goes on (without mention of Kelvin) to develop Kelvin's thermodynamic definition of absolute temperature, taking the development from Fermi's little 1936 book Thermodynamics. Reading the 1850 paper of Clausius, contrary to Weinberg's assertion, I think one can hardly find thermodynamic temperature defined by a ratio of quantities of heat in a Carnot cycle, as in Fermi's book and as proposed by Kelvin.

In ordinary language, heat is what makes a thing hot.

The rest of this article concerns thermodynamics, for which heat is energy in transfer to or from a thermodynamic system, by mechanisms other than thermodynamic work or transfer of matter. The various mechanisms of energy transfer that define heat are stated in the next section of this article.

Like thermodynamic work, heat transfer is a process involving more than one system, not belonging to any one system. In thermodynamics, energy transferred as heat contributes to change in the system's cardinal energy variable of state, its internal energy. This is to be distinguished from the ordinary language conception of heat as belonging to single system.

The measurement of energy transferred as heat, performed by measuring its effect on the states of interacting bodies, is called calorimetry. For example, heat can be measured by the amount of ice melted, or by change in temperature of a body in the surroundings of the system.

Feynman's lectures
This edit https://en.wikipedia.org/w/index.php?title=Heat&diff=next&oldid=1114283454 was made at 2022 on 8 Oct 2022 by anonymous IP editor 99.113.71.3.

Mechanisms of transfer that define heat
The mechanisms of energy transfer that define heat include conduction, through direct contact of immobile bodies, or through a wall or barrier that is impermeable to matter; or radiation between separated bodies; or friction due to isochoric mechanical or electrical or magnetic or gravitational work done by the surroundings on the system of interest, such as Joule heating due to an electric current driven through the system of interest by an external system, or through a magnetic stirrer. When there is a suitable path between two systems with different temperatures, heat transfer occurs necessarily, immediately, and spontaneously from the hotter to the colder system. Thermal conduction occurs by the stochastic (random) motion of microscopic particles (such as atoms or molecules). In contrast, thermodynamic work is defined by mechanisms that act macroscopically and directly on the system's whole-body state variables; for example, change of the system's volume through a piston's motion with externally measurable force; or change of the system's internal electric polarization through an externally measurable change in electric field. The definition of heat transfer does not require that the process be in any sense smooth. For example, a bolt of lightning may transfer heat to a body.

Convective circulation allows one body to heat another, through an intermediate circulating fluid that carries energy from a boundary of one to a boundary of the other; the actual heat transfer is by conduction and radiation between the fluid and the respective bodies. Convective circulation, though spontaneous, does not necessarily and immediately occur simply because of some slight temperature difference; for it to occur in a given arrangement of systems, there is a threshold that must be crossed.

Although heat flows spontaneously from a hotter body to a cooler one, it is possible to construct a heat pump which expends work to transfer energy from a colder body to a hotter body. In contrast, a heat engine reduces an existing temperature difference to supply work to another system. Another thermodynamic type of heat transfer device is an active heat spreader, which expends work to speed up transfer of energy to colder surroundings from a hotter body, for example a computer component.

Mechanisms of transfer that define heat
The mechanisms of energy transfer that define heat include
 * conduction, through direct contact of immobile bodies, or through a wall or barrier that is impermeable to matter; Thermal conduction occurs by the stochastic (random) motion of microscopic particles (such as atoms or molecules). In contrast, thermodynamic work is defined by mechanisms that act macroscopically and directly on the system's whole-body state variables; for example, change of the system's volume through a piston's motion with externally measurable force; or change of the system's internal electric polarization through an externally measurable change in electric field.
 * radiation between separated bodies;
 * friction due to isochoric mechanical or electrical or magnetic or gravitational work done by the surroundings on the system of interest, such as Joule heating due to an electric current driven through the system of interest by an external system, or through a magnetic stirrer.
 * The definition of heat transfer does not require that the process be in any sense smooth. For example, a bolt of lightning may transfer heat to a body.

Convection allows one body to heat another, through an intermediate circulating fluid that carries energy from a boundary of one to a boundary of the other; the actual heat transfer is by conduction and radiation between the fluid and the respective bodies.

When there is a suitable path between two bodies with different temperatures, heat transfer by conduction and radiation occurs necessarily, immediately, and spontaneously from the hotter to the colder system. Convection, though spontaneous, does not necessarily and immediately occur simply because of some slight temperature difference; for it to occur in a given arrangement of systems, there is a threshold that must be crossed.

Although heat flows spontaneously from a hotter body to a cooler one, it is possible to devise a heat pump which expends work from a source in the surroundings to transfer energy from a colder body to a hotter body. In contrast, a heat engine reduces an existing temperature difference to supply work to another system. Another thermodynamic type of heat transfer device is an active heat spreader, which expends work to speed up transfer of energy to colder surroundings from a hotter body, for example a computer component.

heat as substance versus heat as process
Since the days of Heraclitus, who said that no man crosses the same river twice, and of Aristotle, who thought in terms of 'substances', philosophy has practically distinguished two kinds of ultimate ontological actual or natural entities, 'process' and 'substance'. It might be said that substances are subject to change, but processes are not, for they are change. Or that substances are changed by processes, and that processes change substances.

This is relevant to the word 'heat'. In ordinary language, one can speak of heat as a substance, while, in thermodynamics, where one can think of a thermodynamic system as a substance, heating is properly thought of as a process, so that the word 'heat' properly refers to a process as contrasted with a substance. This is the import of the overthrow of the caloric theory of heat, which rests entirely on calorimetry and a sort of 'conservation of heat'. In ordinary language and in thermodynamics, 'friction' refers to a process that produces heat.Chjoaygame (talk) 10:25, 2 July 2023 (UTC)

Calorimetry relies on conservation and dispersal of heat, while the mechanical theory of heat thinks of production of heat through dissipation of work or of potential energy, and it thinks of consumption of heat through spontaneous work. Chemical reactions convert chemical potential energy into internal energy. Friction converts mechanical energy into internal energy. Internal energy can supply work as well as heat.

A change of the internal energy of a body consists of three components:
 * change of thermal energy:                  $$Q=\int_i^f T \ dS$$
 * change of mechanical energy:           $$W=\int_i^f P \ dV$$
 * change of chemical potential energy: $$R=\Sigma_j\int_i^f \mu_j \ dN_j.$$

Those components of change are not in general separately conserved. They jointly draw on or contribute to the common pool of internal energy. In a thermodynamic process, those components change in various proportions, so that
 * $$\Delta U=Q-W+R.$$

Here the symbol $$R$$ refers to the change in chemical potential energy, which is negative in a chemical reaction, signifying dissipation of chemical potential energy, but positive when matter enters the working body.

For fictive idealised processes, one can imagine the components to occur separately.

For a compound system consisting of two bodies $$\text{A}$$ and $$\text{B}$$ that are initially in thermodynamic equilibrium across an arrangement of walls, then subject to a thermodynamic operation that increases some permeabilities of the walls, in such a way that the bodies actually further interact, after the further interaction it always happens that
 * $$\Delta S_\text{A}+\Delta S_\text{B} > 0,$$

where $$\Delta S_\text{A}=\int_i^f dS_\text{A}$$  and   $$\Delta S_\text{B}=\int_i^f dS_\text{B}.$$

This is one statement of the second law of thermodynamics.

Simply irreversible heat production
Friction, in rubbing, in viscosity, in electrical conduction, and in hammering, is simply irreversible; one cannot undo friction. It was the turning point in physicists' escape from the caloric theory.

In friction, there is conversion of work into heat. The process is a transformation of energy as well as a transfer of energy. The arriving form of energy, in the body or thermodynamic system, is different from the departing form of energy, in the surroundings.

Some of the heat generated by friction can be recovered as work, but not by simple reversal of friction.

Adkins
Adkins starts with a definition of temperature, partly based on the zeroth law. He uses the ideal gas scale, calling it 'thermodynamic temperature'. I wonder how Kelvin would feel about that? Buchdahl would call it an 'empirical temperature'.

Now, as to heat in Adkins, I didn't find what I could recognize as an explicitly 'introductory' definition. I found a general exposition of the move from the Laplace–Lavoisier doctrine of caloric to the current thermodynamical theory of heat.

One of the factors in the move was the cannon boring experiment of https://en.wikipedia.org/wiki/Benjamin_Thompson, in his article https://en.wikipedia.org/wiki/An_Experimental_Enquiry_Concerning_the_Source_of_the_Heat_which_is_Excited_by_Friction.

Thompson's idea was accepted by https://en.wikipedia.org/wiki/Julius_von_Mayer in 1842, as follows:
 * Without recognizing the causal connection between motion and heat, it is just as difficult to explain the production of heat by friction as it is to give any account of the motion that disappears.

Mayer gave a calculation of the mechanical equivalent of heat, relying on frictional generation of heat in paper pulp, and on calorimetry.

A further factor in the move to the current theory was the water paddle experiment of https://en.wikipedia.org/wiki/James_Prescott_Joule, another version of heat generation by friction. That form of heat generation was examined by Joule, and described in his 'first law', https://en.wikipedia.org/wiki/Joule_heating.

Explicitly defining heat, Adkins writes on page 32:
 * ... We call it the internal energy, $$U.$$ Thus, when a change of state is brought about by the performance of work alone, the work done on the system is simply the change in the internal energy in going from the initial to the final state:
 * $$ \Delta U=W.$$          (3.1)


 * U is a function of state because W is independent of path.


 * 3.4.   Heat 
 * Equation (3.1) applies to a thermally isolated system. However, we know that it is also possible to change the state of a system without doing work on it. We may use heat alone, or any combination of heat and work. Thus, when a system is not thermally isolated equation (3.1) is no longer valid. It must now be modified to
 * $$ \Delta U=Q+W$$          (3.2)
 * We have thus defined heat as a form of energy entirely equivalent in its effect on the total energy of a system to energy communicated by the performance of some kind of work.

No mention of temperature here. Apparently, for a closed system, heat is defined by exclusion of work, along with the postulate of conservation of energy.

Eventually, Adkins is not quite clear about his definition of heat. He writes:


 * We have thus defined heat as a form of energy entirely equivalent in its effect on the total energy of a system to energy communicated by the performance of some kind of work. The distinction between heat and work is not always clear-cut in the sense that it is not always easy to decide whether a particular energy contribution should be classed as heat or work.

Moreover, Adkins is not quite clear about his definition of work. I think his unease in decision is due to his apparent failure to be clear, for a closed system, about the difference between work defined solely in the surroundings, and thermodynamic work defined by changes in the thermodynamic system's ordinary physical state variables other than temperature or entropy. An energy transfer as thermodynamic work done by the system on its surroundings is defined by both the changes in its ordinary physical state variables other than temperature and entropy, and the ordinary physically defined force × distance work. Apart from the idealization of an infinitely slow process, an energy transfer as work done by the surroundings on the system, defined through ordinary physical work in the surroundings, involves friction in the system, and is not identical with the associated thermodynamic work. Adkins does not tell us how the work done by forces in the surroundings reaches the system without the operation of the second law, that observes that friction is likely to occur.

At this stage, Adkins is not considering transfer of matter.

Enough on Adkins for the moment.Chjoaygame (talk) 01:10, 4 June 2023 (UTC)

Anderson
Anderson, G., 2005, Thermodynamics of Natural Systems, Cambridge University Press, is rather chatty in his introductory chapters. He writes:


 * A chemical reaction involves the rearrangement of atoms from one structure or configuration to another, normally accompanied by an energy change.
 * It was discovered quite early that most chemical reactions are accompanied by an energy transfer either to or from the reacting substances. In other words, chemical reactions usually either liberate heat or absorb heat.
 * To change the temperature of the crystal, heat must be applied to it. This sets up a temperature gradient between the inside and the outside of the crystal, and heat travels into the crystal, raising its temperature.
 * In everyday conversation we use words like heat, work, and energy quite frequently, and everyone has a sufficiently good idea of their meaning for our ideas to be communicated. Unfortunately, this type of understanding is not sufficient for the construction of a quantitative model of energy relationships like thermodynamics. To get quantitative about anything, or, in other words, to devise equations relating measurements of real quantities, you must first be quite sure what it is you are measuring. This is not too difficult if you are measuring the weight of potatoes and carrots; it is a more subtle problem when you are measuring heat, work, and energy. Historically, it took several decades of effort by many investigators in the nineteenth century to sort out the difficulties that you are expected to understand by reading this chapter!
 * • Heat (q) is the energy that flows across a system boundary in response to a temperature gradient.
 * • Work (w) is the energy that flows across a system boundary in response to a force moving through a distance (such as happens when a system changes volume).
 * In everyday conversation we use words like heat, work, and energy quite frequently, and everyone has a sufficiently good idea of their meaning for our ideas to be communicated. Unfortunately, this type of understanding is not sufficient for the construction of a quantitative model of energy relationships like thermodynamics. To get quantitative about anything, or, in other words, to devise equations relating measurements of real quantities, you must first be quite sure what it is you are measuring. This is not too difficult if you are measuring the weight of potatoes and carrots; it is a more subtle problem when you are measuring heat, work, and energy. Historically, it took several decades of effort by many investigators in the nineteenth century to sort out the difficulties that you are expected to understand by reading this chapter!
 * • Heat (q) is the energy that flows across a system boundary in response to a temperature gradient.
 * • Work (w) is the energy that flows across a system boundary in response to a force moving through a distance (such as happens when a system changes volume).
 * • Work (w) is the energy that flows across a system boundary in response to a force moving through a distance (such as happens when a system changes volume).

Apparently, Anderson, despite all his care, has forgotten about friction as a source of heat. Also, he is rather vague about what he means by "in response to a force moving through a distance." What is the cause of the force? It makes a difference whether the force is generated by the system in a process of spontaneous expansion, or by some factor in the surroundings. The force itself passes the work energy, which is therefore not a response to the force but is an aspect of the force itself.

In his next chapter, about the first law of thermodynamics, Anderson goes on to talk about water entering and leaving a pond, in an analogy that is almost shamelessly chatty, and lacking in thermodynamic insight. He goes on to say:


 * For “real” work processes, the work done is invariably less than the reversible work (Equation 3.7), usually much less, and usually of more interest to engineers than to geochemists.


 * Planck divided processes into natural, ideal, and unnatural: For him, natural processes can actually occur, and I guess correspond with Anderson's “real” work processes. Ideal processes occur in the notebooks of physicists. Unnatural processes violate the second law and do not occur.


 * ... such as work done by frictional forces, that you can review in a physics text.

Anderson goes on to talk about temperature without having given a thermodynamic definition of it. What he says is pretty much covered by what Buchdahl calls 'empirical temperature', and makes sense in that light. Anderson is largely concerned with chemical reactions and enthalpy. He is aiming to define "chemical energy". His actual words are in the first paragraph of his chapter on the first law:


 * 3.1.1 Temperature
 * One of the early triumphs of the study of thermodynamics was the demonstration that there is an absolute zero of temperature. However, there are several different temperature scales, for historical reasons. All you need to know about this is that the kelvin scale (named after William Thompson, Lord Kelvin) has an absolute zero of 0 K and a temperature of 273.16 K at the triple point where water, ice, and water vapor are at equilibrium together. The melting point of ice at one atmosphere pressure is 0.01 degrees less than this, at 273.15 K (Figure 3.1).

That is perhaps all that Anderson thinks the student needs to know about thermodynamic temperature at that point. Anderson goes on to postulate a state variable called 'entropy'. He says of it:


 * The central fact about entropy as used in science is that it involves the distribution of energy in a system. Energy tends to become “spread out,” or delocalized, if not prevented from doing so.

Soon, Anderson says:


 * ... in fact the heat engine approach is very useful in the derivation of Equation (4.3), and also the kelvin temperature scale.

But he doesn't pursue this, saying that it is scarcely necessary for the purpose of his book.

Later, Anderson remarks:


 * Heat flows can be measured in various ways. One way is to observe some process in which heat is liberated under controlled conditions, resulting in a rise in temperature, and then duplicate that temperature rise using an electrical heater. The energy used by the heater can be measured exactly, and will equal the energy released by the process considered.

Evidently, an electrical heater can be used to generate heat, as noted by Joule.Chjoaygame (talk) 09:15, 4 June 2023 (UTC)

Ansermet & Brechet
Now to look at Principles of Thermodynamics by J.-P. Ansermet and S.D. Brechet, 2019, Cambridge University Press. They start with a picture of Joule, with a caption that says "In 1840, he stated the law that bears his name on power dissipated by a current passing through a resistance." Their actual text begins with 1839 work by Marc Séguin on the heat engine. They go on to mention that in 1842 Julius Robert von Mayer, in a treatise, asked "what is the change in temperature of a stone when it hits the ground after falling from a given height?" They remark that Joule actually measured that in 1845. I would say that the rise in temperature was due to friction of impact within the stone.

On the first law of thermodynamics, they say


 * • PQ represents the thermal power associated with heat exchange with the environment through conduction.
 * • PC represents the chemical power associated with matter exchange with the environment through convection.


 * Any physical process performing work is called a mechanical action. Any physical process in which heat is exchanged is called a heat transfer. A physical process in which matter is exchanged is called a matter transfer or mass transfer. When a heat transfer takes place through a matter transfer, it is called a heat transfer by convection. When a heat transfer occurs without matter transfer, it is called a heat transfer by conduction. In general, a matter transfer leads simultaneously to a mechanical action and to a heat transfer.

Perhaps following Prigogine and Defay, they are happy to talk of rates of energy flow, which does not respect the rule of classical thermodynamics, which refers situations of changes of state from one thermodynamic equilibrium to another. I do not like the confusion that is introduced by talking of heat transfer as well as of heat "exchange". I think that talk of heat "exchange" is slippery. Max Born is careful to say that the energy transfer that accompanies matter transfer in itself cannot be resolved into heat transfer and work. The two latter forms of transfer, if simultaneous with matter transfer, to be identified, must occur by pathways separate from matter transfer. For example, radiative transfer of heat can be distinguished from energy transfer accompanying matter transfer. Maxwell said that matter transfer by convection was not a form of heat transfer. There is no mention of radiative transfer nor of friction here.

Ansermet & Brechet go on to remark that


 * The chemical work could also be called convective chemical heat.

Soon they remark that


 * We consider two colliding object that remain attached after impact. It can be shown that this type of collision has the maximum kinetic energy change.

In such a collision, the colliding bodies exhibit conversion of the kinetic energy of their relative motion into internal energy. Since there is a temperature increase in the bodies, one might be tempted to say that this occurred due to the internal friction in the collision. One might even consider talking of generation of heat. But Ansermet & Brechet talk only of kinetic energy and of internal energy, not of friction, nor of heat in this process. To say that the product is internal energy is to avoid saying whether it is transferred as heat or as work; that is equivocation like that of Adkins.

Ansermet & Brechet consider a fan in a room. They consider a viscous frictional torque associated with the motion of the fan, and calculate it by considering entropy production, but do not mention heat in this scenario. Again, to say that the product is entropy is to avoid saying whether the energy transfer is as heat or as work; that is equivocation like that of Adkins.

They consider a damped harmonic oscillator, and ask the student to calculate the power P(t) due to the friction force, but they do not use the word 'heat' in this scenario.

In a section on heat in their chapter on the second law, they write:


 * Let us begin with our experience of everyday life to illustrates [sic] various forms of heat transfers. When a stone warms up because it is exposed to the sun, it receives ‘heat’ by a thermal process that occurs in the absence of any macroscopic external force. It is due to heat transfer by radiation. When two objects at different temperatures are connected to each other, heat transfer takes place by conduction until both objects reach the same temperature. A third type of heat transfer takes place through convection. It is due to matter transfer from one region of space to another, which is at a different temperature. It is clearly distinct from heat transfer by radiation or conduction, since in both of these no matter transfer occurs.

Maxwell and Born would have qualms about that. Benjamin Thompson and Planck would be unhappy that it does not mention friction or rubbing.

Ansermet & Brechet deal with what Benjamin Thompson and Planck would call generation of heat sometimes by talking of entropy production, other times of heat production. They write:


 * Simple experiments points [sic] to the existence of entropy production, no matter in which way the process is carried out. For instance, entropy is produced in a fire or by rubbing hands together. It is also produced by an electric current flowing through a resistance. Many historical experiments, such as that of Earl Rumford (hollowing out of canons) or that of Humphry Davy (two ice blocks rubbed against each other), led to the conclusion that there are processes which cause an entropy production.
 * In an isolated system, entropy can increase, but it cannot decrease. All experiments lead to this conclusion. For instance, a drill produces heat while it is drilling.

Enough about Ansermet & Brechet for the moment.Chjoaygame (talk) 10:56, 4 June 2023 (UTC)

Atkins
Now to look at Atkins, P., de Paula, J., Keeler, J., 2018, Physical Chemistry, eleventh edition, Oxford University Press.

Their first sentence, for closed systems, that could be considered as a start to defining heat reads:


 * Experiments have shown that the energy of a system may be changed by means other than work itself.

This expresses the admirable ideas of Bryan (1907) and of Carathéodory (1909) that are prime ingredients of rigorous modern thermodynamics.

In my opinion, Atkins et al. then go overboard by writing:


 * The distinction between work and heat is made in the surroundings. The fact that a falling weight may stimulate thermal motion in the system is irrelevant to the distinction between heat and work: work is identified as energy transfer making use of the organized motion of atoms in the surroundings, and heat is identified as energy transfer making use of thermal motion in the surroundings.

I agree that thermodynamic quantities are always measureable through the surroundings. But that includes the internal state variables of the system. Atkins et al. demand that all features of a process of transfer of energy are defined by considerations that exclude the externally measured internal state variables of the system. They dismiss friction and rubbing, which Planck considered important; sad to say, it isn't easy to find English translations of Planck saying so. Atkins et al. use the notion of 'organized motion of atoms in the surroundings'. That is a notion foreign to thermodynamics proper, and hard to define in simple terms. Pressure in the surroundings is easily thought of as a manifestation of disorganized motion of atoms or molecules, but is able to do work as defined in the surroundings. In a real process, however, it will cause friction within the system, so that not all that work as defined in the surroundings will reach the system as thermodynamic work, which, for its definition, requires consideration of the externally measured internal state variables of the system. This is an example of what Adkins means by loss of clarity of thought when he talks about thermodynamics as a strictly macroscopic theory, as in his above quote.

Atkins et al. go on to remark that


 * ... no work is done when a system expands freely. Expansion of this kind occurs when a gas expands into a vacuum.

When a gas expands into a vacuum, there is transfer of matter from the originally enclosed body of gas to the originally empty space. The process is set going by the thermodynamic operation of removal of the partition between the two spaces. In the view of Max Born, such a process does not allow a distinction between heat and work because it includes transfer of matter. This is one reason why the first law is mainly about closed systems. This seems to be forgotten by Atkins et al..

It is becoming evident that I am inclined to prefer the thinking of the best and most reliable sources, as distinct from less reliable sources.Chjoaygame (talk) 02:14, 5 June 2023 (UTC)

Attard
Attard, P., 2002, Thermodynamics and Statistical Mechanics: Equilibrium by Entropy Maximisation, Elsevier, Academic Press.


 * Because no dissipative mechanisms have been introduced to this stage, the simple harmonic motion of the piston continues forever, and one can only speak of the equilibrium state in a statistical sense as the average position of the piston. In practice energy is lost due to friction and to the internal viscosity of the system. Assuming that the latter dominates, then when the motion of the piston has died out, dK = 0 and dE1 = — dE2, so that all of the previous equilibrium analysis holds. Effectively the system has been heated by internal motion even though it is enclosed in adiathermal walls.

Many texts tell this story of friction. There is no mention here of microscopic factors such as unorganised motion of molecules. No mention of temperature here. Chjoaygame (talk) 19:09, 6 June 2023 (UTC)

Baierlein
Baierlein, R., 1999/2005, Thermal Physics, 6th printing, Cambridge University Press.


 * What are the common characteristics of these diverse means of heating and cooling? The following provides a partial list.
 * 1. There is net transfer of energy (to or from the system, be it frying pan or muffin or soda).
 * 2. The amount of energy transferred may be controlled and known at the macroscopic level but not at the microscopic level.
 * 3. The transfer of energy does not require any change in the system's external parameters.




 * In a fundamental way, one distinguishes two modes of energy transfer to a physical system:
 * 1. by heating (or cooling);
 * 2. by changing one or more external parameters.
 * To be sure, both kinds of transfer may occur simultaneously (for example, if one irradiates a sample at the same time that one changes the external magnetic field), but the distinction remains absolutely vital.
 * Energy transfer produced by a change in external parameters is called work.




 * Elementary physics often speaks of three ways of heating: conduction, convection, and radiation. You may wonder, why is convection not mentioned here? Convection is basically energy transport by the flow of some material, perhaps hot air, water, or liquid sodium. Such "transport" is distinct from the "transfer" of energy to a physical system from its environment.
 * To summarize: think of "heating" as a process of energy transfer, a process accomplished by conduction or radiation.

Evidently, for Baierlein, thermodynamic work is defined in terms of the external parameters of the system itself, without mention of ordinary physical work in the surroundings. For a closed system, for Bairlein, heating is defined by exclusion of thermodynamic work. Baierlein here forgets Joule's experiments.

Later, talking about the Carnot engine, Baierlein mentions rubbing and friction, but doesn't mention hammering or heat when he does so:


 * (b) No dissipative processes, such as frictional rubbing or viscous damping of fluid motion, accompany the process.

Conduction more or less implies that the source of the transferred heat has a temperature. Laser radiation is an example of heat transfer when the temperature of the source is not counted. Baierlein doesn't tell us whether frictional rubbing, viscous damping of fluid motion, or hammering, are counted as work or as heat.Chjoaygame (talk) 20:12, 6 June 2023 (UTC)

Blundell
Blundell, S.J., Blundell, K.M., 2006, Concepts in Thermal Physics, Oxford University Press. Introductory comment:


 * • In Chapter 2 we explore the concept of heat, defining it as “energy in transit”, and introduce the idea of a heat capacity.

Formal definition:


 * We therefore make the following definition:
 * heat is energy in transit.

Heating by transfer of heat from one thermodynamic system to another, and heating by rubbing a thermodynamic system with something in the surroundings:


 * To see this, consider your cold hands on a chilly winter day. You can increase the temperature of your hands in two different ways: (i) by adding heat, for example by putting your hands close to something hot, like a roaring fire; (ii) by rubbing your hands together. In one case you have added heat from the outside, in the other case you have not added any heat but have done some work. In both cases, you end up with the same final situation: hands which have increased in temperature. There is no physical difference between hands which have been warmed by heat and hands which have been warmed by work.
 * Notice in this last example that the power in the heater is supplied by electrical work. Thus it is possible to produce heat by doing work. We will return to the question of whether one can produce work from heat in Chapter 13.
 * Notice in this last example that the power in the heater is supplied by electrical work. Thus it is possible to produce heat by doing work. We will return to the question of whether one can produce work from heat in Chapter 13.

The conversion of ordinary physical work into heat occurs in the process of transfer.

In the section on the first law, some historical information. Lavoisier's 1789 notion of caloric. Thompson's 1798 heating by friction. Mayer's 1842 frictional generation of heat in paper pulp. Joule's frictional paddle experiment (1840 to 1845).Chjoaygame (talk) 06:14, 7 June 2023 (UTC)

Bridgman
Bridgman, P.W., 1943, The Nature of Thermodynamics, Harvard University Press.
 * .... the spontaneous appearance of temperature differences, as for example generation of heat by friction or collision, ...
 * When the bodies are thus in contact it is an experimental fact that there is a transfer of heat if there is a temperature gradient in the material of the two bodies in the directions normal to the surface of separation. This sort of heat transfer is said to be by conduction.
 * The second method by which heat transfer may take place occurs when two bodies are not in contact, but confront each other across a vacuous space, with their opposing surfaces at a difference of temperature; this method of transfer is "radiational" transfer.
 * The second method by which heat transfer may take place occurs when two bodies are not in contact, but confront each other across a vacuous space, with their opposing surfaces at a difference of temperature; this method of transfer is "radiational" transfer.
 * The second method by which heat transfer may take place occurs when two bodies are not in contact, but confront each other across a vacuous space, with their opposing surfaces at a difference of temperature; this method of transfer is "radiational" transfer.

Considering the first law, Bridgman analyzes heat production by friction:


 * We have the paradoxical result that the work received by the block from the pavement across the surface of separation is not equal to the work done on the pavement by the block. This failure of equality of direct and reaction work always occurs at a surface where there is tangential slip and there are forces in the direction of slip. This sort of thing does not occur very often in the conventional thermodynamic analysis; I think that many physicists have a sort of instinctive feeling that direct and reaction work are always equal. Obviously this can be the case only when there is no discontinuity in the motion at the surface, as at a piston which is compressing a gas.

I suppose the last phrase refers to the interface between the piston and the gas, not to that between the piston and the cylinder where there is friction. The difference between work done on the system, and work received by the system, by such a thing as a rotating paddle, was observed long ago by Bryan to be due to friction, and is the basis of the original experiments, by Davey, Thompson, Mayer, and Joule, that blew away the caloric theory and measured the mechanical equivalent of heat, but Bridgman is right to remark that this sort of thing does not occur very often in the conventional thermodynamic analysis. Perhaps the reason for this is that friction is not quite so easy to account for mathematically? Chjoaygame (talk) 06:41, 7 June 2023 (UTC)

Bryan
Bryan, G.H., 1907, Thermodynamics: an Introductory Treatise dealing mainly with First Principles and their Direct Applications, B.G. Teubner, Leipzig.

Bryan was writing when thermodynamics had been established empirically, but people were still interested to specify its logical structure. The work of Carathéodory also belongs to this historical era. Bryan was a physicist while Carathéodory was a mathematician.

Bryan started his treatise with an introductory chapter on the notions of heat and of temperature. He gives an example of where the notion of heating as raising a body's temperature contradicts the notion of heating as imparting a quantity of heat to that body.

He defined an adiabatic transformation as one in which the body neither gains nor loses heat. This is not quite the same as defining an adiabatic transformation as one that occurs to a body enclosed by walls impermeable to radiation and conduction.

He recognized calorimetry as a way of measuring quantity of heat. He recognized water as having a temperature of maximum density. This makes water unsuitable as a thermometric substance around that temperature.

His second chapter started with the recognition of friction as a source of heat, by Benjamin Thompson, by Humphry Davy, by Robert Mayer, and by James Prescott Joule.

He stated the First Law of Thermodynamics, or Mayer–Joule Principle as follows:
 * When heat is transformed into work or conversely work is transformed into heat, the quantity of heat gained or lost is proportional to the quantity of work lost or gained.

He wrote:
 * If heat be measured in dynamical units the mechanical equivalent becomes equal to unity, and the equations of thermodynamics assume a simpler and more symmetrical form.''

He explained how the caloric theory of Lavoisier and Laplace made sense in terms of pure calorimetry.

Having rationally defined quantity of heat, he went on to consider the second law, including the Kelvin definition of absolute thermodynamic temperature.

In section 41, he wrote:
 * 41. Physical unreality of reversible processes. In Nature all phenomena are irreversible in a greater or less degree. The motions of celestial bodies afford the closest approximations to reversible motions, but motions which occur on this earth are largely retarded by friction, viscosity, electric and other resistances, and if the relative velocities of moving bodies were reversed, these resistances would still retard the relative motions and would not accelerate them as they should if the motions were perfectly reversible.

He then stated the principle of conservation of energy.

He then wrote:
 * In connection with irreversible phenomena the following axioms have to be assumed.
 * (1) If a system can undergo an irreversible change it will do so.
 * (2) A perfectly reversible change cannot take place of itself; such a change can only be regarded as the limiting form of an irreversible change.

On page 46, thinking of closed systems in thermal connection, he wrote:
 * We are thus led to postulate a system in which energy can pass from one element to another otherwise than by the performance of mechanical work.

On page 47, he wrote:
 * When energy flows from on system or part of a system to another otherwise than by the performance of work, the energy so transferred i[s] called heat.

On page 48, he wrote:
 * Another important exception occurs when sliding takes place between two rough bodies in contact. The algebraic sum of the works done is different from zero, because, although the action and reaction are equal and opposite the velocities of the parts of the bodies in contact are different. Moreover, the work lost in the process does not increase the mutual potential energy of the system and there is no intervening medium between the bodies. Unless the lost energy can be accounted for in other ways, (as when friction produces electrification), it follows from the Principle of Conservation of Energy that the algebraic sum of the quantities of heat gained by the two systems is equal to the quantity of work lost by friction.

I don't know whether Max Born knew of Bryan's work when he persuaded Carathéodory to undertake a mathematical investigation of the foundations of thermodynamics, or whether Carathéodory knew of Bryan's work, as he prepared his celebrated 1909 paper.

In my opinion, Bryan's definition of heat is the best available, and has been accepted by many thermodynamicists, and by the preponderance of past editors of this Wikpedia article. I regard Bryan's Treatise as a Wikipedia reliable source.Chjoaygame (talk) 04:48, 23 June 2023 (UTC)

Callen
Callen's first edition (1960), talking about closed systems (no transfer of matter), said on page 7:
 * Energy can be transferred to a mechanical mode of a system, such a flux of energy being called mechanical work. Similarly, energy can be transferred to an electrical mode of a system. Mechanical work is typified by the term $$- P \ dV$$ ($$ P$$ is pressure, $$V$$ is volume), and electrical work is typified by the term $$- E \ d \mathcal P$$ ($$ E$$ is electric field, $$\mathcal P$$ is electric dipole moment). These energy terms and various other mechanical and electrical work terms are treated fully in the standard mechanics and electricity references. But it is equally possible to transfer energy to the hidden atomic modes of motion as well as to those which happen to be macroscopically observable. An energy transfer to the hidden atomic modes is called heat.

Callen's second edition (1985, with material about statistical mechanics) is practically the same here.

No mention of temperature there. He was talking about an energy transfer into the system from its surroundings.

One may ask, did Callen admit that friction involves energy transfer to the hidden atomic modes? I presume that it does, and so that Callen's definition of heat includes heat production by friction, converting mechanical work into heat.

In the second edition, Callen continued:
 * Of course this descriptive characterization of heat is not a sufficient basis for the formal development of thermodynamics, and we shall soon formulate an appropriate operational definition.

Later, Callen continued:
 * There exist walls, called adiabatic, with the property that the work done in taking an adiabatically enclosed system between two given states is determined entirely by the states, independent of all external conditions. The work done is the difference in the internal energy of the two states.

Callen didn't say explicitly here whether the work is done with our without friction. But he continued by writing:
 * As a specific example suppose we are given an equilibrium system composed of ice and water enclosed in a rigid adiabatic impermeable wall. Through a small hole in this wall we pass a thin shaft carrying a propellor blade at the inner end and a crank handle at the outer end. By turning the crank handle we can do work on the system. The work done is equal to the angular rotation of the shaft multiplied by the viscous torque.

Callen assessed the work done as that done through that done in turning the crank. Callen regarded such work as measuring the difference in internal energies of the final and initial states of the working body.

He went on to write:
 * ''The fact that the energy difference of any two equilibrium states is measurable provides us directly with a quantitative definition of the heat: The heat flux to a system in any process (at constant mole numbers) is simply the difference in internal energy between the final and initial states, diminished by the work done in that process.

He didn't explicitly say that Joule's experiment did not measure a quantity of heat.

He went on to use the concept of quasi-static processes, indicating that he would later define them, using inexact differentials, and writing:
 * With the quantitative expression $$\text{đ}W_M=-P \ dV$$ for the quasi-static work, we can now give a quantitative expression for the heat flux. In an infinitesimal quasi-static process at constant mole numbers the quasi-static heat $$\text{đ}Q$$ is defined by the equation
 * $$\text{đ}Q=dU-\text{đ}W_M$$    at constant mole numbers            (1.2)
 * or
 * $$\text{đ}Q=dU+P \ dV$$    at constant mole numbers            (1.3)

Thus his inexact differential $$\text{đ}W_M$$ is effectively translated into an exact differential $$-P\ dV.$$

In this view of Callen, it seems that Joule did not measure a quantity of heat produced by friction. He measured a change in internal energy, and then equated that to a quantity of heat measured by calorimetry.

Soon, Callen wrote, on page 27:
 * The induction from experimental observation of the central principle that provides the solution of the basic problem is subtle indeed. The historical method, culminating in the analysis of Caratheodory, is a tour de force of delicate and formal logic. Callen didn't mention as a person, or his definition of entropy in terms of differentials of heat.

Evidently, Callen regarded the work of Carathéodory as masterly. Callen didn't use differentials of heat to define entropy. Callen just postulated its existence as an extensive state variable.Chjoaygame (talk) 08:31, 11 July 2023 (UTC)

Çengel
Çengel, Y.A., Boles, M.A., Kanoğlu, M., Thermodynamics: An Engineering Approach, 9th edition, 2019. Talking first about the zeroth law, on page 17:
 * It is a common experience that a cup of hot coffee left on the table eventually cools off and a cold drink eventually warms up. That is, when a body is brought into contact with another body that is at a different temperature, heat is transferred from the body at higher temperature to the one at lower temperature until both bodies attain the same temperature (Fig. 1–34). At that point, the heat transfer stops, and the two bodies are said to have reached thermal equilibrium. The equality of temperature is the only requirement for thermal equilibrium.

In my opinion, this really belongs to the preliminary statement that thermodynamics deals with bodies in their own states of internal thermodynamic equilibrium, and in equilibrium with connected bodies. The authors then proceed to talk about temperature, not waiting for the second law to tell them how to define thermodynamic temperature.

On page 56, the authors write:
 * An energy interaction is heat transfer if its driving force is a temperature difference. Otherwise it is work, as explained in the next section.

On page 60, they write:
 * Heat is defined as the form of energy that is transferred between two systems (or a system and its surroundings) by virtue of a temperature difference (Fig. 2–15). That is, an energy interaction is heat only if it takes place because of a temperature difference. Then it follows that there cannot be any heat transfer between two systems that are at the same temperature.
 * Heat is energy in transition. It is recognized only as it crosses the boundary of a system.
 * Heat is energy in transition. It is recognized only as it crosses the boundary of a system.

On page 62, they write:
 * Work, like heat, is an energy interaction between a system and its surroundings. As mentioned earlier, energy can cross the boundary of a closed system in the form of heat or work. Therefore, if the energy crossing the boundary of a closed system is not heat, it must be work. ... More specifically, work is the energy transfer associated with a force acting through a distance.

On page 65, they write:
 * In an electric field, electrons in a wire move under the effect of electromotive forces, doing work.

They do not explain precisely how these electromotive forces act through a distance.

On page 66, they focus on mechanical work, writing:
 * There are several different ways of doing work, each in some way related to a force acting through a distance (Fig. 2–28).
 * There are two requirements for a work interaction between a system and its surroundings to exist: (1) there must be a force acting on the boundary, and (2) the boundary must move. Therefore, the presence of forces on the boundary without any displacement of the boundary does not constitute a work interaction.
 * There are two requirements for a work interaction between a system and its surroundings to exist: (1) there must be a force acting on the boundary, and (2) the boundary must move. Therefore, the presence of forces on the boundary without any displacement of the boundary does not constitute a work interaction.

They apparently feel no need to remark that their aforementioned electrical work violates their second requirement for "work": the boundary doesn't move. This is, however, a mere pedagogical convenience, or perhaps oversight, for they subsequently treat electrical separately from mechanical work.

On page 66, they write:
 * Energy transmission with a rotating shaft is very common in engineering practice (Fig. 2–29).

They do relate this to the distance moved by a point in the rotating parts, measuring distance moved in a suitable way. But the boundary of the system is not displaced and doesn't move.

No mention so far of friction, but on page 68, they write:
 * This discussion together with the consideration for friction and other losses form the basis for determining the required power rating of motors used to drive devices such as elevators, escalators, conveyor belts, and ski lifts.

On page 70, they discuss other forms of work, including electrical work:
 * Some work modes encountered in practice are not mechanical in nature. However, these nonmechanical work modes can be treated in a similar manner by identifying a generalized force $$F$$ acting in the direction of a generalized displacement $$x$$.

These engineers have discarded the foundational idea that friction generates heat. Thus, they reverse the thermodynamic tradition expounded by Bryan and by Carathéodory of defining heat by its not occurring through thermodynamic work, nor through transfer of matter. These engineers define thermodynamic work by its not occurring through heat.Chjoaygame (talk) 13:16, 22 June 2023 (UTC)

The reversal of the orthodox thermodynamic tradition is an example of circular reasoning. Quantity of energy transferred as heat is defined in terms of "work", while "work" is defined in terms of heat. This might be resolved by giving "work" two distinct and logically unconnected definitions, committing an act of logical equivocation. Wikipedia should avoid logical equivocation in its presentations.

More should be said. While it is possible to define empirical temperatures and so to define quantity of energy transferred as heat when it is between two bodies that each possess its respective temperature, it is convoluted and undesirable to need to redefine thermodynamic temperature after the acceptance of the second law. One might argue that the second law precedes the first law in logic, though that would be a hard road to hoe: how to define entropy without a prior definition of the distinction between heat and work transfers. A further problem with defining heat in terms of temperature difference is that not all sources of radiation, nor all sources of conducted heat, have a definite and uniquely defined temperature, so that the two-body definition of heat transfer doesn't work. From the orthodox thermodynamic viewpoint, the two-body temperature difference definition is merely a special case of the proper general definition by exclusion of thermodynamic work. The solution to the latter problem is to stay with the traditional thermodynamic base case of a system and its surroundings: the system has properly and uniquely defined thermodynamic state variables; but the surroundings are not so constrained; in the surroundings, from the viewpoint of thermodynamics, anything goes.

These points were, over several years long ago, established in this talk page, but they seem to have been discarded recently. The article should perhaps thoroughly explain this logic.

For Wikipedia, a good resolution is to avoid circular and convoluted reasoning, and to stay with the orthodox thermodynamic position, and to declare, solely for this specific purpose, that Çengel, Boles, and Kanoğlu 9th edition is not a reliable source.Chjoaygame (talk) 03:16, 23 June 2023 (UTC)

Denbigh
Denbigh K., The Principles of Chemical Equilibrium: with Applications in Chemistry and Chemical Engineering, 4th edition, 1981, Cambridge University Press.

On page 10, Denbigh wrote:
 * ... we shall speak of any change taking place inside an adiabatic wall as being an adiabatic process.

This is thinking in terms of calorimetry, not so much in terms of the idea of Locke, Thompson, Mayer, and Joule, that friction generates heat.

On page 18, Denbigh wrote:
 * In the discussion of Joule's experiments we were concerned with the change in state of a body contained within an adiabatic enclosure. It would have been wrong to have spoken of the temperature rise of the water as having been due to heat (although this is sometimes done in a loose way); what we were clearly concerned with were changes of state due only to work. However it is also known from experience that the same changes of state can be produced, without the expenditure of work, by putting the body into direct contact (or through a non-adiabatic wall) with something hotter than itself. That is to say the change of internal energy, $$U_A-U_B$$ can be obtained without the performance of work. We are therefore led to postulate a mode of energy transfer between bodies different from work and it is this which may now be given the name heat. Our senses and instruments provide us with no direct knowledge of heat (which is quite distinct from hotness). The amount of heat transferred to a body can thus be determined, in mechanical units, only by measuring the amount of work which causes the same change of state.

Denbigh is thinking of heat as defined by calorimetry, relying on two bodies, each with a defined temperature. This thinking seems to show that, after all, Joule did not measure the mechanical equivalent heat, because he did not heat the water in the vat. Denbigh would perhaps reply that, nevertheless, the water changed its internal energy by the same amount as it would change if the process had been one of heating by conduction and radiation. That reply, however, relies on the Joule experiment having converted all the externally applied work into heat. If only some of the externally applied work were transformed into heat, more complicated reasoning would be necessary, as indicated by Bryant and by Bridgman. This may explain why Planck talks of surface rubbing as distinct from internal friction.

Denbigh on page 19 wrote:


 * ... it follows from the above definition of heat that the heat gain of the first body is equal to the heat loss of the second.

This might be called 'the principle of calorimetry', and is the main basis of the caloric theory of heat. Bryant and Bridgman would reply that they do not accept such an equality as a general principle. It does not cover friction in such processes as drilling, rubbing, grinding, or hammering.

Denbigh made some concessions to the idea of thermodynamic work as defined by changes of state variables other than thermal, i.e., other than entropy and temperature. For discussion of heat, the internal energy is always one such state variable. Denbigh mentioned Joule's measurements of the energy changes due to friction between iron blocks, but he did not elaborate. He also wrote the following:


 * Similarly, in the irreversible process of friction, the kinetic energy of a body as a whole is converted into the random energy of its component molecules.

For example, in hammering. This didn't deal with rubbing. Apart from the latter two brief mentions, Denbigh conveniently ruled out discussion of friction.

For the definition of work, however, Denbigh wrote:


 * Similar expressions may be obtained for the stretching of wires, the work of magnetization, etc.‡
 * ‡ A very clear account of work terms is given by Zemansky, Heat and Thermodynamics (New York), McGraw-Hill, 1968, and by Pippard, loc. cit.

The 'work' terms are sometimes taken to exclude 'chemical work'.

Eventually, Denbigh disallows the heat produced by friction. He relies on a roundabout calorimetric definition, supposing that heat comes from a convenient "heat bath" of water at its temperature of maximum density, and writing:
 * Consider now a type of process $$A \rightarrow B$$ in which a body $$X$$ both absorbs heat and has work $$w$$ done on it. In this process let its change of internal energy be $$U_B-U_A$$. We shall suppose that the heat comes from a heat bath, that is, a system of constant volume which acts as a reservoir for processes of heat transfer, but performs no work (e.g. a quantity of water at its temperature of maximum density). Let its change of internal energy in the above process be $$U^\prime_B-U^\prime_A$$. Then for the body $$X$$ and the heat bath together we have,
 * $$w=[(U_B-U_A)+(U^\prime_B-U^\prime_A)],$$
 * the right-hand side being the total change of internal energy. But according to the above definition $$U^\prime_B-U^\prime_A$$ is equal to the negative of the heat lost by the bath and is equal therefore to the negative of the heat gained by $$X$$. If we denote this heat by $$q$$, we therefore have $$q=-(U^\prime_B-U^\prime_A)$$. Substituting in the previous equation we obtain
 * $$U_B-U_A=q+w$$                           (1·8)
 * as a statement of the first law for a body which absorbs heat $$q$$ and has work $$w$$ done on it, during the change $$A \rightarrow B$$. This law therefore states that the algebraic sum of the heat and work effects of a body is equal to the change of the function of state, $$U$$, i.e. the algebraic sum is independent of the choice of path $$A \rightarrow B$$.

A chemist is hardly interested in friction at this stage of thinking, and this perhaps explains why Denbigh defies Thompson, Mayer, and Joule, and rules out friction as a generator of heat. Friction is more the province of physicists such as Planck.Chjoaygame (talk) 11:46, 1 July 2023 (UTC)

Dugdale
Dugdale wrote on page 4:
 * To this day calorimetry requires 'the most scrupulous attention to many circumstances which may affect the result'. A great deal of scientific effort still goes into the accurate measurement of heat capacities over a wide range of temperatures and indeed this is still one of the primary measurements in thermodynamics.

On page 20, he wrote:
 * We now define the difference between $$\Delta U$$ and $$W$$ (this difference is zero in adiabatic changes) as a measure of the heat $$Q$$ which has entered the system in the change. We shall treat the heat entering a system as positive. Thus
 * $$Q = \Delta U - W.$$

On page 21, he wrote:
 * Let me emphasise again that in the approach outlined here (due originally to Born) the thermodynamic concept of quantity of heat has been introduced and defined in terms of purely mechanical quantities.

Dugdale gives plenty of detail on Thompson's and on Joule's experiments, described by them as production of heat by friction, but he interprets them as occurring through work. Nevertheless, he gives much attention to calorimetry, as noted above.

On page 21, he wrote:
 * ... heat is a form of energy in transit and cannot be said to exist except when changes of state are occurring.




 * Note that the thermodynamic concept of heat conflicts, in some important ways, with the common usage of the word. We say that heat is transferred from one body to another and that, for example, the heat lost by one body is gained by the other. There is thus a strong implication that the heat was originally inside the first body and ended up after the transfer inside the other body. It is precisely this notion that we have to get rid of in order to think clearly about heat, work and internal energy.

Dugdale is not interested in friction, and puts his faith in a principle of calorimetry, that the heat lost by one body is gained by the other. He defines work in terms of what happens in the surroundings, apparently not in terms of the change it produces in the state variables of the system. Yet, for the interpretation of experiments, he also relies on the definition of the state of the system in terms of 'work' variables, including internal energy.Chjoaygame (talk) 10:24, 30 June 2023 (UTC)

Dunning-Davies
Dunning-Davies, J., 2011. Concise Thermodynamics: Principles and Applications in Physical Science and Engineering, 2nd edition, Woodhead Publishing, Oxford UK.

On page ix, Dunning-Davies wrote:
 * Thermodynamics is concerned with heat. Notions of "hot" and "cold", of one body being warmer than another, and the idea of the "flow of heat" are all central to the subject and, in science, all retain the meanings they have in our everyday lives. Initially, curiously enough, it is probably this latter point which is most difficult for many to accept but that is the absolute truth, thermodynamics is concerned with notions and concepts which are, in a non-scientific way, familiar to everyone. If this seemingly trivial point is borne in mind always, academic study of thermodynamics takes on a whole new perspective and is not a difficult subject to understand and appreciate.

Evidently, Dunning-Davies is not too concerned or overfamiliar with the cave man's ability to generate heat by friction between sticks, or with the coachman's concern that sometimes the heat generated by friction of his axle with it bearing can set the coach on fire, or with the blacksmith's heating of his work by hammering. Those primitive fellows are not overfamiliar with the caloric theory of heat. Apparently, Dunning-Davies is happy with the ordinary language word 'heat' as a scientific term. He sees no need to explicitly define it in this context. He will remain content to talk of two systems being brought into thermal contact. Does that include mutual radiative exposure?

On page 1, Dunning-Davies, without explicitly defining it, introduces a term 'thermal properties' as follows: he remarks that "...the laws of thermodynamics ... are simply expressions of common experience of the thermal properties of matter and radiation." On page 2, again without explicitly defining it, in the context of the caloric theory, he uses the term "thermal contact".

On page 5, Dunning-Davies focuses on two bodies that each possess a temperature, not worrying about the general approach to thermodynamics that requires the system to have a temperature, but does not impose any such requirements on the surroundings. He wrote:
 * As has been mentioned already, everyone is familiar with such elementary notions as 'A is warmer than B', 'B may gain heat from A', and the qualitative notion of the 'flow of heat'. Also, everyone knows that, when the flow of heat between two systems has ceased, those systems are said to be in thermal equilibrium.

On page 13, Dunning-Davies wrote:


 * Now consider an isolated system in which there is no thermal interaction with the surroundings. It is a 'fact of experience' that, if work is done on the system in some way, the system attains a new equilibrium state and it does not matter how the work which achieves this is done: for example, a gas may be compressed, or stirred, or have an electric current passed through it. It was one of Joule's great contributions to thermodynamics to demonstrate experimentally that this is the case. The result is that energy is given to the system during the process and, since no thermal interaction is involved, the process is said to be adiabatic.
 * ...It follows that, if a system is caused to change from some initial state to a final state by adiabatic means, the work done is the same no matter how it is done.. Hence, there must exist a function of the coordinates of the system whose value in the final state minus its value in the initial state equals the work done in going from one state to the other. This function of state is called the internal energy and is denoted by $$U$$. For the isolated system
 * $$W_{\text{a}}=U_2-U_1$$                        (3.1)
 * where $$U_2$$ and $$U_1$$ are the final and initial values respectively of the internal energy and $$W_{\text{a}}$$ is the work done in this adiabatic process; the suffix $$\text{a}$$ indicating that the process is adiabatic.
 * Suppose now that the system is not isolated as above but that thermal interaction between the system and its surroundings is allowed. In this case, the system may be taken from the state with internal energy $$U_1$$ to that with internal energy $$U_2$$ by a process which is not necessarily adiabatic. Such a process may be achieved by performing work which may be mechanical – for example, the use of a stirrer, non-mechanical – for example, the use of a heating element, or a combination of the two. Let $$W_{\text{na}}$$ denote the mechanical work done on the system in a process which is not necessarily adiabatic; the suffices $$\text{na}$$ indicating that the process is not necessarily adiabatic. Then
 * $$W_{\text{a}}-W_{\text{na}}=Q$$                        (3.2)
 * and for all such processes
 * $$Q+W_{\text{na}}=U_2-U_1$$              (3.3)
 * Here $$Q$$ is zero for adiabatic processes only. In a non-adiabatic process, $$Q$$ may be thought of as making up the deficit of mechanical work by heat. Hence, the amount of heat is defined in terms of mechanical work only. The convention adopted is that positive values of $$Q$$ will mean heat supplied to the system. Also, it should be noted that, although it has not been stated explicitly, attention has been confined to closed systems; that is, systems which do not transmit mass to, or receive mass from, the surroundings.

Dunning-Davies is not precise about exactly how to specify adiabatic and non-adiabatic work.

On page 26, Dunning-Davies wrote:
 * These forms of the law are those used at the birth of thermodynamics as a subject in its own right. As mentioned already, the laws were deduced from experiment and observation, and many of the ideas were borrowed from engineering. The notions and experiences of the engineer were used to obtain the laws of heat transformation and it is a tremendous achievement that a theory with many highly abstract concepts should be established by this approach. However, the approach to be adopted here is more mathematical in nature than some earlier arguments and is a modification of the method introduced at the beginning of this century by the mathematician Constantin Carathéodory. Carathéodory became interested in the problem of the formulation of thermodynamics at the instigation of his colleague, the physicist Max Born, and his highly mathematical original paper appeared in 1909. Because of the mathematical complexities of his approach, his work passed largely unnoticed, until the postwar work of such as Buchdahl, Landsberg, Turner and Zemansky made it far more accessible to scientists in general.

Evidently, Dunning-Davies knows the highly mathematical work of Carathéodory but seems unimpressed by the prior more thermodynamic work of Bryant.

Dunning-Davies so loves the caloric theory of heat that he sets up the above roundabout way of defining heat through mechanical processes only, apparently not impressed by Thompson's, Mayer's, and Joule's methods of allowing straightforward mechanical definition of quantity of heat by measuring its production in friction. Why do things the easy and obvious way when you can do them a hard way?Chjoaygame (talk) 10:06, 1 July 2023 (UTC)

Giles
Giles, R., 1964, Mathematical Foundations of Thermodynamics, Pergamon Press, Oxford UK.

On page 1, Giles wrote:


 * A familiar way of introducing the concept of absolute temperature in elementary expositions of thermodynamics is through the consideration of a Carnot cycle, in which a reversible heat engine operates between two heat reservoirs at different temperatures. This approach reveals clearly the essential nature of absolute temperature and has immediate physical appeal. The derivation of the concept of entropy, on the other hand, depends on considerations of a mathematically much more sophisticated nature, so that the physical significance of this concept remains initially relatively obscure.

On page 2, introducing another way of defining entropy, Giles wrote:


 * With this approach to entropy it is not necessary to define absolute temperature by means of a Carnot cycle; instead it can be obtained from entropy by a process of differentiation, just as entropy is usually obtained from temperature by integration. We thus obtain a way of introducing entropy which is physically very satisfying, since it emphasises the essential property of entropy: that its increase measures the irreversibility of a process. However, this approach is not entirely satisfactory from a logical point of view, since it still depends on the qualitative concept of temperature (through the use of a heat reservoir) and also on the possibility of making quantitative comparisons of energy changes (in the measurement of $$E$$).

Still on page 2, about a better way of defining entropy, Giles wrote:
 * The virtue of this approach to entropy is not only that it is independent of the concepts of temperature and energy, but that it is actually independent of any quantitative concepts at all. For it presents the measurement of entropy as resulting from a sequence of experiments of a qualitative nature, the result of each experiment being simply yes or no.

After some consideration of frictionless mechanical processes, and then explicitly defining entropy, looking at a thermodynamic system A connected to a mechanical device M in the surroundings, on page 109, Giles wrote:


 * If M is, for instance, a spinning flywheel this might be done by allowing M to rub on A until some energy, in the form of frictional heat, had passed from M to A; or an auxiliary electrical heater might be used as described in § 1.5.

On page 115, Giles wrote:
 * Further, we have, by Theorem 9.2.3, for any infinitesimal quasi-static process
 * $$\text{d}E=T \ \text{d}S - P \ \text{d}V$$                        12.1 (2)
 * and, in particular, for an infinitesimal quasi-static adiabatic process $$\text{d}E=- P \ \text{d}V$$. These results accord with the description of $$T$$ and $$P$$, as defined above, as absolute temperature and pressure.
 * Equation 12.1 (2) expresses the energy transferred to the system in an infinitesimal quasi-static process as the sum of two terms, $$T \ \text{d}S$$ and $$- P \ \text{d}V$$, which we may call, respectively, the heat supplied to the system and the work done on the system'. It should be noted that the terms "heat" and "work", thus defined, apply only to quasi-static processes; the present formulation of thermodynamics provides no such division of the energy transferred in a non-quasi-static process.

As Giles observes, his definition of heat here relies on the concept of a quasi-static process. Is this perhaps necessary for a definition of heat? For example, the definition of thermodynamic work, for a finite increment of volume at constant pressure requires that the process be slow enough to allow the pressure of the system to be defined throughout it; this definition also requires that the process be slow enough to allow the temperature to be defined throughout it. This definition demands the simultaneous definition of heat and thermodynamic work.

We may observe that this definition of heat does not consider such an abrupt process as hammering to produce heat. Hammering, drilling, fluid friction, and rubbing, convert energy from the surroundings directly into heat. The energy from the surroundings can be measured directly without regard to the intimate details of the process, and, provided it is all converted to heat, it can measure the quantity of heat directly. That is the merit of the works of Thompson, Mayer, and Joule. It might reasonably be objected that in such processes, some of the energy from the surroundings is converted into heat in the surroundings. For example, the hammer will become hot. It seems to follow that some kind of idealization is necessary for the precise definition of thermodynamic quantities.

Eventually, Giles defines heat through his prior definition of entropy. He relies on entropy as measuring the whole irreversibility of any thermodynamic process. He is presenting the idea of heat after he has settled on the second law of thermodynamics. This is reasonable and logically defensible, though it is not the commonest way to define heat. This mathematically oriented reasoning of Giles competes with the older physically oriented work of Clausius, that defined entropy in terms of infinitesimal increments of heat, and with the older physically oriented work of Bryan and mathematically oriented work of Carathéodory that defined heat as a residual from work. It is often felt that defining things in terms of adiabatic work is straightforward, and is evidently based on simple physics.Chjoaygame (talk) 09:41, 3 July 2023 (UTC)

Grandy
Grandy, W.T., 2008, Entropy and the Time Evolution of Macroscopic Systems, Oxford University Press, Oxford UK.

Leading up to an account of entropy, on page 3, Grandy wrote:
 * The point here is that there exists a sense of something missing when we contemplate heat, some kind of lack of information that is present with work. When a block of wood is moved forcefully across a table, with some downward pressure, the work done on the block goes partly into giving it some kinetic energy, and partly into providing some thermal energy to both block and table; this is verified by increased temperatures. The thought that not all the work went toward kinetic energy conveys a sense of loss, that part of the input energy was degraded to an unorganized form. From a physical point of view this sort of mechanical uncertainty in energy transfer is the essence of heat, and it encompasses its characterization as a form of motion. It is this essence we wish to examine and clarify in what follows, in the course of which we shall find that it is not confined to the notion of heat.

Grandy does not go on to consider the details of thermodynamics, such as an explicit definition of 'heat', because he is concerned with statistical mechanics.Chjoaygame (talk) 05:08, 4 July 2023 (UTC)

Guggenheim
Guggenheim, E.A., 1967, Thermodynamics: An Advanced Treatment for Chemists and Physicists, North Holland, Amsterdam.

On page 9, Guggenheim excluded friction from his book, writing:
 * When these branches of physics are idealized so as to exclude friction, viscosity, hysteresis, temperature gradients, temperature dependence of properties, and related phenomena, the fundamental property of energy can be described in two alternative ways.

On pages 9–10, Guggenheim wrote:
 * Let us now consider in greater detail the interaction between a pair of systems, supposed isolated from the rest of the universe. Using superscripts $$^\text{A}, ^\text{B}$$ to relate to the two systems we have
 * $$\text{d}U^\text{A}+\text{d}U^\text{B}=0$$                       1.10.1
 * or
 * $$\text{d}U^\text{A}=-\text{d}U^\text{B}$$                           1.10.2
 * but in general this is not equal to the work $$w_\text{BA}$$ done by $$\text{B}$$ on $$\text{A}$$. In other words there can be exchange of energy between $$\text{A}$$ and $$\text{B}$$ of a kind other than work. Such an exchange of energy is that determined by a temperature difference and is called heat. If then we denote the heat flow from $$\text{B}$$ to $$\text{A}$$ by $$q_\text{BA}$$, we have the following relations
 * $$\text{d}U^\text{A}=w_\text{BA}+q_\text{BA}$$                   1.10.3
 * $$\text{d}U^\text{B}=w_\text{AB}+q_\text{AB}$$                   1.10.4
 * $$w_\text{BA}+w_\text{AB}=0$$                        1.10.5
 * $$q_\text{BA}+q_\text{AB}=0$$                          1.10.6
 * This set of relations together constitutes the first law of thermodynamics.

On page 12, Guggenheim wrote:
 * We may now say that the work $$w$$ is converted into energy; to speak of its conversion to heat would be nonsense.

Guggenheim is clear that heat cannot be generated by friction. The caveman, the coachman, and poor old Thompson, Mayer, and Joule would turn in their graves. One wonders what did happen in the experiments of the latter authors. Work was converted into 'energy'. Into internal energy? Work is a process term; internal energy is a state term. Heat is a process term.

Evidently, Guggenheim recognizes that, in thermodynamics, heat is a process notion, and that it is defined by exclusion of work.

But also evidently, Guggenheim isn't interested in the tradition that thermodynamics is based on statements about a system and its surroundings, while he prefers to think in terms of two interacting thermodynamic systems; and, not admitting the idea of friction, he isn't interested in the Thompson–Mayer–Joule–Bryant–Bridgman–Planck idea that it generates heat, so that it isn't necessary that $$w_\text{BA}+w_\text{AB}=0$$ and $$q_\text{BA}+q_\text{AB}=0$$. Friction is essentially a process notion, referring to the surroundings, and is not discussed in detail in thermodynamics; only its effects are recognised there.Chjoaygame (talk) 07:04, 4 July 2023 (UTC)

Keenan
Keenan J.H., 1941, Thermodynamics, John Wiley & Sons.

On page 6, Keenan wrote:
 * Heat is that which transfers from one system to a second system at lower temperature, by virtue of the temperature difference, when the two are brought into communication.

On page 9, referring to paddlewheel experiments without mentioning Joule's name, Keenan wrote:
 * Experiments of this sort have been carried out, and they show that the work done in raising the weight is proportional to the heat delivered by the system to the calorimeter.

No mention there of friction. Actually, Keenan here inverts the usual idea that the 'system' is the calorimetric vat, and that the 'surroundings' are the location of the falling weight.

On page 67, omitting from his book mention of Joule's measurements of the mechanical equivalent of heat, and having excluded friction till this point, Keenan wrote:
 * We shall show with the aid of the Second Law that no process is reversible which involves (a) friction, (b) transfer of heat across a finite interval of temperature, or (c) unrestrained expansion to lower pressure:
 * (a) An example of a change of state involving friction is the change in a viscous fluid system at constant volume resulting from rotation of a paddle wheel in the fluid. The only effects of this process are a rise in the temperature of the fluid and the fall of a weight which causes the paddle wheel to rotate (Fig. 32).

On page 114, Keenan observed that the work done by the prime mover may exceed the work received by the moved element, the difference being due to friction:
 * Friction between piston and cylinder and between moving parts and bearing surfaces will absorb some work for each increment of the piston stroke; and, if the net work done by the fluid on the piston over that increment is less than the work absorbed, it is better to eliminate that part of the stroke.

This is in accord with the view of Bryan and Bridgman, but Keenan does not enter it into his definition of heat. Keenan neatly avoids talk of heat here, just talking about "work absorbed". What is 'absorption' of work?

Likewise, on page 132, Keenan avoided talk of heat when he wrote:
 * ... a stage with high stream velocities will suffer serious losses of work from friction.

"Losses of work"? What does that mean? Keenan wrote anything except that friction produces heat.Chjoaygame (talk) 11:22, 4 July 2023 (UTC)

Kittel
Kittel, C., Kroemer, H. (1980). Thermal physics, 2nd ed., W.H. Freeman, USA.

On page 227, Kittel & Kroemer wrote:
 * Heat and work are two different forms of energy transfer. Heat is the transfer of energy to a system by thermal contact with a reservoir. Work is the transfer of energy to a system by a change in the external parameters that describe the system. The parameters may include volume, magnetic field, electric field, or gravitational potential. ...


 * The most important physical process in a modern energy-intensive civilization is the conversion of heat into work. ...


 * The fundamental difference between heat and work is the difference in the entropy transfer.... This energy transfer is what we defined above as heat, and we see it is accompanied by entropy transfer. Work, being energy transfer by a change in external parameters—such as the position of a piston—does not transfer any entropy to the system. There is no place for entropy to come from when only work is performed or transferred.

The authors seem to assume that, for a closed system, transfer of energy is either by work or by thermal contact with a reservoir. Yet, for them, work is the transfer of energy to a system by a change in the system's external parameters. Here, as external parameters, they list volume, magnetic field, electric field, and gravitational potential. The present note considers volume to be a prototypical external parameter, but magnetic and electric fields are not so simple. At this point, Kittel & Kroemer mention electric field, an intensive variable, but they say nothing about the dielectric polarization that is its conjugate extensive state variable. They do not say precisely what they mean by an 'external parameter'. They seem to partly exclude friction from their considerations. But on page 232, they wrote:
 * Part of the work generated may be converted back to heat by mechanical friction.

For conversion of heat into work, it is evident that they refer to devices that operate through a sequence of several processes each initiated by respective thermodynamic operations, and that they are not thinking of a single separate process initiated by a single separate thermodynamic operation. On the other hand, it does seem that friction can be considered as a single separate process that converts work into heat.

Nolting
Nolting (2017) defines 'work' by listing the various forms of thermodynamic work, defined by integrals of conjugate thermodynamic state variables. He makes no particular reference to external mechanical force × distance notions.

On page 29 he writes about heat:
 * The system receives and gives off, respectively, this form of energy when it changes its temperature without any work is done on it or by it.

This says nothing about latent heat, and it is a pity that it doesn't mention internal energy at this stage. Consequently, heat is here based partly on temperature, which has not yet received its thermodynamic definition.

Nolting goes on to write:
 * When we therefore, backed by empirical facts, postulate that there does exist an independent energy form ‘heat’, and when we further assume that it is, like any other type of energy, an extensive variable then we can use:
 * $$dE_H = T dS$$
 * $$T$$ is an intensive and $$S$$ an extensive quantity. $$E_H$$ is the energy of heat. The extensive variable $$S$$ we will later call entropy. It will define, in the final analysis, the energy form heat.

It seems that, instead of our preferred idea of defining entropy through heat, Nolting is happy to define heat through entropy, though he hasn't yet presnted the second law. Here, he goes on to define temperature through entropy. It seems that Nolting is not too fussed about logical development through empirical facts.

Partington (1913)
In his Textbook of Thermodynamics (1913), Partington writes:
 * When work is done by a force against friction, as in dragging a weight up a rough incline, or projecting a mass on a rough plane, the gain of potential or kinetic energy is always less than the work done by the force. In addition, however, a rise of temperature is observed in the system, or in those parts where the friction is located—in other words, Heat is produced. This, being obtained from work spent on the system, is a form of energy. The reverse process, in which heat is converted into work, is utilised in ali steam engines. The heating of a rapidly moving bullet on striking a target is an instance of the conversion of kinetic energy into heat. The reverse process occurs in the Trevelyan rocker.

Partington also wrote:
 * There is a fixed relation between the measure of a quantity of work and that of the quantity of heat obtained from it by complete conversion.

Partington thinks that heat and work are interconvertible, and that Joule proved it:
 * That such a mechanical equivalent exists is a consequence of the fact that heat and work are interconvertible. The further fact that it is a fixed constant and independent of the process of conversion was proved by the experiments of Joule (1843-1880), referred to below.

He further writes:
 * The entire agreement between the values of the mechanical equivalent of heat obtained by many different methods establishes the proposition that it is independent of the process in which the conversion of work into heat occurs, and depends solely on the choice of the units of these two magnitudes. This result was first established by Joule.

So Joule was indeed measuring the mechanical equivalent of heat.

Petrucci
According to Petrucci, Herring, Madura, and Bissonnette, 11th edition:
 * Heat is energy transferred between a system and its surroundings as a result of a temperature difference. Energy that passes from a warmer body (with a higher temperature) to a colder body (with a lower temperature) is transferred as heat.

They also show a picture of Joule, with the caption:
 * Joule’s primary occupation was running a brewery, but he also conducted scientific research in a home laboratory. His precise measurements of quantities of heat formed the basis of the law of conservation of energy.

Evidently, Joule did measure quantities of heat, but it remains perhaps mysterious how he did so, if the above definition is adhered to. We may remark that there, the authors refer to the law of conservation of energy, not to the first law of thermodynamics.

Pippard
On page 14, Pippard writes:
 * It should be most particularly noted that in none of these experiments is any process carried out which can be legitimately called 'adding heat to the system'. All are experiments in which the state of an otherwise isolated mass of water (or other fluid) is changed by the performance of mechanical work. It would be a purely inferential, and phenomenologically quite unjustifiable, interpretation of the experiments to regard the mechanical work as transformed into heat, which then raises the temperature of the water.

In effect, Pippard is rejecting the relevant definition of work as 'thermodynamic work' defined by the change of thermodynamical state variables. He is defining work as defined in the surroundings, mechanically, without regard to its being an ingredient of a thermodynamic process.

Pippard then writes:
 * If the state of an otherwise isolated system is changed by the performance of work, the amount of work needed depends solely on the change accomplished, and not on the means by which the work is performed, nor on the intermediate stages through which the system passes between its initial and final states.

Considering Joule's paddle wheel experiment: How do we define 'the system'. Pippard seems to think that the paddles are part of the system, and are adiabatically separated from the surroundings. He doesn't actually demand measurement of the change of volume of the water. It may tacitly be assumed that it is zero, I think?

Why does Pippard think that Joule measured the mechanical equivalent of heat, when he thinks that the experiment did not add heat to the water? Perhaps he doesn't really believe that Joule did measure the mechanical equivalent of heat? He writes:
 * According to the statement made above the total work performed in each process should be the same. Unfortunately, it does not seem that experiments of this kind have ever been carried out carefully. This is historically merely a consequence of the rapid and universal acceptance of the first law of thermodynamics, and of the kinetic theory of heat, which followed the work of Joule. We must therefore admit that the statement which we have enunciated here, and which is equivalent to the first law of thermodynamics, is not well founded on direct experimental evidence.

After all, Pippard seems to think that Joule didn't measure the mechanical equivalent of heat. Oh, dear! All of Pippard's care for logical rigour has overthrown Joule !! What a clever fellow is Pippard !! Planck was wasting our time rattling on about friction !!

Pippard wriggles out of this by writing:
 * Its manifold consequences, however, are so well verified in practice that it may be regarded as being established beyond any reasonable doubt.

How does Pippard eventually define heat? He does so partly by dismissing the thought of the paddle being considered as part of the surroundings, and as itself being heated by the performance of mechanical work. He requires perfectly adiathermal performance of mechanical work:
 * This does not mean that any fault is to be found with the concept of internal energy, but that the equating of ΔU with W is only correct under adiathermal conditions.

He writes:
 * Such a manner of introducing and defining heat may appear somewhat arbitrary, and in justification it is necessary to show that the quantity Q exhibits those properties that are habitually associated

with heat. In point of fact the properties concerned are not many in number, and may be summarized as follows: (1) The addition of heat to a body changes its state. (2) Heat may be conveyed from one body to another by conduction, convection or radiation. (3) In a calorimetric experiment by the method of mixtures, or any equivalent experiment, heat is conserved if the experimental bodies are adiabatically enclosed.

Evidently, Pippard thinks that Maxwell was mistaken to say that convection is transport of internal energy, not heat transfer as such. He doesn't admit that heat can be generated by friction. How does convection transfer heat from one body to another? My impression is that, according to Maxwell, convection occurs within a fluid body during a process, and is not a transfer of energy as heat from one body to another.

I would say that Pippard defines quantity of heat calorimetrically, especially when I see him write that "heat is conserved if the experimental bodies are adiabatically enclosed". But if the bodies are not adiabatically enclosed, heat is transferred by conduction or radiation.

So this is a stumbling block for the definition of heat as transfer of energy other than by thermodynamic work or the transfer of matter. It is the calorimetric definition of heat. Evidently, according to Pippard, mechanical work cannot be transformed into heat. Poor old Joule.

Reif
Reif, F. (1965). Fundamentals of statistical and thermal physics, McGraw-Hill, New York.

This standard text is oriented by statistical mechanics. The statistical mechanical world is not that of macroscopic thermodynamics. Statistical mechanics is not interested in general in the system's surroundings, where hammers, pulleys, and frictional and other devices are located. For statistical mechanics, more interest lies in such interactions as between two bodies each initially in its respective thermodynamic equilibrium.

The relevant point here is that work is defined by changes in the system's external parameters, not by the arrangements of frictional and other devices in the surroundings.

On page 68, considering processes in closed systems, Reif wrote:
 * In a macroscopic description it is useful to distinguish between two types of possible interactions between such systems. In one case all the external parameters remain fixed so that the possible energy levels of the systems do not change; in the other case the external parameters are changed and some of the energy levels are thereby shifted. We shall discuss these types of interaction in greater detail.
 * The first kind of interaction is that where the external parameters of the system remain unchanged. This represents the case of purely "thermal interaction."

By 'external parameter', Reif means extensive thermodynamic state variables other than the thermodynamic variables entropy and internal energy. The prime relevant example of such an 'external parameter' is volume. Such variables can be measured externally to the working body, for example by measuring the length, breadth, and width of the working body. Reif means to exclude internal variables such as the various intensive state variables such as pressure and temperature, and to exclude transient density fluctuations within the body; the latter are supposed to average out to zero over time in thermodynamic equilibrium.

When all the external parameters remain unchanged in a process, the internal parameters can still change. It is these that change in the kinds of process that Reif is considering. For example, temperature and pressure can change in such processes. For example, when the body is heated, the pressure and temperature will usually increase. In bodies composed of some mildly unusual substances, such as water at temperatures in a certain range near freezing, heating with increase in temperature can result in decrease of pressure. (This makes water unsuitable as a thermometric substance in that temperature range.)

The situation can be described in more detail in the light of the second law of thermodynamics, which defines entropy $$S,$$ and thermodynamic temperature $$T.$$

If the process, defined by different initial and final external parameter values, is imagined as isentropic, devoid of friction, and adiabatic (no heat conduction, no radiative transfer), then the quantity of work done by the system is mathematically uniquely defined, and is given by an integral of the form
 * $$W=\int_i^f P\ dV = \int_i^f \text{đ}W$$

that describes any such process obeying the fundamental equation of the system throughout.

If, on the other hand, the process is imagined as entirely due to heat transfer, in Reif's words, "purely thermal", then an integral of the form
 * $$Q=\int_i^f T\ dS = \int_i^f \text{đ}Q$$

will describe any such process obeying the fundamental equation of the system throughout.

One can consider more general processes, irreversible, with both work and heat transfer, including friction, obeying the fundamental equation of the system throughout, for which
 * $$\Delta U= Q-W = \int_i^f \text{đ}Q - \int_i^f \text{đ}W.$$

Such integrals are path integrals, for which the path is not uniquely determined. This is why the symbols $$\text{đ}W$$ and $$\text{đ}Q$$ are said to denote inexact differentials.

In this view, Joule did not do thermodynamic work on his vat of water; instead, he heated it through friction. So he directly measured the mechanical equivalent of heat, a substantial achievement, commemorated in the name of the SI unit of quantity of energy.

Reif then specializes to consider a case in which the surroundings are of the same character as the working body. This excludes such processes as stirring with a paddle, because the paddle is driven by devices in the surroundings that are quite different in character from the working body. Such processes are not the main interest of statistical mechanics, but they belong to thermodynamics in general.

Callen's first edition (1960), talking about closed systems (no transfer of matter), said on page 7:
 * Energy can be transferred to a mechanical mode of a system, such a flux of energy being called mechanical work. Similarly, energy can be transferred to an electrical mode of a system. Mechanical work is typified by the term $$- P \ dV$$ ($$ P$$ is pressure, $$V$$ is volume), and electrical work is typified by the term $$- E \ d \mathcal P$$ ($$ E$$ is electric field, $$\mathcal P$$ is electric dipole moment). These energy terms and various other mechanical and electrical work terms are treated fully in the standard mechanics and electricity references. But it is equally possible to transfer energy to the hidden atomic modes of motion as well as to those which happen to be macroscopically observable. An energy transfer to the hidden atomic modes is called heat.

This is the converse of Reif's definition of heat, in the sense that Callen's "hidden atomic modes" are the subject of Reif's "first kind of interaction where the external parameters of the system remain unchanged".

Schroeder
Schroeder, D.V., Introduction to Thermal Physics, 2000, Addison Wesley Longman, San Francisco. Schroeder is writing from the viewpoint that starts from microscopic physics, as against the thermodynamic viewpoint that starts with macroscopic physics. He leads with
 * Heat is defined as any spontaneous flow of energy from one object to another, caused by a difference in temperature between the objects. We say that "heat" flows from a warm radiator into a cold room, from hot water into a cold ice cube, and from the hot sun to the cool earth. The mechanism may be different in each case, but in each of these processes the energy transferred is called "heat."
 * Work, in thermodynamics, is defined as any other transfer of energy into or out of a system. You do work on a system whenever you push on a piston, stir a cup of coffee, or run current through a resistor. In each case, the system's energy will increase, and usually its temperature will too. But we don't say that the system is being "heated," because the flow of energy is not a spontaneous one caused by a difference in temperature. Usually, with work, we can identify some "agent" (possibly an inanimate object) that is "actively" putting energy into the system; it wouldn't happen "automatically."
 * The definitions of heat and work are not easy to internalize, because both of these words have very different meanings in everyday language. It is strange to think that there is no "heat" entering your hands when you rub them together to warm them up, or entering a cup of tea that you are warming in the microwave. Nevertheless, both of these processes are classified as work, not heat.
 * Notice that both heat and work refer to energy in transit. You can talk about the total energy inside a system, but it would be meaningless to ask how much heat, or how much work, is in a system. We can only discuss how much heat entered a system, or how much work was done on a system.
 * Footnote: Many physics and engineering texts define W to be positive when work-energy leaves the system rather than enters. Then equation 1.24 instead reads ΔU = Q − W. This sign convention is convenient when dealing with heat engines, but I find it confusing in other situations. My sign convention is consistently followed by chemists, and seems to be catching on among physicists.

Schroeder does make the important point that "both heat and work refer to energy in transit.

But, like Çengel et al., Schroeder defines thermodynamic work by exclusion of heat.

This reverses the logic of Bryant and Carathéodory, who define heat by exclusion of work. Schroeder's definition of work, by exclusion of heat, is in contrast with the usual idea in physics, that work is defined mechanically, in terms of such things as the ability to lift a weight. Thermodynamics began with the idea that spontaneous work is done by the working body of a heat engine, not with Schroeder's idea that


 * Usually, with work, we can identify some "agent" (possibly an inanimate object) that is "actively" putting energy into the system; it wouldn't happen "automatically".

Schroeder doesn't seem to consider friction within the system such as occurs in Joule's paddle wheel experiment.

In the above quote from Schroeder, there is no mention of friction. His first mention of friction is in the following footnote:


 * Even for quasitatic compression, friction between the piston and the cylinder walls could upset the balance between the force exerted from outside and the backward force exerted on the piston by the gas. If W represents the work done on the gas by the piston, this isn't a problem. But if it represents the work you do when pushing on the piston, then I'll need to assume that friction is negligible in what follows.

Though Schroeder is not focusing on friction, that remark is compatible with the above remark of Bryant:


 * Another important exception occurs when sliding takes place between two rough bodies in contact. The algebraic sum of the works done is different from zero, because, although the action and reaction are equal and opposite the velocities of the parts of the bodies in contact are different. Moreover, the work lost in the process does not increase the mutual potential energy of the system and there is no intervening medium between the bodies. Unless the lost energy can be accounted for in other ways, (as when friction produces electrification), it follows from the Principle of Conservation of Energy that the algebraic sum of the quantities of heat gained by the two systems is equal to the quantity of work lost by friction.

And with the above remark of Bridgman:


 * We have the paradoxical result that the work received by the block from the pavement across the surface of separation is not equal to the work done on the pavement by the block.

This may be interpreted by saying that ordinary physical work done by a mechanism in the surroundings must sometimes be distinguished from thermodynamic work done on its surroundings by a thermodynamic system, as for example by a heat engine.

Perhaps it is, as Schroeder thinks, "strange to think that there is no "heat" entering your hands when you rub them together to warm them up." Perhaps rubbing one's hands together mainly has the effect of increasing the blood flow through the hands? It is not quite the same as rubbing two pieces of ice together.

Classical theoretical texts on thermodynamics define changes in the internal energy of a thermodynamic system strictly in terms of thermodynamic work done by a body enclosed in a container with adiabatic walls. In practice, perhaps most measurements of change in internal energy are done by calorimetry, as for example in Joule's paddlewheel experiment.

In thinking about thermodynamic work, one should bear in mind that thermodynamics is primarily about differences between thermodynamic states. This is why thermodynamic work is defined by differences between thermodynamic states. Thermodynamics is not simply about forces that an "agent" in the surroundings can exert to do work on the thermodynamic system. It is about forces that a thermodynamic system can exert to do work on its surroundings; such work can be received in the surroundings partly as work against friction, i.e., as heat.

It is perhaps worth remarking at this point that "chemical work", referring to such quantities as $$\mu \ \text {d} N$$, might safely be called 'chemical work-like change'. This is because "chemical work" is defined neither by mechanical forces that the surroundings exert on the system, nor by mechanical forces that the system exerts on the surroundings, but by changes in the state variables of the system.

Schroeder is a chemist who approaches thermodynamics as secondary to microscopic physics, apparently not a physicist who learnt thermodynamics as a macroscopic topic from Carnot, Joule, Mayer, Joule, Bryant, Carathéodory, and Planck. One may ask, which is better for Wikipedia, that it give priority to the thinking such as Fourier's, in terms of partial differential equations and the caloric theory, or that it reflect the knowledge of a cave man or pre-industrial coachman, that friction generates heat? I am inclined to bear in mind that Wikipedia is often enough quoted just from the first defining sentence of an article, as if that authoritatively settles a question.Chjoaygame (talk) 04:09, 29 June 2023 (UTC)

Zemansky
Zemansky, M.W., Dittman, R.H. (1997). Heat and Thermodynamics: An Intermediate Textbook, 7th ed., McGraw-Hill, New York.

Zemansky & Dittman

On page 49, defining thermodynamic work, the authors wrote:
 * Internal work cannot be discussed in macroscopic thermodynamics. Only the work that involves an interaction between a system and its surroundings is analyzed. When a system does external work, the changes that take place can be described by means of macroscopic quantities referring to the system as a whole, in which case the changes may be imagined to accompany the raising or lowering of a suspended weight, the winding or unwinding of a spring, or, in general, the alteration of the position or configuration of some external mechanical device. This may be regarded as the ultimate criterion as to whether external work is done or not. It will often be found convenient throughout the remainder of this book to describe the performance of external work in terms of, or in conjunction with, the operation of a mechanical device, such as a suspended weight or deformed spring. Unless otherwise indicated, the word work, unmodified by any adjective, will mean external work.

On page 73, the authors wrote:
 * Therefore, we adopt as a calorimetric definition the following: heat is that which is transferred between a system and its surroundings by virtue of a temperature difference only.

On page 78, the authors wrote:
 * Let us now imagine two different experiments performed on the same closed system. In one experiment, we measure the adiabatic work necessary to change the state of the system from $$i$$ to $$f$$ in order to obtain $$U_f-U_i.$$ In the other experiment, we cause the system to undergo the same change of state, so we have the same $$U_f-U_i,$$ but the process is diathermic, and we measure the diathermic work $$W$$ done. The result of all such experiments is that the nonadiabatic work $$W$$ is not equal to $$U_f-U_i.$$ In order that this result shall be consistent with the law of the conservation of energy, we are forced to conclude that energy has been transferred by means other than the performance of work. This energy, whose transfer between the system and its surroundings is required by the law of the conservation of energy and which has taken place only by virtue of the temperature difference between the system and its surroundings, is what we previously called heat. Therefore, we give the following as our thermodynamic definition of heat: When a closed system whose surroundings are at a different temperature and on which diathermic work may be done undergoes a process, then the energy transferred by non-mechanical means, equal to the difference between the change of internal energy and the diathermic work, is called heat. Denoting heat by $$Q$$, we have


 * $$Q=(U_f-U_i)-W\text{(diathermic)},$$
 * or
 * $$U_f-U_i=Q+W,$$                  (4.2)
 * here the sign convention has been adopted that $$Q$$ is positive when it enters a system and negative when it leaves a system. Like internal energy and work, heat is measured in joules in the SI system. Equation (4.2) is known as the mathematical formulation of the first law of thermodynamics.
 * It should be emphasized that the mathematical formulation of the first law contains three related ideas: (1) the existence of an internal-energy function; (2) the principle of the conservation of energy; (3) the definition of heat as energy in transit by virtue of a temperature difference.

On page 80, the authors wrote:
 * We have seen earlier that the work done on or by a system is not a function of the coordinates of the system, so the calculation of the work depends on the path of integration by which the system is brought from the initial to the final state. The same situation applies to the heat transferred in or out of a system.

On page 81, the authors wrote:
 * Imagine two systems: a system $$A$$ in thermal contact with a system $$B$$, and the composite system is surrounded by adiabatic walls. For system $$A$$ alone,
 * $$U_f-U_i=Q+W;$$
 * and for system $$B$$ alone,
 * $$U^\prime_f-U^\prime_i=Q^\prime+W^\prime.$$
 * Adding, we get
 * $$(U_f+U^\prime_f)-(U_i+U^\prime_i)=Q+Q^\prime+W+W^\prime.$$
 * Since $$(U^\prime_f-U^\prime_f)-(U^\prime_f-U^\prime_f)$$ the change in energy of the composite system and $$W+W^\prime$$ is the work done on the composite system, it follows that $$Q+Q^\prime$$ is the heat transferred to the composite system. Since the composite system is surrounded by adiabatic walls,
 * $$Q+Q^\prime=0,$$
 * and
 * $$Q=-Q^\prime.$$                  (4.3)
 * In other words, within an adiabatic boundary, the heat lost (or gained) by system $$A$$ is equal to the heat gained (or lost) by system $$B.$$ Equation (4.3) is the basis of calculations of the intermediate temperature after a piece of hot metal has been dropped into a sample of cold water contained in a calorimeter. One is allowed to consider the quantity of heat to be conserved within the adiabatic container, but heat is generally not a conserved quantity, as Rumford's experiments showed.

The authors' consideration of heat and the first law is only partly done at this stage. They consider it further later in their text. They continue here by writing


 * A process involving only infinitesimal changes in the thermodynamic coordinates of a system is known as an infinitesimal process. For such a process, the general statement of the first law becomes
 * $$dU=\text{đ} Q+\text{đ} W.$$                  (4.4)
 * If the infinitesimal process is quasi-static, then $$dU$$ and $$\text{đ} W$$ can be expressed in terms of thermodynamic coordinates only. An infinitesimal quasi-static process is one in which the system passes slowly from an initial equilibrium state to a neighboring equilibrium state.
 * Equation (4.4) shows that the exact differential $$dU$$ is the sum of two inexact differentials, $$\text{đ} Q$$ and $$\text{đ} W.$$ It is surprising that the inexactness of the right side of the equation is not found on the left side. It should be recognized that $$dU$$ refers to a property within the system (internal energy), whereas $$\text{đ} Q$$ and $$\text{đ} W$$ are not related to properties of the system; rather, they refer to the surroundings, where the surroundings interact with the system by means of processes of transferring energy. The quantity $$\text{đ} W$$ was found in the last chapter to be expressible in terms of the product of an intensive generalized force and an extensive generalized displacement, as shown in Table 3.1. But, the quantity $$\text{đ} Q$$ itself is not yet expressed in terms of thermodynamic (system) coordinates only.

The authors are defining 'work' only in terms of generalized force and generalized displacement as measured for the surroundings, not in terms of such quantities as measured for the working body itself. Their result is that 'work' as measured by their definition leads to two mathematical changes in the working body, namely 'work' as measured for the working body itself by an integral in terms of the system's internal variables, and a quantity $$T dS$$ defined in terms of two characteristically thermodynamic variables, $$T$$, the thermodynamic temperature, and $$dS$$, the differential of the entropy $$S,$$ which are defined only through the second law. Thus, in effect, they might define two kinds of work, that defined for the working body, and that defined for the surroundings. They do not talk about this distinction, and so they hold fast to the caloric definition of 'heat', in contrast to that apparently assumed by Thompson, Mayer, and Joule, in terms of mechanics, by which work coming from the surroundings is converted by friction to heat going into the system. Some textbook writers are careful to notice this distinction: for example, Bryan, and Bridgman, who recognize the two kinds of 'work'. On the no-distinction side, for example, Guggenheim (1967) recognized only one kind of 'work' and ridiculed the idea of surroundings work being converted by friction into system heat; on page 12, he wrote
 * We may now say that the work $$w$$ is converted into energy; to speak of its conversion to heat would be nonsense.

Authors who work with the no-distinction idea do the integrations for the calculation of work in a process indirectly, by integrating increments of heat measured by calorimetry. Apparently they are not interested in the integrations for 'work' in terms of the state variables of the system. The result is that 'work' done on the system by the surroundings is always in physical reality contaminated by 'heat' in a way that is not evident or directly traceable in the quantity of 'work' as defined by the processes entirely within the surroundings. In other words, for them, the differentials $$T \ dS$$ and $$S \ dT$$ do not measure 'heat' directly. The caloric theory of heat lives on.

Thermodynamic work
Borgnakke, C., Sonntag, R.E. (2009). Fundamentals of Thermodynamics, 7th edition, John Wiley & Sons, Inc.

On page 90, they wrote
 * Work and heat are energy in transfer from one system to another and thus play a crucial role in most thermodynamic systems or devices. To analyze such systems, we need to model heat and work as functions of properties and parameters characteristic of the system or the way it functions.

Very often, thermodynamics assumes that ordinary physical work is well defined, and so it takes 'work' as the basic quantity of energy, and then defines 'heat' as a residual from 'work', as do Borgnakke & Sonntag. (Some writers, e.g. Schroeder (2000), and perhaps Çengel, Boles & Kanoğlu (2019), define heat by calorimetry and then define work as a residual from heat.)

On page 90, they also wrote
 * Work is usually defined as a force $$F$$ acting through a displacement $$x$$, where the displacement is in the direction of the force. That is,
 * $$W=\int^2_1 F \ dx$$              (4.1)
 * This is a very useful relationship because it enables us to find the work required to raise a weight, to stretch a wire, or to move a charged particle through a magnetic field.
 * However, when treating thermodynamics from a macroscopic point of view, it is advantageous to link the definition of work with the concepts of systems, properties, and processes. We therefore define work as follows: Work is done by a system if the sole effect on the surroundings (everything external to the system) could be the raising of a weight. Notice that the raising of a weight is in effect a force acting through a distance. Notice also that our definition does not state that a weight was actually raised or that a force actually acted through a given distance, but only that the sole effect external to the system could be the raising of a weight. Work done by a system is considered positive and work done on a system is considered negative. The symbol $$W$$ designates the work done by a system.

The logic of definition here is perhaps thrown into doubt by the following sentence, which they wrote on page 104:
 * In each of these quasi-equilibrium processes, work is expressed by the integral of the product of an intensive property and the change of an extensive property.

The logic of Borgnakke & Sonntag seems to require that the work done measured by the lifting of the weight should be equal to the work measured by the integral.

In the first above sentence, we are talking about the putative 'sole effect' of thermodynamic process; we have not heard explicitly about the thermodynamic operation that initiated the process, or how it is ensured that the process be quasi-equilibrium, or how concomitant heat transfer is ruled out. The second sentence, about "the integral of the product of an intensive property and the change of an extensive property", clarifies things. Physically thinking, concomitant heat transfer can partly be ruled out by requiring that the working body be contained by adiabatic walls. If we think, for example, of a gas expanding against the resistance of a piston in a cylinder in the surroundings, we could require the piston to be placed so that it can move up only by lifting a weight on top of it. We must think of the friction of the piston against the cylinder. If it is zero because of excellent lubrication, the gas itself will determine the speed of the lift. If the weight is great, it will move upwards slowly. A requirement is that the motion must be slow enough that the pressure in the gas remains defined throughout the process. This is necessary for the correctness of the above integral requirement. Do we require also that the upwards movement should not transiently overshoot its final position? Yes, we do require that. If the gas makes itself oscillate about its final position, then there will be internal friction, within the gas, that diverts some of the energy of expansion to remain as internal energy in the gas, so that the whole of the energy of expansion did not eventually reach the weight to lift it. Some of the energy of expansion is dissipated as heat in the gas. The process was not devoid of heat transfer and it was not isentropic; there was some heat transfer from the surroundings to the gas, when the weight gave up some of its potential energy as it compressed the gas. We do not have throughout the process that $$\text{d}S=0$$.

If the raising of the weight is to be isentropic, then the pressure–volume relation should measure the work done. There is no auxiliary variable to allow moderation according to the principle of Le Chatelier. But if the process is not isentropic, then the possibility of entropy change will allow moderating feedback through temperature change.

dated lead initial sentences or definitions
Dated 22:48, 8 August 2001, edit https://en.wikipedia.org/w/index.php?title=Heat&oldid=256829.
 * In general heat tends to "flow" from a region of high temperature to a region of low temperature.

Comment: Heat is like a substance that flows. No mention of friction. Considers convection as a form of heat transfer.

Dated 15:50, 15 December 2005, edit https://en.wikipedia.org/w/index.php?title=Heat&diff=prev&oldid=31477735.
 * Heat is the process of transferring thermal energy.

Comment: a new approach, immediately undone.

Dated 09:36, 23 January 2006, edit https://en.wikipedia.org/w/index.php?title=Heat&diff=next&oldid=36281983.
 * Heat is a form of energy associated with the motion of atoms, molecules and other particles matter is composed of. It can be created by chemical reactions (such as burning,) nuclear reactions (such as fusion reactions taking place inside the Sun,) or electromagnetic dissipation (as in electric stoves.) Heat can be transferred between objects by radiation, conduction and convection. Temperature is used to indicate the level of elementary movement associated with heat. Heat can only be transferred between objects, or areas within an object, that have different temperatures.

Comment: No mention of friction. Muddled thinking: "can be created by chemical reactions"; I would say that chemical potential energy can convert into internal energy; internal energy can be transferred as heat.

Dated 08:42, 25 January 2006, https://en.wikipedia.org/w/index.php?title=Heat&diff=next&oldid=36538164.
 * Heat is a form of energy associated with the motion of atoms, molecules and other particles matter is composed of. It can be created by chemical reactions (such as burning,) nuclear reactions (such as fusion reactions taking place inside the Sun,) electromagnetic dissipation (as in electric stoves,) or mechanical dissipation (such as friction.) Heat can be transferred between objects by radiation, conduction and convection. Temperature is used to indicate the level of elementary movement associated with heat. Heat can only be transferred between objects, or areas within an object, that have different temperatures.

Comment: mentions creation of heat by friction.

Dated 01:54, 3 March 2006, https://en.wikipedia.org/w/index.php?title=Heat&diff=next&oldid=41816652.
 * In physics, heat is defined as energy in transit.

Comment: using the phrase "energy in transit".

heating
In ordinary English, heat is not a process: it is a quantity of energy. In ordinary English, heating is a process. In physics, heat is energy in transfer by certain mechanisms. Often enough, in ordinary English, and in eighteenth century physics, with the caloric theory, heat is perhaps vaguely a substance. But we do not defer to the caloric theory, because, by the nineteenth century in physics, the work of Rumford, Mayer, Joule, and others had shown that heat is generated by friction, thereby replacing the caloric theory with the mechanical theory of heat. For thermodynamics, friction is the conversion of energy of mechanical motion of contiguous bodies into heat. For thermodynamics, this may be explained, though not defined, by saying that heat is macroscopic energy in transfer through atomic, photonic, or other microscopic mechanisms. Callen writes "But it is equally possible to transfer energy via the hidden atomic modes of motion as well as via those that happen to be macroscopically observable."