Talk:Internal energy

External energy
Does anyone know what "external energy" is then? Is that enthalpy? Or am I making words up? -- postglock 07:41, 24 October 2005 (UTC)


 * I would make a good bet that "external energy" would mean the "internal energy" of the area outside the "well defined boundary. 68.6.112.70 00:34, 6 April 2006 (UTC)

energy of a system due to their common motion and position. So the total energy of a flying test-tube is its external KE and PE analysed classically as a projectile, plus its internal energy (due to the molecular motions and reactions).

"Body or system with well defined boundaries"
Can this be changed to "closed system" which is much more often used. I'm not sure if they're the same thing, but it looks like they are - and the definition now is sorta cumbersome. 68.6.112.70 00:34, 6 April 2006 (UTC)


 * Cleaned per request.--Sadi Carnot 19:28, 25 April 2006 (UTC)

Major Changes
I have made major changes to the sections following the introduction. The main problems were:

PAR 01:49, 26 April 2006 (UTC)
 * $$P\Delta V$$ only represents mechanical work when pressure is held constant. Using infinitesimals is just as simple, as well as being correct.
 * The whole discussion about the sign of PdV belongs in the first law article, it does not help the reader to understand internal energy.
 * There was no extended intuitive explanation of the internal energy. I'm not sure the one I added is the best.
 * There is no expression for the internal energy in the entire article, only the change.
 * The other thermodynamic stuff seemed to have no point. I tried to rewrite the other thermodynamic material with the motivation of providing a number of expressions for the internal energy U (not the differential dU or the change &Delta;U).

U=TS-PV?
It is written here that
 * $$U=TS-PV\,$$

I tried to check it for a monoatomic ideal gas in 3D, and saw that it is not true. IT is true only for
 * $$U=TS-PV+\mu N \,$$

so: eman 13:30, 2 June 2006 (UTC)
 * 1) It should be cleared that the $$\mu N $$ term is mandatory.
 * 2) This erise the question of how much this expression is usefull (and indeed, I don't recall ever using it).


 * You're right. Strictly speaking, there are many types of "U"s in thermodynamics.  At constant values for all intensive variables, $$U=TS-PV+\mu N \,$$, but often the chemical potential is incorporated into internal energy and the new thermodynamic potential is still called potential energy but it's represented as $$U[\mu]=U-\mu N \,$$ where the chemical potential is a natural variable.  So for this internal energy, $$U[\mu]=TS-PV \,$$. And then there's the multi-component, multi-phase systems. See  for the whole business.  Maybe chemists, engineers, and physicsts have emphasized slightly different things in the past when it comes to nomenclature and a lot of the rigorous nomenclature is unfamiliar (at least to me), but I guess it's good that rigorous nomenclature is out there and hopefully it will be taught to undergrads soon.  Whether the exact distinctions are too esoteric for this encyclopedia is debateable. Flying Jazz 04:01, 29 June 2006 (UTC)


 * The use we make of it in physics grad school here is just $$U=TS-PV\,$$ when N is a constant, and hence $$\mu N \,$$ tells nothing, and $$U=TS-PV+\mu N \,$$ when the system is connected to a particle reservoir, so N can change. --euyyn (talk) 00:05, 30 April 2008 (UTC)

Why is the rest mass not part of the internal energy?
Much of the mass of an atom lies in the nucleus, and that mass is not entirely due to the individual protons and neutrons, but also to their motions; similarly the mass of a proton is not just the mass of its three quarks but mostly due to their motions. For all we know all masses are due to internal motions, and it is the latter that makes up internal energy.

If one includes the rest mass as internal energy, then it is possible to know the internal energy of a system - measure its mass, convert to energy as mc^2 and subtract the external energy. Of course, this would include the nuclear energy which is usually excluded from thermodynamics texts. Chrystomath 2006.10.11


 * The reason to exclude it is merely pragmatic. For 99% of the purposes of thermodynamics, the temperature is not high enough to have nuclear reactions, and you don't have neutrons going around, breaking nuclei. So including mc^2's in the expression only gives you a bunch of terms which remain constant all the time. One just needs to move the origin of energies (remember there's no thing as "absolute energy", only differences) to get rid of them.
 * About your question on why can't we measure internal energy by measuring mass and substracting rest masses and all the binding energies (nuclear and electrical at least) I'll meditate / ask a professor. --euyyn (talk) 00:49, 12 March 2008 (UTC)


 * Just to complement the discussion the rest mass is generally not considered as a part of the internal energy because we deal with an idealized model that includes simplification(s). One simplification consists in considering an idealized situations in which no nuclear reactions occur so that rest mass can be omitted. With a change o zero of energy, one coulf let the rest energy in negative value of internal energy. Whereas, it is not very intuitive, physics does not change by changing the zeros of energy. For conceptual clarity this of things could be included. Though, I 'm not sure that it would not become to complicated because it includes ideas from scientific modeling which are not much widspread in society. Manouchk (talk) 10:58, 26 May 2024 (UTC)

Does potential energy of fields count or not?
In the first section, it says that internal energy does not include potential energy due to gravitational or electrostatic field,s but later on it says that for the distribution of internal energy in a gas, some of it can come from gravitational, electric, or magnetic fields. Was this just a couple of edits that weren't checked, or do the fields in the gas come from other gas molecules and not outside? It seems like the second one would make more sense, but some clarification would be useful.

edit: looked up how to sign. 12.182.100.224 17:42, 24 October 2006 (UTC)

Possible error in the "The first law of thermodynamics section"
"Q is heat added to a system" "W is the mechanical work done on a system"

according to "Thermal Physics" By C. B. P. Finn (Page 27) this is just one convention, and some text books define positive Q as heat traveling from the system to the surroundings and possative w as mechanial work done by the system. As long as your consistant with your definition both conventions can work.

Obviously we should stick with the more widely used convention, but it might be worth mentioning that the alturnative convention exists. Otherwise a reader could get very confused if they come across the other convention. 81.137.148.225 16:09, 5 March 2007 (UTC) Melissa


 * The following choices of meaning for variable Q and W, "Q is heat added to a system" "W is the mechanical work done on a system", is compatible with the following equation of evolution of
 * the internal energy : $$ \mathrm{d} U = \delta Q - \delta W, $$
 * This conventional choice have to be compatible with the equation of evolution of internal energy. If Q as heat traveling from the system to the surroundings, then the equation would be different ($$ \mathrm{d} U = - \delta Q - \delta W, $$) Manouchk (talk) 11:10, 26 May 2024 (UTC)


 * The just foregoing comment is mistaken. It should read:
 * The following choices of meaning for variable Q and W, "Q is heat added to a system" "W is the mechanical work done by a system", is compatible with the following equation of evolution of the internal energy : $$ \mathrm{d} U = \delta Q - \delta W, $$
 * where I have bolded the correction to the word by. This is the more traditional version for physicists.Chjoaygame (talk) 02:33, 28 May 2024 (UTC)

Internal Energy - v - Enthalpy
According to the wikipedia Enthalpy entry "H = U +pV". However, according to the Internal Energy overview, the Internal Energy (U) already includes Strain Energy (at least for solids): is this not some form of double accounting?

Contradiction through bad wording
The following is clearly wrong, since it provides a definition which is both circular and contradictory:
 * only changes in the internal energy can be measured, and the total internal energy of a given system is the difference between the internal energy of the system and the internal energy of the same system at absolute zero temperature.

How should it be worded to make it correct? --Starwed 07:18, 20 June 2007 (UTC)

Serious problems with this article
Just like many other wikipedia articles on statistical physics and thermodynamics, this page also suffers from serious problems. I explained that [[Wikipedia talk:WikiProject Physics#Numerous errors in wikipedia's thermodynamics and statistical physics articles :(]|here]

In case of this article, it goes wrong already in the second paragraph of the lead:

"The internal energy is a thermodynamic potential and for a closed thermodynamic system held at constant entropy, it will be minimized."

And setting up that argument using Euler's theorem on homogeneous functions for U while keeping N constant is more difficult than bending spoons.

Count Iblis (talk) 21:32, 20 May 2008 (UTC)

Internal energy
If one write heat absorbed or added into the system, one restrict the transfer only to an endothermic process. It is the reason why I propose heat exchanged or transferred, that is more general.
 * A transformation can be endothermic Q>0 or exothermic Q<0, not only for chemical reactions but also for physical processes: for instance phase transition, state change.


 * As for the sign rule:
 * See: Heat

''Heat is the process of energy transfer from one body or system to another due to a difference in temperature. The total amount of energy transferred through heat transfer is conventionally abbreviated as Q. The conventional sign convention is that when a body releases heat into its surroundings, Q < 0 (-); when a body absorbs heat from its surroundings, Q > 0 (+).''
 * Maghemite (talk) 14:06, 23 May 2009 (UTC)

The idea behind the current version is that "heat absorbed" is "minus heat removed from the system". We can, of course, mention this more explicitely. The problem with simply assuming the sign rule is that if someone (say some high school student) only reads what is written here then he/she may think that in an exothermic process in which heat is released, the heat goes into the system and counts positive.

This mistake is easily made. If some lay person thinks about steam condensing into water, he may wrongly think that the latent heat ends up in the water (because if it costs energy to evaprate water, then surely you get heat when it condenses...). The fact that this is heat that is transferred from the steam/water to the environment may elude the reader. The wording of the previous version may then confirm this mistaken view.

That's why it is better to simply consider a system with some system boundary. Energy that enters the system boundary (in other forms than associated with changes in external varables) is heat transferred to the system. It doesn't matter if this is due to phase transitions, chemnical reactions or not. Is then obvious that energy leaving the system in this way counts negative, but one can explicitely mention this.

Of course, one can discuss endothermic process and exothermic processes, but that should be done after we define heat. Count Iblis (talk) 15:00, 23 May 2009 (UTC)

Internal energy? Dead simple, it is ......
what you define it to be! Or rather what you define your system to be. Systems in thermodynamics are no different than any other "system". A system is an assembly of (disparate) entities that influence an outcome in some way. The system analysis works out how these entities influence the outcome so that the system may be understood or even influenced in a particular way, should the need arise.

In thermodynamics the simplest real system is probably comprises a quantity of helium gas. But helium gas is far from being ideal because it deviates from the ideal gas. An ideal gas has no interatomic forces at work and its atoms exchange momentum (and energy) only by elastic collisions. Such an ideal actually falls at the first "reality check" because, not being a photon, a gas particle needs mass to have momentum and with mass there comes at least some gravitational force.

So you have to decide what your system is and then work out what are the forces etc. you are going to incorporate in your system analysis.

I notice that the opening paragraph does not include gravitational potential energy as "internal energy". Well you would be hard put to explain the stability or otherwise of a system comprising a large ball of helium, held together in space by its own gravity, if you excluded its gravitational potential energy. --Damorbel (talk) 13:13, 2 December 2009 (UTC)

This article has even worse problems, and the above is only the beginning
Look, here's the basic problem: internal energy is a nice path-independent state function, which means it has an exact differential dE or dU (let's call it dE). For what happens when you improperly use exact differentials of path-dependent quantities, see inexact differential-- this is why we use δw and δq for the first law, not dW and dQ. It's dE = δq - δw for a reason. Anyway, the point of using dE is that the first law of thermo only NEEDS a dE, because it says that dE is zero for the universe, and dE = -dE for transferring energy into, an out of, systems. We never have to worry about the absolute value of E, because it's only changes in E we worry about in thermodynamics. At worst, we can integrate and get ΔE, but that's all we ever need to do. Change in internal energy is fine (using a definite integral), but we still have no need to figure out the absolute value of E.

If we do the indefinite integral ∫dE we get a constant of integration, which can be whatever we like. That's your E at your initial conditions. Pick your favorite value, even zero. And thermo problems will all still work fine, no matter what we choose it to be. All the answers are the same. So for this reason, we really don't have to make a choice. Or we can respect others when they make other choices than we do, knowing that it isn't going to matter. In physics, the only kind of E that everybody in all inertial frames agrees on (the one that gives inertia and gravity and invariant mass), is the "rest" or COM frame E from E = mc^2, where m is the invariant mass. But there are other frame-dependent definitions of E also-- it just depends on which ones you like.

I've seen people want to define E as atomic kinetic energies in monatomic gases, and other kinds of heat associated energies (like vibration potentials) in solids. And then there's this article, which tries to include bond energies (what, are they negative?) and nuclear energies (what, are they negative too, up to Fe-56 or Ni-62, and then rise for fissional nuclides? Or must they actually be fissile nuclides??). Madness.

When we talk about dE or even ΔE, we're talking about well-defined thermodynamics, the science. When we talk about some absolute value of E as "internal energy", and we don't mean something from physics like rest energy or invariant energy, then we're talking about aesthetics, philosophy, religion, semantics, and probably messy politics. We got all that back when user:Sadi Carnot WP:OWNed this article, back in 2007. Now that he has gone to his reward, could the rest of us fix it, so it's not so wrong and confusing? I'll be glad to take a whack at it, if you all like. S B Harris 22:37, 27 February 2010 (UTC)


 * I agree in principle, but just to be sure, what modifications would you make to this definition of the internal energy and similar definitions for other thermodynamic potentials?


 * $$U=TS-pV + \sum_{i}\mu_{i}N_{i}\,$$


 * Would a simple change in the introduction suffice, explaining that the potentials so defined are thermodynamically to within an irrelevant constant, maybe not for statistical mechanics, or do you want every thermodynamic potential to be changed from e.g. U to &Delta; U with corresponding deltas in the definitions? PAR (talk) 23:28, 27 February 2010 (UTC)

No, the equations for thermodynamic potentials are fine as they are, just like those for electrical potentials. I would add a bit more (there's some already) to make it explicitly understood that (as in electromagnetic potentials) these variables don't mean anything absolute by themselves, and can only be used to calculate real things if you use them in differential form and then integrate between states (like differentiating electrical potential against distance, then integrating between spacial points). Or, since the whole point is that this has been done for you already by the concept, just directly subtract two of them from each other, or substract one from a reference. Like subtracting voltages. I can't say my cat has an electrical potential of 25 volts and leave it at that. And I can't say something has an "internal energy" of 200 kJ and leave it at that, either! The same goes for the terms of this internal E potential equation-- what is the "chemical potential" of a 5 carat diamond? One has to ask "with respect to WHAT?" A gram of amorphous carbon black, or coal, or graphite, or nanotubes...?

Because potentials have to be subtracted from each other to give any meaningful answers as to what they mean, those terms that don't change under the conditions of interest, can be dropped. Thus, if no chemistry happens, one doesn't have to worry about chemical potentials, and so those don't appear in ΔE. If we put them all in, regardless, how would we know which ones to include? You have to know the chemical reaction to write the chemical potential for it, and now we're back to the same problem. For nuclear reactions, there would be nuclear potentials, even. But we can't decide all that aprioi, as this article attempts to do for us. It's just not part of the essential definition. As a potential, thermodynamic E doesn't HAVE an absolute physical definition. Even its mathematical one, depends on how many sorts of energy changes you're going to be looking at. So it varies by circumstance. S B Harris 02:02, 28 February 2010 (UTC)


 * I agree with everything you are saying, you are right. But from what I can tell, only the introduction needs to be fixed, the mathematics, with the proper definitions does not. PAR (talk) 03:41, 28 February 2010 (UTC)
 * Agree as to the into of the thermo potential equations. I've been seeing those thermo potential equations for years. They are correct, but rarely are the variables and applications explained well, and thus they can be misinterpreted. As here. I'm not sure that even my chem prof really knew where the potential expressions came from-- he just wrote them down as apriori definitions from God, used only to derive the Gibbs partial diff relations with. Sigh. As for THIS article on "internal energy", it's got to be noted that as a "exact quantity" rather than a "difference quantity" it's not well-defined, so if you're looking for an exact quantity, there ISN'T an equation for it. And of course those tables showing what it is, and is composed of, are all wrong. Or rather, are not right. You can define it that way, or any other way. Any subset of an objects' total energy content can serve as a reference. S  B Harris 04:28, 28 February 2010 (UTC)


 * So you will rewrite the introduction? PAR (talk) 08:23, 28 February 2010 (UTC)


 * We can also say that a system is described by some Hamiltonian and you can always add some constant to that Hamiltonian. The ambiguity in the internal energy then seems to be that constant. However, this does not fully capture what Sbharris is saying. What is really going on is that we always deal with effective Hamiltonians where the high energy physics above some energy scale is integrated out. What then can happen is that the Hamiltonian contains several parts describing several subsystems and to those you can add different constants with impunity, as long as you stick to the domain of validity of the effective Hamiltonian


 * Perhaps this is best illustrated with examples. We can mention some object inside an oven, which can be pictured as matter plus a photon gas. Both have some internal energies, but the zero point can be chosen inconsistently for both parts. But then in the early universe we had a gas of photons, positrons and electrons in full thermal equilibrium. The electrons and postrons were at chemical potential of zero and here one of course has to take into account the rest energy of electrons. If we then further discuss these two exampoles, we can say that according to the more fundamental Hamiltonian, the first system is not really in thermal equilibrium as the chemical potential of the matter is not the same as that of the photons.There are then degrees of freedom that are almost perfectely isolated from each other (in this case the number of electrons and protons) while other degrees of freedom are in good thermal contact. Count Iblis (talk) 13:26, 28 February 2010 (UTC)

Yes, after the big bang, the idea was that as temp dropped, each degree of freedom (including ones we don't normally think of, like pair-production from heat and light) dropped out and froze out, and after that, didn't contribute to "heat capacity." This is typical. The article as it is written wants to define which contributions to absolute "internal energy" are thermodynamically active, and that question cannot be answered. So yes, I'll be glad to take a stab at the new intro. S B Harris 20:31, 28 February 2010 (UTC)

Split thermal energy to its own page
I propose that we move the sections on thermal energy to their own page. As it currently stands, a reader trying to learn about thermal energy first has to wade through a bunch of material on the more general internal energy. The fact that typing "thermal energy" lands you on the "internal energy" page could foster misconceptions that the two are necessarily the same thing. Judging from the discussions at the old thermal energy page, the merge was based on two incorrect assumptions: 1) that thermal energy is necessarily the same thing as internal energy, and 2) that any article which is small and confusing necessarily needs to be merged into a more substantial article. As to the first point, thermal energy is only one component of many that be considered as part of the internal energy. If you're doing mechanics, sure you can think of internal energy as identical to thermal energy and have no problems. After all, if components like chemical bond energy are inaccessible to you then you may as well imagine that they're not even there in the first place! (In fact many mechanics textbooks do just that.) But chemists need to consider bond energy as part of the internal energy; for them thermal energy is only one part of internal energy. Similarly other scientists may be interested in other parts of the internal energy. My point is that for many people thermal energy and internal energy are not the same thing. As to the second point, if the article is small and confusing, clarify it and expand it! Merging just hinders future growth. I think they're better off as separate articles. Riick (talk) 15:21, 25 August 2010 (UTC)


 * Support - I read the fairly brief merger discussions at the old page and it seems that their opinion was more that thermal energy could be adequately described within this article rather than that they were identical concepts. However the result is as you describe, thermal energy doesn't get a distinct treatment of its own.  The fact that a reconstituted thermal energy article might initially be brief is no reason not to create it;  if a good structure is in place perhaps that will facilitate others making improvements ("Structurist Wikipedians").  This is a main reason I have tried to organize the thermodynamics template recently, to make the topic area more accessible.


 * It would be nice if, in some way, the new thermal energy article dealt with the very point you are making about varying definitions in different fields. In my mind that "cultural" context belongs in the article just as much as the technical stuff. I am not sure, however, exactly how to source that kind of thing, though I made an attempt recently at convection (terminology section). There seem to be many articles with that very issue however, so I don't see it as an impediment.


 * I suggest however that for real consensus the original merge discussion participants weigh in? David Hollman (Talk) 15:49, 25 August 2010 (UTC)


 * I merged the two articles last October. Before the merge, the thermal energy article was pretty poor, and my goal in performing the merge was that anyone who wants to learn about the concept would be better off reading the merged article than the old thermal energy article.  In my view, this is the criterion that should be used to judge whether any proposed new thermal energy article should be created.
 * I think the internal energy article is entirely clear about the fact that internal energy includes kinetic energy of the molecules, potential energy due to their interactions, chemical bond energy, nuclear energy, (mass-energy equivalent?), etc. As you say, one generally ignores any energies which aren't accessible to the system of interest, and sets the 0 level appropriately (just as we make an arbitary choice to set the gravitational potential energy to be 0 when bodies are infinitely far apart, or at sea level, depending on what's convenient in any particular context).
 * The other problem (and this was the main reason I decided to merge the articles rather than try to improve the thermal energy article) is that the idea that you can divide the internal energy up neatly into these different components breaks down for anything more complicated than a monoatomic ideal gas. Even in a real gas you have molecular vibrations, van der Waals interactions, etc., which involve both kinetic and potential (i.e. chemical) energy, and in condensed matter it's even more difficult.
 * In summary, I don't have any strong objections to you splitting off a separate article, but I don't think it's as clear a case as you think. Djr32 (talk) 23:27, 3 September 2010 (UTC)


 * The fact that thermal energy cannot be cleanly partitioned from chemical energy and such is actually one of the things I'd like the article to touch on. In addition, the fact that there are several conflicting definitions of "thermal energy" out there (molecular motion? latent + sensible? sigma heat? Q?) deserves some mention as well. My view is that such topics could be covered more clearly within a separate article.
 * My main concern though is that with the current setup, someone looking up thermal energy could read only the introduction part of this (internal energy) article, and say "Oh I get it; thermal energy is all the energy within the system; it's just another word for internal energy." One could argue that's their own fault for not reading the entire article, but I would argue that if we can prevent such a mistake by splitting the article, then readers are better off with it being split. Riick (talk) 17:04, 5 September 2010 (UTC)


 * I think all of these things should go into this article (and particularly be worked into the introduction), irrespective of whether there is a separate thermal energy article. I suspect that if this article were made better that would address the problem better than creating a separate thermal energy article.  Djr32 (talk) 21:05, 11 September 2010 (UTC)


 * I echo Riick's concerns: By redirecting Thermal Energy to this page, we imply that it is a synonym for Internal Energy, when in fact it is a subset. If we don't split Thermal off to its own article, then the redirect should be to a section of this article about Thermal Energy. Unfortunately, the article doesn't seem to be structured that way. The table in Composition and interactions does a good job of showing how the components are categorized. Maybe Thermal Energy should redirect here.  Spiel496 (talk) 13:50, 14 September 2010 (UTC)


 * I don't think the redirect implies that thermal energy is a synonym for internal energy, redirects are also used for subtopics which are best described in the context of a wider article (as stated in Redirect).
 * I edited the lede a bit the other day, and the second sentence now reads:
 * It includes the kinetic energy due to the motion of particles (translational, rotational, vibrational), the potential energy associated with the vibrational and electric energy of atoms within molecules or crystals, the energy in all of the chemical bonds, and the energy of the free, conduction electrons in metals.
 * Perhaps all of these concerns could be addressed by adding a sentence along the lines of "Blah, blah and blah are sometimes collectively referred to as thermal energy." Djr32 (talk) 19:03, 14 September 2010 (UTC)

Thermal energy disambiguation page
This subheading is intended to seperate the related discussions of split and disambiguation. Added by Riick (talk) 20:01, 24 September 2010 (UTC)


 * I am starting to think that a disambiguation page may be a good way to deal with this. It seems that many of the meanings of "thermal energy" are not directly about internal energy at all, so why should someone be forced to come here for those meanings? If someone wants to know about "thermal energy" (meaning heat), then they should go to the heat article. If someone wants to know about "thermal energy" (meaning energy recovered from a heat source) then they should go to geothermal heating, heat engine, thermal power station, or the like.  It is only when someone wants to know about "thermal energy" meaning molecular motion that they might come here. With a disambiguation page, someone can select the meaning of thermal energy they are looking for and then dive right into the appropriate article.  As a fringe benefit, it would also provide a nice way to clarify from the start that "thermal energy" (meaning molecular motion) is a subset of internal energy, not a synonym. Riick (talk) 01:13, 24 September 2010 (UTC)


 * Support I support Riick's proposal for a disambiguation page.  Dolphin  ( t ) 02:37, 24 September 2010 (UTC)

Thermal energy
This is not a simple yes or no answer. Surely the term thermal energy has some ambiguity concerns associated. I am not saying that it is ambiguous, rather many authors do not seem to agree, especially here on WP where most are very narrowly swayed by one particular reference source or even none. Surely, the term is not part of standard physics definitions. There is no source, as far as I have ever read, that shows an equation to define thermal energy, like is customary for enthalpy, entropy, etc. The term's origin seem to come from an engineering view point, and is clearly associated with something that is also described by the terms heat and temperature, like all things of thermal character. Heat itself is used rather differently by many authors. It is instructive and important to examine history for the meaning of these terms. What thermal energy is not, however, is clear: it is NOT synonymous with internal energy. It is a component of it, but that must be defined. Some people equate it with heat as a process, some with some kind of energy content. Often it appears that the term is used to avoid using heat, as modern physics describes heat as energy in transit, or just as the process of transit, but not as something contained in a system, in contrast to historical use, or even contemporary popular use by non-scientists.

Summarizing my collective readings and experience on the thermal energy term, it is safest to state that thermal energy is the thermodynamic equivalent of the term mean kinetic energy (a description from classical mechanics), giving rise to matter's temperature, given emphasis to the statistical nature of an average or mean property. It may be expressed in microscopical terms as the average energy of motion of an ensemble or macroscopically as being a measure of temperature, by the proportionality through the Boltzmann constant. When thermal energy is in transit, it is what is the physical interpretation of thermodynamic heat. Thus thermal energy can be both, heat as well as a component of internal energy.

As a result, I don't think a disambiguation page makes sense, dab pages do not inform better, they simply redirect attention. The subject needs clarification. While it may be sensibly argued that thermal energy is part of internal energy, it may equally sensibly be argued that it can be transferred between systems like heat. It probably deserves an article of its own, there is nothing wrong with discussing the merits of the term, if such merits can be demonstrated by reliable references. Expanding the internal energy article to explain thermal energy seems to stretch the scope too much. Kbrose (talk) 20:52, 24 September 2010 (UTC)

Latent Heat
The section Composition and Interactions contains a table where latent heat is defined as energy associated with the phase of a system. It would be better worded as heat absorbed or released at the transition between two different phases of a system. Of course it may be zero for second order transition, but this is not in contradiction with the second statement. I cannot implement this myself because I do not find the table when editing the page. —Preceding unsigned comment added by RDR (talk • contribs) 07:42, 19 September 2010 (UTC)
 * I agree - done. The table is at Template:Composition of internal energy, by the way.  I've also moved your comment to the bottom of the talk page.  Djr32 (talk) 08:45, 19 September 2010 (UTC)
 * This presentation of latent and sensible heat in this context is really out of place, these are not forms of internal energy, rather these are descriptions of any energy that is latent (has no associated change of temperature or other observable) or sensible, which the opposite of latent. This table should be scrapped, as the other compositional energies aren't reflected properly either. Kbrose (talk) 23:33, 24 September 2010 (UTC)

The first law of thermodynamics
The way this is presented here in the beginning of the article (with W the work done on the system) is not consistent with the rest of the article, the displayed diagram and the main first law of thermodynamics article. Count Iblis (talk) 22:57, 24 September 2010 (UTC)
 * Yes, I agree with that in principle, but I have changed the presentation slightly. The point of this equation, I believe, was originally to consider all external sources of work, not just pV. Eliminated the section altogether, as there was very little discussion of 1st law. Kbrose (talk) 23:29, 24 September 2010 (UTC)

composition of internal energy
I have removed the Template:Composition of internal energy table of internal energy composition in perhaps a WP:BOLD move, but it is necessary to improve the amateurish flavor of the article. The table is just not sustainable in critical review, as discussed on the talk page Template Talk:Composition of internal energy. To replace the content, I have started to replace it by discussion in prose, marking the section under construction for now. Kbrose (talk) 03:48, 25 September 2010 (UTC)

add a section?
shouldn't there be a section about the direct relationship between internal energy and temperature w/ degrees of freedom? E= f/2 * NkT I would add it, but I don't quite understand where it comes from, and its relationship to the equation of state (dE=TdS-PdV) Pjbeierle (talk) 02:49, 29 June 2011 (UTC)

mistake
It is not right to say: "The potential energy includes all energies given by the mass of particles, by the chemical composition, i.e. the chemical energy stored in chemical bonds"
 * -- you never "store" potential energy in a bond. Potential chemical energy is highest when the atoms are in their free state, any and all bonds represent a subtraction from this.AtomAnt (talk) 18:45, 11 July 2013 (UTC)

the second one
The second one appears in the fourth paragraph:


 * "The other cardinal function of state of a thermodynamic system is its entropy, as a function, $S(U,V,{N_{j}})$, of the same list of extensive variables of state, except that the entropy, $S$, is replaced in the list by the internal energy, $U$."Chjoaygame (talk) 21:22, 20 April 2014 (UTC)

Cardinal State Function (first sentence)
In thermodynamics, the internal energy is one of the two cardinal state functions of the state variables of a thermodynamic system.

What does cardinal mean in this context? Which state function is the other "cardinal state function"? There is a good list of state functions in the "state function" section. What makes the cardinal state fubctions cardinal? what are the others called?

Thanks

ChrisR


 * Fair comment. The two cardinal state functions are internal energy and entropy. They are essentially characteristic of thermodynamics. By that I mean that they are jointly necessary components of thermodynamics, more or less by definition. Without internal energy and entropy, a discussion is in general not about thermodynamics. Cardo, cardinis (m.), is Latin for pivot, the thing upon which everything turns.


 * That entropy is the other cardinal state function is noted in the lead, not in the first sentence, but in the last sentence of the fourth paragraph. The reference for it is also given there (usually one does not over-pepper the lead with multiple citations). The term is used by Tschoegl, whose reliable text I think is the most systematic current one.


 * The internal energy is a special kind of state function that is called a potential, because it has an extremum principle. There are state functions that are not potentials. The entropy is also special, in that it has an extremum principle like the one that makes the internal energy special, though it doesn't have a special name. Its Legendre transforms do have a distinct generic name, Massieu functions.


 * These functions are amongst the characteristic functions, ones that tell all the thermodynamics of a system. They are pivotal amongst others because they are the two extensive state functions that are functions only of extensive state variables; none of the their arguments is intensive.


 * The others are just the others, they don't get a special name. There are dozens and dozens of them, all told. Most of them don't have distinguishing ordinary language names.


 * The term is used in this prominent place in the lead to help bring to the reader's attention the pivotal part played by the internal energy in thermodynamics. In one sense, one might say that the first law of thermodynamics is just about internal energy, and how it changes, for a thermodynamic system.Chjoaygame (talk) 02:43, 24 November 2014 (UTC)Chjoaygame (talk) 02:52, 24 November 2014 (UTC)Chjoaygame (talk) 03:23, 24 November 2014 (UTC)


 * We still need to insert a clear and concise definition in this article or elsewhere in Wikipedia, preferably with a source. Would it be correct to say that the cardinal state functions are a minimum set which are sufficient to define all the thermodynamic properties of the system, such that all other thermodynamic state functions can be calculated from the cardinal ones.
 * A Google search for a source was not too helpful. I did find one textbook here which seems to say that a cardinal property is *any* function of state, but I think that contradicts what you are saying, and also seems wrong because in that case cardinal property would be just a synonym for function of state. Have you a better source? Dirac66 (talk) 02:55, 16 August 2019 (UTC)

New edit
I am talking here rather than overwriting the latest edit, by Sbharris. He is right to object to the word 'stored' in reference to chemical bond energy. But I think he is very zealous about it. I think chemical and nuclear bond energies have a logical place in the list from which he removed them. Just not worded so as to make them seem positive by default. Also, I am not over-convinced of a need for a detailed discussion at that point of just how to take positive and negative microscopic potential energies into account. They are not directly macroscopically identifiable as heat or work. Usually, the split into microscopic kinetic and potential energies is outside the scope of macroscopic thermodynamics. Also I note that in the new discussion, the word 'stored' has crept back in.Chjoaygame (talk) 05:10, 24 November 2014 (UTC)
 * I'll take the "stored" out as a generic. And of course the potentials are positive and negative. But surely one can consider some energy as being stored in plutonium-239. The potential there is positive. Put enough of it together and it goes bang. A plutonium atom is like a loaded dart gun, just waiting for a trigger. The energy in TNT is not really stored in particular bonds. Rather, heat it enough or shock it, and some bonds are broken, others are formed, and you get more energy get from the new ones than the old ones. I can point to the electric fields that store the energy in plutonium (these go away when it fissions-- or at least decrease), but you can't do the same thing with TNT. S  B Harris 06:16, 24 November 2014 (UTC)


 * None of this focuses on the concerns I expressed.Chjoaygame (talk) 07:26, 24 November 2014 (UTC)


 * Perhaps I should be more explicit.


 * Your initial edit summary said you were addressing a last-year's talk-page comment that reads
 * mistake
 * It is not right to say: "The potential energy includes all energies given by the mass of particles, by the chemical composition, i.e. the chemical energy stored in chemical bonds"
 * -- you never "store" potential energy in a bond. Potential chemical energy is highest when the atoms are in their free state, any and all bonds represent a subtraction from this.AtomAnt (talk) 18:45, 11 July 2013 (UTC)


 * I think you were right to address that comment, which was itself right. But you have let that expand into a paragraph about nuclear energy, with tutorial material about positive and negative nuclear potential energy moieties.


 * Splitting internal energy into microscopic kinetic and potential energy moieties is usually beyond the scope of macroscopic thermodynamics. Macroscopic thermodynamics is firstly about transfer quantities. The microscopic splitting distracts from that.


 * If you want to introduce details about splitting internal energy into microscopically defined moieties of kinetic and potential energy, perhaps you could introduce a new section for the purpose, though I think it would probably not be a good idea. On 25 Sep 2010, Editor Kbrose removed a now inaccessible table that purported to show the "composition" of internal energy. In effect your edits seem to be re-introducing the idea that underlies that table.


 * I don't want to overwrite you, but to make myself clear perhaps that may be better than too much talk here.Chjoaygame (talk) 20:11, 24 November 2014 (UTC)


 * With respect, done.Chjoaygame (talk) 00:40, 25 November 2014 (UTC)

Contradiction
This article contradicts itself. In the definition:

In thermodynamics, the internal energy of a system is the energy contained within the system, including the kinetic energy of motion of the system as a whole and the potential energy of the system as a whole due to external force fields.

and in the section "Description and definition":

''Internal energy does not include the energy due to motion or location of a system as a whole. That is to say, it excludes any kinetic or potential energy the body may have because of its motion or location in external gravitational, electrostatic, or electromagnetic fields.''

The latter is correct, IMHO, or at least the more usual definition. In many cases it doesn't matter, though, if you are only considering $$\Delta U$$ for some process not depending on external potentials. --Feldkurat Katz (talk) 19:30, 21 April 2017 (UTC)
 * I just noticed that "including" is a recent edit from an IP, so I have reverted it. --Feldkurat Katz (talk) 21:49, 21 April 2017 (UTC)

Initial Definition of Internal Energy - Difficulty
The article starts by saying, "In thermodynamics, the internal energy of a system is the energy contained within the system, excluding the kinetic energy of motion of the system as a whole and the potential energy of the system as a whole due to external force fields."

--> A difficulty I have with the phrase "energy contained within a system" leaves one thinking of the myriad of forms of energy that the definition does not exclude. I think the definition should state the only form of energy to be included is internal kinetic energy of the molecules, and then explain other forms of energy that are excluded for clarity. I am tempted to edit the initial statement to say:

"In thermodynamics, the internal energy of a system is primarily (and for ideal gasses, entirely) a measure of the the sum of current kinetic energy of the molecules within the system boundary, where movement is considered relative to an internal reference point. The measure is not strictly a measure of E = mV2 due to effects of inter inter-molecular forces of closely spaced molecules, or where molecules have complex shapes.

Some forms of energy excluded from the concept of internal energy are:
 * Potential energy of the system as a whole due to its position in a gravity, electric, or magnetic field
 * Kinetic energy of the system as a whole due to the movement of the system relative to an external reference point
 * Embodied energy in the molecular mass; E = mC2

Internal energy does not include potential changes such as:
 * Potential internal chemical reactions of the constituent molecules. e.g., a mix of H2 and O2 ignores what would occur if we create H20
 * Potential chemical reactions of the constituent molecules with external molecules
 * Potential changes in molecular position or arrangement due changes in externally applied electric or magnetic fields
 * Potential molecular movement due to electron or proton exchanges at interface points with charged plates
 * Potential deformation of the boundary that has not yet occurred.

Thermodynamics is deeply involved with these forms of energy, but in general they are not part of the basic concept of current internal energy until a change in molecular movement has occurred." 73.34.109.242 (talk) 14:51, 31 August 2018 (UTC)JJH


 * No, most of this is false. internal energy is a concept that includes all energy inside the system, that is without the need for any external reference points. The name is quite properly chosen. If you had a container of just energy to start with to make a new system, it is that energy that is needed to remake the entire system, its atoms, molecules, interactions, and whatever is needed to create the exact state of the system.  In thermodynamics, however, most of all that is not of interest, it is always constant for the processes covered, and is therefore never accounted for.  In addition, processes of thermodynamic interest always involve only changes in internal energy; the absolute value therefor never matters, and the thermodynamicist may choose any reference point that is convenient. The nuclear physicist feels differently about what that reference point should be. Kbrose (talk) 17:22, 16 August 2019 (UTC)
 * Isn't OP's point more that the definition should make clear that it isn't just 'the kinetic energy of motion of the system as a whole and the potential energy of the system as a whole due to external force fields' that is in excluded, but a whole bunch of other things as well? He isn't saying that other forms of energy should be included in the definition, just that it should be made clearer that they aren't. Martijn Meijering (talk) 18:02, 16 August 2019 (UTC)


 * I don’t object to the above ideas being present in the article but I object to them constituting the first paragraph of the lead because it violates Make technical articles understandable.
 * I would prefer to see the first para say something like “In thermodynamics the internal energy of an ideal gas is a property that depends solely on the temperature of the gas. The internal energy of a system ... ... ...” Dolphin ( t ) 21:45, 16 August 2019 (UTC)

macroscopic and microscopic
This edit carries the following cover note: "when it comes to the term thermal energy, it is not needed to distinguish a macroscopic vs microscopy account. T.E. concept is valid and known regardless, but it is the microscopic view that provides a pictorial detail, but this is pretty much true for all thermodynamic properties."

Many standard texts of macroscopic thermodynamics do not use the phrase 'thermal energy', though it is occasionally used, perhaps loosely, in that subject, for example by Maxwell. Macroscopic thermodynamics texts routinely write of internal energy and its Legendre transforms. Those macroscopic energies express sums of microscopic potential and kinetic energies, a distinction not directly available in macroscopic thermodynamics; this is why heat and work are distinguished but not separately conserved. In macroscopic thermodynamics, temperature is a derivative of macroscopic energy with respect to macroscopic entropy.

Statistical mechanics works with microscopic information when it is available. It routinely distinguishes microscopic potential and kinetic energies. It uses the term 'thermal energy' to refer specifically to microscopic kinetic energies. In statistical mechanics, temperature is measured by microscopic kinetic energy per degree of microscopic freedom. This is now recognised by use of the Boltzmann constant to define the magnitude of the kelvin.

There is an analogy between macroscopic entropy and number of degrees of microscopic freedom per mole.Chjoaygame (talk) 19:56, 30 October 2019 (UTC)

Reasons for undo of faulty good faith edit
I have undone |this edit. It was a good faith edit but it was faulty. The faults were as follows.

Thermodynamic work is always by mechanisms by which the system can spontaneously do work on its surroundings. Work done by the surroundings on the system, such as the edit proposed, is not necessarily received by the system as thermodynamic work. For example, Joule's experiment, in which the surroundings do mechanical work, agitating a paddle, transfers energy to the system as heat, not as thermodynamic work. This is why Joule's experiment is said to measure the mechanical equivalent of heat.

A process does not introduce heat to a system; it introduces energy as heat.

The mathematical notation used in the edit differed from that used in the body of the article.Chjoaygame (talk) 09:13, 15 June 2020 (UTC)

Definition clarification
In section "Description and definition" the following statement appears to be unclear:

"Statistical mechanics considers any system to be statistically distributed across an ensemble of N microstates. Each microstate has an energy Ei and is associated with a probability pi. The internal energy is the mean value of the system's total energy, i.e., the sum of all microstate energies, each weighted by their probability of occurrence:
 * $$U = \sum_{i=1}^N p_i \,E_i\ .$$"

The expression represents the mean microstate energy. In this context it cannot be "... the mean value of the system's total energy". --Gozo032 (talk) 10:33, 9 August 2020 (UTC)


 * Agreed that the statement is dubious. It is an attempt to cram a complicated definition into few words; something that cannot be readily done. The lead is already long. Not the place for the more complicated statistical mechanical definition.Chjoaygame (talk) 11:05, 9 August 2020 (UTC)


 * The $$E_i$$ here denote total microstate-defined system energies, that can vary as microscopic quantities of heat come into and out of the system.Chjoaygame (talk) 11:17, 9 August 2020 (UTC)


 * [removed as noncontributive] Clarifications by Chjoaygame appreciated. (talk) 11:55, 9 August 2020 (UTC)


 * Yes, here 'microscopic configuration' means 'configuration as described through its microscopic constituents'. I think the usage is established, and I wouldn't try to 'correct' it. The English language is not compositional.Chjoaygame (talk) 01:05, 10 August 2020 (UTC)

Missing $$n$$ in $$ d U = C_V d T $$
In section  Internal energy of the ideal gas  we have $$ U = C_V n T, $$ whereas in section Changes due to temperature and volume we have $$ d U = C_V d T $$. Is this a different definition of $$ C_V $$ or am I missing something? Mungbean (talk) 14:22, 11 March 2021 (UTC)


 * I think you are right to bring attention to this.


 * Current internet IUPAC
 * Heat capacity, $$C$$
 * Heat brought to a system to increase its temperature divided by that temperature increase. At constant volume $$C_V = (\frac{\partial U}{\partial T} )_V$$, at constant pressure $$C_p = (\frac{\partial H}{\partial T})_p$$, where $$U$$ is the internal energy and $$H$$ the enthalpy of the system.


 * specific heat capacity, $$c$$
 * Heat capacity divided by mass.


 * Atkins & de Paula 8th edition (2006), page 39
 * The molar heat capacity at constant volume, $$C_{V,\mathrm m} = C_V/n$$, is the heat capacity per mole of material, and is an intensive property (all molar quantities are intensive). ... For certain applications it is useful to know the speciﬁc heat capacity (more informally, the ‘speciﬁc heat’) of a substance, which is the heat capacity of the sample divided by the mass, usually in grams: $$C_{V,\mathrm s}=C_V/m$$.


 * Adkins 3rd edition (1983), page 6
 * It is often convenient to refer to extensive quantities in terms of their values per unit mass of the system. They are then called specific variables. Often, extensive variables are represented by capital letters and the derived specific quantities by the corresponding small letter. Thus, the volume of unit mass is called the specific volume and is given the symbol $$v$$.


 * Another useful convention is to add a suffix $$m$$ to an extensive quantity when the amount of substance referred to is one mole. Thus, $$C_p$$ is the heat capacity at constant pressure (unit, J K-1) and $$C_{mp}$$ is the molar heat capacity at constant pressure (unit, J K-1 mol-1). The molar suffix is frequently dropped if there is no danger of confusion.
 * Is there a danger of confusion here? Evidently, yes.Chjoaygame (talk) 22:00, 11 March 2021 (UTC)

Edits from 17 September 2021
I see that the edits from the previous day re mass transfer have been reverted using the claim of a presumed banned user. This is an absurd situation.--178.138.192.192 (talk) 11:05, 18 September 2021 (UTC)

The reverting editor seems to have reverted to a state of the article which uses nonstandard terminology "matter transfer" instead of the standard name mass transfer.--178.138.192.192 (talk) 11:10, 18 September 2021 (UTC)

I see that the presumed banned user is user:Incnis Mrsi. Definitely I am not him. I have been confounded.--178.138.192.192 (talk) 00:15, 20 September 2021 (UTC)

new edit of 21:37, 15 August 2022
I refer to a new edit https://en.wikipedia.org/w/index.php?title=Internal_energy&type=revision&diff=1104599545&oldid=1104487599

Thank you, editor JoKalliauer, for your edit. Your edit summary reads "(unreferenced, and imho more confusing. The potential energy of parts in the system is included)".

References in the lead are not quite the same as references in the body of the article, which may be demanded to be sentence by sentence or clause by clause, or even word by word. In this case the relevant references are and they refer jointly to the two preceding sentences.

It is not clear to me what you mean by "The potential energy of parts in the system". Please would you clarify exactly what you mean by that?Chjoaygame (talk) 01:31, 16 August 2022 (UTC)

I agree with you that the words "including the energy of displacement of the surroundings of the system" are not too clear. I have long been unhappy with them, and I would be happy to see them removed.Chjoaygame (talk) 01:36, 16 August 2022 (UTC)


 * I mean if a particle (e.g. a atom) within a closed system in an NVE-ensemble moves and changes the potential energy and increases the kinetic energy. Both the potential as well as the kinetic energy of this particle are part of the internal energy.
 * I do not mean the potential energy of the closed system regarding to the outside.
 * I do not mean the potential energy of the closed system regarding to the outside.


 * Lets see the German version:

"In the presence of external fields ( e.g. electric field, magnetic field, gravitational field ), the potential energy that the particles have in relation to a fixed point relative to the system is often also included."


 * Example: If you look at the earth moving around the sun, and the earth is one object. The kinetic energy of the earth rotating around the sun is not part of the internal energy, but a car driving on the earth is part of the internal energy of the earth.


 * I allowed myself to add the book-titles to your references I hope it is okay., if not revert or correct.


 * — Johannes  Kalliauer  - contrib. 14:17, 17 August 2022 (UTC)


 * I was hoping to make progress by talking on the talk page. But that didn't work. For the present, I will retire.Chjoaygame (talk) 22:23, 17 August 2022 (UTC)


 * Did I say something wrong?  — Johannes  Kalliauer  - contrib. 14:51, 18 August 2022 (UTC)


 * Thermodynamics is not a universal account of all of nature. It is a topic with defined scope, dealing with thermodynamic systems and processes. A thermodynamic system is in its own state of internal thermodynamic equilibrium. The earth moving around the sun, with motor cars driving around on it, is not in its own state of internal thermodynamic equilibrium. As a matter of fact, the earth is subject to solar radiation coming in and infrared radiation being emitted, nothing like a thermodynamic equilibrium.Chjoaygame (talk) 11:59, 11 January 2024 (UTC)

On consistency in the section on U for the ideal gas
The symbol "C_V" is usually the (non-molar) isochoric heat capacity (see eg. the next section following this and the article on heat capacity), so to be consistent it seems preferable to add "m" or ",m" in the subscript. One might argue that the definition of U(S,V,n) then would become very cluttered, so an alternative is to use lower case "c" (ie. c_V) to be at least internally consistent in the use of "C_V" in the article. The symbol "n" is usually number of moles (and that seems to be the convention in this article also), but then suddenly it is stated that it means mass in the 3rd(?) paragraph in the section in question; of course #moles and mass are not unrelated, but I think it should say something along the lines of "moles of particles" unless I'm missing something. Finally, in the definition of U(S,V,n) for IG: how can a dimensionful quantity such as "V" or "n" be raised to a non-integer power? 2A01:799:952:4500:9C23:942B:FA7:4A29 (talk) 20:05, 9 January 2024 (UTC)


 * This does need attention and fixing.Chjoaygame (talk) 11:51, 11 January 2024 (UTC)