Talk:Internal energy

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

message: 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)
replies: text: Cleaned per request.--Sadi Carnot 19:28, 25 April 2006 (UTC)
thread_title: "Body or system with well defined boundaries"

message: I have made major changes to the sections following the introduction. The main problems were:
* 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 ΔU).
PAR 01:49, 26 April 2006 (UTC)
thread_title:  Major Changes 

message: 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:
#It should be cleared that the \mu N  term is mandatory.
#This erise the question of how much this expression is usefull (and indeed, I don't recall ever using it). 
eman 13:30, 2 June 2006 (UTC)
replies: text: 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)
replies: text: 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)
thread_title:  U=TS-PV? 

message: 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)
replies: text: 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)
thread_title:  Why is the rest mass not part of the internal energy? 

message: 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)
thread_title: Does potential energy of fields count or not?

message: 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)
thread_title:  Contradiction through bad wording 

message: 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)
thread_title:  Serious problems with this article 

message: *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.
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.
*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)
thread_title:  Internal energy 

message: 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)
thread_title:  Internal energy? Dead simple, it is ...... 

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

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

message: 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)
thread_title: Thermal energy

message: 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)
replies: text: 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)
replies: text:  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)
thread_title: Latent Heat

message: 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)
replies: text: 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)
thread_title:  The first law of thermodynamics 

message: 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)
thread_title: composition of internal energy

message: 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)
thread_title: add a section?

message: 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)
thread_title: mistake

message: The second one appears in the fourth paragraph:
::"The other cardinal function of state of a thermodynamic system is its entropy, as a function, , of the same list of extensive variables of state, except that the entropy, , is replaced in the list by the internal energy, .<Callen, H.B. (1960/1985), Thermodynamics and an Introduction to Thermostatistics, (first edition 1960), second edition 1985, John Wiley & Sons, New York, ISBN 0–471–86256–8, Chapter 5.><Münster, A. (1970), Classical Thermodynamics, translated by E.S. Halberstadt, Wiley–Interscience, London, , p. 6.><Tschoegl, N.W. (2000). Fundamentals of Equilibrium and Steady-State Thermodynamics, Elsevier, Amsterdam, , p. 17.>"Chjoaygame (talk) 21:22, 20 April 2014 (UTC)
thread_title:  the second one 

message: 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)
replies: text: 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)
thread_title:  Contradiction 

message: 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)
thread_title:  macroscopic and microscopic 

message: I have undone 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)
thread_title:  Reasons for undo of faulty good faith edit 

message: 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)
replies: text: 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)

text: 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)
replies: text: [removed as noncontributive] Clarifications by Chjoaygame appreciated. (talk) 11:55, 9 August 2020 (UTC)
replies: text: 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)
thread_title:  Definition clarification 

message: 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)
thread_title:  Edits from 17 September 2021 

message: 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)
replies: text: This does need attention and fixing.Chjoaygame (talk) 11:51, 11 January 2024 (UTC)
thread_title:  On consistency in the section on U for the ideal gas