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Does anyone know what "external energy" is then? Is that enthalpy? Or am I making words up? -- postglock 07:41, 24 October 2005 (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).
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)
I have made major changes to the sections following the introduction. The main problems were:
PAR 01:49, 26 April 2006 (UTC)
It is written here that
I tried to check it for a monoatomic ideal gas in 3D, and saw that it is not true. IT is true only for
so:
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
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)
"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
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?
The following is clearly wrong, since it provides a definition which is both circular and contradictory:
How should it be worded to make it correct? -- Starwed 07:18, 20 June 2007 (UTC)
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)
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.
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 (+).
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)
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)
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 H arris 22:37, 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 H arris 02:02, 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 H arris 20:31, 28 February 2010 (UTC)
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)
This subheading is intended to seperate the related discussions of split and disambiguation. Added by Riick ( talk) 20:01, 24 September 2010 (UTC)
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)
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)
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)
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)
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)
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"
The second one appears in the fourth paragraph:
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
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)
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 for some process not depending on external potentials. -- Feldkurat Katz ( talk) 19:30, 21 April 2017 (UTC)
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:
Internal energy does not include potential changes such as:
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
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)
I have undone . 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)
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:
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)
In section Internal energy of the ideal gas we have whereas in section Changes due to temperature and volume we have . Is this a different definition of or am I missing something? Mungbean ( talk) 14:22, 11 March 2021 (UTC)
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)
I refer to a new edit https://en.wikipedia.org/?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 [1] [2] 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)
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.
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)
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Does anyone know what "external energy" is then? Is that enthalpy? Or am I making words up? -- postglock 07:41, 24 October 2005 (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).
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)
I have made major changes to the sections following the introduction. The main problems were:
PAR 01:49, 26 April 2006 (UTC)
It is written here that
I tried to check it for a monoatomic ideal gas in 3D, and saw that it is not true. IT is true only for
so:
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
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)
"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
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?
The following is clearly wrong, since it provides a definition which is both circular and contradictory:
How should it be worded to make it correct? -- Starwed 07:18, 20 June 2007 (UTC)
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)
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.
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 (+).
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)
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)
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 H arris 22:37, 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 H arris 02:02, 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 H arris 20:31, 28 February 2010 (UTC)
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)
This subheading is intended to seperate the related discussions of split and disambiguation. Added by Riick ( talk) 20:01, 24 September 2010 (UTC)
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)
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)
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)
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)
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)
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"
The second one appears in the fourth paragraph:
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
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)
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 for some process not depending on external potentials. -- Feldkurat Katz ( talk) 19:30, 21 April 2017 (UTC)
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:
Internal energy does not include potential changes such as:
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
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)
I have undone . 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)
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:
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)
In section Internal energy of the ideal gas we have whereas in section Changes due to temperature and volume we have . Is this a different definition of or am I missing something? Mungbean ( talk) 14:22, 11 March 2021 (UTC)
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)
I refer to a new edit https://en.wikipedia.org/?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 [1] [2] 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)
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.
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)