# Talk:Thermodynamics

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## "Average" properties

The opening of the current version of the article has (1st line): - ...defines macroscopic variables (such as temperature, internal energy, entropy, and pressure) that describe average properties of material bodies and radiation,... Some of the properties listed do not have average values, they are intensive properties i.e. they are local e.g. temperature.

I propose to remove (soon!) the word average from the above quotation. --Damorbel (talk) 07:39, 30 November 2012 (UTC)

That seems reasonable to me. Indeed I would go further and remove the words 'average properties of'. The words 'properties of' add nothing to the meaning, and indeed are pleonastic to a fault. I think "...defines macroscopic variables (such as temperature, internal energy, entropy, and pressure) that describe material bodies and radiation,...' would be better.Chjoaygame (talk) 12:10, 30 November 2012 (UTC)
Hmmmm! How is it that "The words 'properties of' add nothing"? Are temperature and pressure not properties? I agree they are not the complete properties. As for "variables", surely these are descriptors in e.g. equations - not properties as in properties of materials
There is a further problem here (line 4):-
Thermodynamics does not describe the microscopic constituents of matter, and its laws can be derived from statistical mechanics.
Agreed, thermodynamics does not describe the microscopic constituents of matter. Again, far too general. Surely it would read better as:-
Thermodynamics describes the microscopic and macrosopic properties of energy in matter, and its thermodynamic laws, which may be derived from statistical mechanics.
Surely putting a description of what Thermodynamics is not, must be seen as unnecessarily rather global! --Damorbel (talk) 12:44, 30 November 2012 (UTC)

### response by Waleswatcher

Temperature is of course an average property. For instance in a gas, it is proportional to the average kinetic energy per molecule. In radiation, it is related to the average frequency of the photons. But a randomly chosen individual particle or collection of particles will not have precisely that average energy. Waleswatcher (talk) 14:10, 30 November 2012 (UTC)

How can temperature possibly be an average property? If it was why is there a need for global temperature maps when discussing climate? (See the first drawing in the 'temperature' link.)
I suggest you haven't looked at the link I gave to Intensive properties. Please comment when you have checked this link. --Damorbel (talk) 14:23, 30 November 2012 (UTC)
I'm fully aware of the meaning of "intensive", Damorbel. I'm a professional physicist and use the terms every day. Intensive quantities in thermo are precisely averages (rather than, say, totals). In the case of T, again, it's the average kinetic energy per molecule. Think for a minute - does every molecule in a container of gas have exactly the same kinetic energy at all times? Obviously not - and yet we characterize a huge collection of molecules by one number, T. Clearly, it's an average. Waleswatcher (talk)
Waleswatcher, did you look at my link? In the thermodynamics article the word average is used far too loosely. What you probably mean is equilibrium temperature, which is the temperature given by the average energy of the particles in a thermal system in equilibrium. What you should know is that a (single) temperature cannot be assigned to a system that is not in equilibrium. --Damorbel (talk) 14:49, 30 November 2012 (UTC)
Your link points to "planetary equilibrium temperature", which is not what we are discussing. We are discussing plain old temperature, which indeed is strictly only defined for equilibrium ("planetary equilibrium temperature" is an example of how one might try to define it away from equilibrium). In any case, since you say "the temperature given by the average energy of the particles", it seems you now agree that temperature is in fact an average? Waleswatcher (talk) 17:26, 30 November 2012 (UTC)
Indeed "planetary equilibrium temperature" is not immediately relevant, that is something for advanced students.
But you seem not to be fully aware of the meaning of "intensive quantities"? Or the meaning of temperature. A temperature can only be defined for a system in equilibrium, a system not in equilibrium has two or more temperatures, the requirement for a single temperature being that the particle energy has a Maxwell Boltzmann distribution
Of course, as I remarked before, the temperature of a thermodynamic system is independent of the size of the system; rather intuitive don't you think? This drives one to the logical conclusion that the smallest system that can have a temperature is a system comprising only one particle!
The meaning of the Maxwell Boltzmann distribution (an important thermodynamic concept) is statistical of course; (possibly from statistical mechanics - do you think?) In a Maxwell Boltzmann distribution the particles have an equal probability of accessing the system states. --Damorbel (talk) 19:58, 30 November 2012 (UTC)

### response by Chjoaygame

There are various viewpoints about temperature. One view, from statistical thermodynamics, is put by Balescu, R. (1975), Equilibrium and Nonequilibrium Statistical Mechanics, Wiley–Interscience, New York, ISBN 0-471-04600-0, on page 43. He writes: "... we cannot define the temperature as an average of a microscopic function taken with an arbitrary distribution function [as implied by Eq. (2.2.4)]: It rather appears as a parameter characterizing the particular distribution function describing the system in thermal equilibrium. He adds in a footnote that the statement of temperature as an average kinetic energy for an ideal gas is correct, but that it is not a definition. Another source might be Chapman, S. Cowling, T.G. (1939/1970), The Mathematical Theory of Non-Uniform Gases. An Account of the Kinetic Theory of Viscosity, Thermal Conduction and Diffusion in Gases, Cambridge University Press, Cambridge UK. They give several discussions of the difference in formal status between the thermodynamic and the kinetic theory of gases definitions of temperature, and proceed to examine how far they give coincident physical results. For the case of mixtures of rare gases, they say on page 8 of the third edition that "The kinetic theory is able to give a fairly satisfactory affirmative answer to this question (4.3), to this extent justifying its procedure as regards temperature definition." They then discuss how this may relate to temperatures for processes involving materials other than gases.

Dear Damorbel, by the way, you write above "... the Maxwell Boltzmann distribution (an important thermodynamic concept)..." This is not in accord with the views of some sources on thermodynamics who take a viewpoint different from the pedagogical strategy, for example, of Kittel & Kroemer and of Reif. The viewpoint of Adkins, C.J. (191968/1983), Equilibrium Thermodynamics, Cambridge University Press, Cambridge UK, ISBN 0-521-25445-0, may be summarized by the following from page 2 of the third edition: "The laws of thermodynamics enable us to interrelate the macroscopic quantities without making any microscopic assumptions at all. The great generality of thermodynamics is a direct consequence of this."Chjoaygame (talk) 03:12, 1 December 2012 (UTC)

#### response by Damorbel

Chjoaygame, I have looked at your ref. "Another source might be Chapman, S. Cowling," and I find what they say on p36 ff. under definitions and theorems section 2.4.1 - Temperature. In this section you will find what I am arguing is the theoretical basis for the concept of temperature. At the bottom of p37 last paragraph, it has:-
The kinetic theory definition of temperature, being applicable whether or not the gas is in a uniform or steady state, is more general than that of thermodynamics and statistical mechanics, where only equilibrium states ... etc., etc.
Now this is your ref. and I recommend its definition of temperature to you (to get a proper idea you will need to read the complete section). With such a definition I suggest the article may be considerably improved. --Damorbel (talk) 12:57, 1 December 2012 (UTC)
You will also be pleased that the (upper) section (2.4) of your ref. provides a definition of Heat that also will improve the Heat article. On p36, section 2.4, it has :-
Heat - The amount of translatory kinetic energy possessed by the molecules in the element r,dr at time t ... etc., etc. --Damorbel (talk) 13:19, 1 December 2012 (UTC)
Chjoaygame, your ref. is also very good on the conservation of energy and momentum, the basis of the thermodynamic laws. Care to comment? --Damorbel (talk) 14:00, 1 December 2012 (UTC)
• I don't have that reference, but unfortunately neither heat nor temperature can be defined generally in terms of kinetic energy, because that's not the case for all systems. Thermal and statistical physics is much more powerful and general than that. For instance there are well-studied systems in which the temperature is negative. Still, in most familiar cases the "temperature is average kinetic/vibrational/rotational energy per molecule" is true, and can and should be used as an example in these articles. Waleswatcher (talk) 13:47, 1 December 2012 (UTC)
Chjoaygame's ref. can be seen here:- http://www.amazon.com/Mathematical-Theory-Non-uniform-Gases-Conduction/dp/052140844X/ref=sr_1_1?s=books&ie=UTF8&qid=1354362881&sr=1-1&keywords=The+Mathematical+Theory+of+Non-Uniform+Gases.+An+Account+of+the+Kinetic+Theory+of+Viscosity%2C#reader_052140844X --Damorbel (talk) 14:00, 1 December 2012 (UTC)
Chjoaygame' you write above:-
"... the Maxwell Boltzmann distribution (an important thermodynamic concept)..." This is not in accord with the views of some sources"
If you read chapter 3 in your Chapman ref. (THE EQUATIONS OF MAXWELL AND BOLTZMANN) you will find an extensive explanation of just why the Maxwell-Boltzmann distribution is fundamental to thermodynamics and why it must be recognised as such. --Damorbel (talk) 14:27, 1 December 2012 (UTC)
• Waleswatcher is right, Damorbel, when he refutes your comment and writes as above: "...neither heat nor temperature can be defined generally in terms of kinetic energy, because that's not the case for all systems ..." As you may see, the kinetic theory of gases definition of temperature is specific for that theory, which is about gases, while, as I have noted several times, though it seems to have escaped your eagle eye, the kinetic theory of gases has not much to say about liquids or solids. The greater generality claimed by Chapman & Cowling is that they refer to a gas not in equilibrium, but their definition does not extend to non-gaseous materials. As I recall, you are habitually very keen to insist that temperature belongs only to an equilibrium state. It is inconsistent of you now to crow about a definition of temperature that claims to be for a non-equilibrium state.
Dear Damorbel, you are lost, not aware of which article you are writing in. You are trying to put the kinetic theory of gases definition into the article on thermodynamics. The thermodynamic definition is primary in an article on thermodynamics; the Chapman & Cowling book on the kinetic theory of gases carefully notes that thermodynamics does not rely on the kinetic theory of gases definition of temperature. Your enthusiasm here shines a light on how you persistently fail to look at context, and so your thoughts are muddled. And you want to drag us into your muddle with you. You endlessly and petulantly demand that we attend to your comments, but, sad to say, they are mostly merely repetitive, and you endlessly fail to hoist in the responses we offer you.Chjoaygame (talk) 14:52, 1 December 2012 (UTC)
Chjoaygame, you write above:-
the Chapman & Cowling book on the kinetic theory of gases carefully notes that thermodynamics does not rely on the kinetic theory of gases definition of temperature
Oh really? Just where is this noted?
So when I see in your ref. Chapman & Cowling on page 37 section 2.4.1 "The temperature T of a gas in a uniform steady state at rest or in uniform translation is defined directly in terms of the peculiar speeds of the molecules, by the relation $\displaystyle \frac 1 2 mv_{rms}^2 = \frac 3 2 k T.$
where k is a constant, the same for all gases, whose value will be assigned later; it is called the Boltzmann constant."
For you, that this is the kinetic definition of temperature is merely an illusion peculiar to me? --Damorbel (talk) 17:45, 1 December 2012 (UTC)
It seems you feel entitled to demand of us that we spoon feed you every word of the way. You have skimmed C & C with your usual selective blindness, passing over the parts that don't suit your fancy. You seem unable to read and pick up related context for yourself, apparently because of your burning and fixed need to see the kinetic theory of gases as the only theory that can define temperature, ignoring its very restricted scope. You seem to feel entitled to demand of us that we spend unlimited time of ours feeding you the information left out by your lack of skilful reading. Should I apologise in advance that the spoon I feed you with is not a silver one?
For obvious copyright reasons, I cannot here quote in full every word that is needed to satisfy your feeling of entitlement. If you want to find out the full meaning of the material in the book you will need to get the contexts by actually reading and thinking about it for yourself.
You have already quoted in italics above the following sentence: "The kinetic-theory definition of temperature ... is more general than that of thermodynamics and statistical mechanics ..." This is making it clear, at least to someone who is not purblinded by a fixed idea to the contrary, that the kinetic-theory definition is not the thermodynamic definition; they are distinct, and C & C are saying that there is an onus of proof for someone who wants to make them equal to one another. Your failure to read context is exemplified by your misleading quote above, "The temperature T of a gas in a uniform ...", from which you left out the important preparatory context "... in theoretical work they use the absolute temperature of thermodynamics. In the kinetic theory, on the other hand, ..." which makes it clear that the kinetic-theory and the thermodynamic definitions of temperature are distinct.
As Waleswatcher has patiently and kindly noted for you above, the kinetic-theory idea of heat is not adequate for materials not covered by the kinetic theory of gases, and is therefore not adequate as a general definition of heat.
I have to ask myself, 'is Damorbel just playing with me, to see how much of my time he can lure me into wasting?' I now feel entitled to say that you have exhausted my patience.Chjoaygame (talk) 19:32, 1 December 2012 (UTC)
Chjoaygame, your argument making a distinction between kinetic theory for gases, and heat energy in liquids and solids, fails because the energy contained in freely coliding gas molecules (particles) is exactly equal to that in the various degrees of freedom in molecules subject to intermolecular forces such as solids, liquids, crystals, vibrating gas molecules such as CO2 and H2O etc. All particles in an equilibrium system, molecules in gases, liquids and solids, electrons confined in a conduction band (but not quantum confined electrons in an atom), have equal amounts of thermal energy, explained by a theorem called the equipartition theorem.
Your ref. book is useful on equipartition, try p.80 section 4.3, or the index. The equipartition theorem is an important theorem in understanding particle thermal physics. Failure to take this theorem into account is making a complete mess of the thermodynamics article , the heat article and the temperature article. --Damorbel (talk) 21:35, 1 December 2012 (UTC)
PS You may not be aware of it but the concept of the equipartition theorem is the same as the fundamental postulate in statistical mechanics, I suspect a distinction created by academics seeking to expand their field of research!--Damorbel (talk) 09:21, 2 December 2012 (UTC)

#### response by Waleswatcher

The true definition of temperature is T=dE/dS. But since both E and S (contrary to PAR) are defined by averages and/or expectation values, T is an average quantity too. Regarding language - "constituents" or "particles"? The former is more accurate and general, but the latter may be better as it is more familiar and clear. Waleswatcher (talk) 04:00, 1 December 2012 (UTC)
Waleswatcher, you write:
The true definition of temperature is T=dE/dS.
I would very much like an explanation of this, what do you have? --Damorbel (talk) 15:29, 5 December 2012 (UTC)
Balescu, as quoted just above, is not alone in the view that in statistical mechanics, the temperature is a parameter of a distribution. Fowler, R., Guggenheim, E.A. (1939, reprinted 1965), Statistical Thermodynamics. A version of Statistical Mechanics for Students of Physics and Chemistry, Cambridge University Press, Cambridge UK, on page 38 write [their italics]: "Thus θ is a parameter helping to define the state of our assembly which must have the same value for all sets of systems in the assembly." The same view is proposed by Tolman, R.C. (1938), The Principles of Statistical Mechanics, Oxford University Press, London, who writes on page 563: "...the parameter θ characterizes only the particular kind of ensembles, with canonical distribution, which we use to represent systems in thermodynamic equilibrium." The kinetic theory of gases, which explicitly defines its own version of temperature as an average kinetic energy, and as distinct from thermodynamic temperature, is closely related to statistical mechanics, but applies mainly to gases, without much consideration of liquids or solids.Chjoaygame (talk) 05:03, 1 December 2012 (UTC)
As is often the case, Chjoaygame, I can't tell what the point of your comment is. I disagree with nothing in your last comment, and nothing in your last comment disagrees with anything I wrote here. Waleswatcher (talk) 09:50, 1 December 2012 (UTC)

## Proposal to community topic-ban User:Damorbel

After his latest efforts at Talk:Boltzmann constant I've made a proposal at WT:PHYSICS that User:Damorbel be community topic-banned from further editing articles and talk pages related to thermodynamics.

The views of those who've interacted with him on this talk page would be useful, since he appears to have edited here extensively as well. Jheald (talk) 21:45, 8 December 2012 (UTC)

## Thermodynamics of small systems

How about including a section with this title? Thermodynamics only applies in the limit of number of constituents goes to infinity (the thermodynamic limit). As systems get small, the laws of classical thermodynamics break down and other equations have to be used instead. Quantities that are constant in classic thermodynamics become stochastic variables (right?). I think that a section discussing this would help make the transition between the behavior of single molecules and that of macroscopic systems clearer (I would certainly appreciate it).

For references, Hill's classic "Thermodynamics of small systems" is almost impossible to obtain. I have found an open access article by John Rowlinson, whose authority cannot be doubted, however it is not as focussed as I'd like. I also found a nice little open access article in PNAS on the thermodynamics of single protein molecules. We need some better candidates, IMHO. Surely there must be a recent review?

What do you think of this idea? AlanParkerFrance (talk) 10:58, 6 January 2013 (UTC)

For my part I suggest it may be difficult to define what a small thermodynmic system is. Thermodynamics is the physics of particles and their interactions, the relevant physical interactions are independent of the systen size. Obviously as the sample size decreases the variation in the measurements such as e.g. pressure must deviate increasingly from the mean. For pressure this variation shows up as random accoustic noise. --Damorbel (talk) 12:04, 6 January 2013 (UTC)

## branch of physics

Here editor 86.158.238.108 has changed the overarching subject named from natural science to physics. I am indifferent about this, but I note that some would say that thermodynamics is also a branch of chemistry and some might say that it is also a branch of engineering. The link to natural science was there for that reason. I have no intention of trying to change the overarching subject named. I don't know if anyone else cares about it.Chjoaygame (talk) 01:07, 6 November 2013 (UTC)

I have reverted that change. You are right. --Bduke (Discussion) 02:16, 6 November 2013 (UTC)

## surroundings and environment

There is a new edit by Editor Zedshort that changes the word 'surroundings' to the word 'environment', with links to an article Environment (systems). That article is more like a dictionary entry than an encyclopaedia article. The sole reference in that article is to Richard Dawkins, not a book about thermodynamics.

The cited references in the present article on thermodynamics are Guggenheim and Kondepudi. On page 9, Guggenheim writes "... the rest of the universe (its surroundings)" twice. On page 4, Kondepudi writes "... dividing the world into a 'system' and its 'exterior'". Looking a little further, I find Bailyn on page 20 writing of a "uniform environment". I find Adkins on page 4 writing that "Everything outside the system is called the surroundings". I find Callen on page 15 writing of the "“walls” that separate it [the system] from its surroundings." Planck on page 114 writes of "such changes in the surrounding medium". On page 108, Pippard writes "If the system is open to the surroundings ...". On page 127 Partington writes: "All things outside the system are spoken of as external bodies. ... so that no heat or work can be exchanged with the surroundings." Kirkwood & Oppenheim on page 1 write "The surroundings are the rest of the physical world. ... An isolated system has no interactions with the surroundings." On page 6, the translator of Münster writes "A system is called closed when it can exchange energy with its surroundings but cannot exchange matter ..."Chjoaygame (talk) 22:24, 12 January 2014 (UTC)

## article structure comment in Introduction

The end of the Introduction section has the following statement

"The present article takes a gradual approach to the subject, starting with a focus on cyclic processes and thermodynamic equilibrium, and then gradually beginning to further consider non-equilibrium systems."

Is it right to describe an Encyclopedia article as if it is a textbook chapter? J mareeswaran (talk) 13:17, 22 August 2014 (UTC)