Talk:Heat/Archive 8

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WP:BOLD and WP:BRD changes to lede

Since two editors now agree on some aspects of heat, I've made some changes to the lede. There wasn't enough room for a discussion of heat engines, so I left that section to later, since I wanted to put more definitional stuff into the lede. I'm not happy that some yahoos in some text have defined heat transfer in terms of friction (if that is the case) for clearly to me that is a case of mechanical work being turned into plain ordinary thermal energy resulting in a temperature differnce, which then causes heat to flow in the standard way. Talking of such indirect methods of heating things only confuses the issue. You MUST have a temperature, or else heat makes no sense (and cannot be defined), and indeed you must have a temperature DIFFERENCE or else entropy does not increase with heat flow and the second law of thermodynamics then makes no sense. So let's keep this simple, at least in the lede, okay? Truthfully, I wish the lede only directly mentioned conduction, convection and radiation as modes of heat transfer.

I've also finessed the question of whether or not latent heat is a part of thermal energy, as some texts say yes and some say no. Since most engineering texts have vapor-deposition as part of heat transfer (indeed the previous paragraph alludes to this) and heat is a transfer of thermal energy, I would certainly hope that latent heat qualifies as a type of thermal energy. It certainly is extractable from systems as ordinary heat, so it would be weird indeed if this type of energy which can be extracted thermally (by a temperature difference, as when steam condenses) is not to be considered thermal energy.

I've also finessed the bit about whether or not thermal energy is a valid concept (as latent heat or sensible heat or a sum of them). I've just mentioned that both latent and sensibile heat require heat flows and can even be defined as the heat flows that bring each into being, and so there really is therefore no overriding reason to regard them as static quantities (although it's easy to see why many scientists do). That can be discussed later in the paper.

Finally, I wish the last paragraph didn't exist since it takes up space. The dab page should take care of it, and WOULD take care of it, if we redirected "heat" to heat (dab) and renamed THIS science page to heat (physics). SBHarris 19:11, 24 April 2012 (UTC)

objection

I object to your edits for several reasons.

• I think they are too detailed, technical, and long-winded for the lead. I like what you added regarding Q etc., but I suggest moving it down into one of the following sections (perhaps Overview).
• I haven't seen a modern, reliable reference that explicitly states that being able to define a temperature is required to define heat (although I agree adjectives like "thermal" come close). While I'm not saying you're wrong, until such a reference appears and is added, stating so unequivocally constitutes original research. The definition before your edit is taken almost verbatim from Reif and Kittel and Kroemer.

So for now I'm reverting your edits (I first tried just trimming them back, but didn't really see a way to salvage part of what you added). Again, I'm not saying you're wrong, I just think the material needs to be sourced, and that much of it isn't appropriate for the lead. Waleswatcher (talk) 21:21, 24 April 2012 (UTC)

A few slightly more technical comments on this. One of your edits stated that heat is always an energy flow from high to low temperature. While that's true practically, defining it that way cuts strongly against the standard treatment. In the standard treatment, it's perfectly valid to (in fact, thermodynamics is to a large extent based on) consider the reversible limit. But in the reversible case, heat can only flow between two systems at the same T (so that the entropy change of one cancels the entropy change of the other). Indeed, your own edits implied reversibility in that you used dQ=TdS, but that itself only holds true when the two temperatures are equal to T. You can define heat for irreversible processes, but it's strictly less than TdS.

I expect you agree with all that, and simply disagree on the best way to communicate in a wiki article. Let's keep trying - I think (although I'm of course biased) that the article now is far better than it was a week ago. Waleswatcher (talk) 21:47, 24 April 2012 (UTC)

response 1 to objection

I agree with all the points made by Waleswatcher. You can actually construct simple counterexamples against having to be able to define a temperature. Take e.g. a system consisting of two subsystems at different temperatures that are thermally insulated from each other. Obviously, there isn't a problem defining heat and work for this system, yet the system is not in thermal equilibrium, albeit it that you can describe it thermodynamically using two temperatures and two additional variables (e.g the volumes of the two subsystems).

Now, I know that this simple, rather trivial counterexample, will lead to a predictable response (that you can define temperature tof the subsystem to which the heat in some case is actually flowing to).

However, note that in thermodynamics, as treated by modern sources, you are given some thermodynamic system, say a box containing a gas which is is in thermal equilibrium, in which case a temperature is defined for that, or it isn't. If you carve it up into subsystems, then the same logic applies to the subsystems. If you make the definition of heat conditional on somehow being able to carve the system up into ever smaller subsystems and to able to define a temperature (gradient), this becomes an unnecessarily messy way of defining heat. More importantly, it would not be rigorous, and you can then still construct counterexampes where this still won't work. Count Iblis (talk) 22:23, 24 April 2012 (UTC)

response 2 to objection

Wait! I didn't require in my lede definition that there be anything reversible about any heat transfer! Obviously, as ΔT approaches zero, the entropy change in the universe approaches zero when the heat is transfered, and that makes for reversiblity. The magnitude of ΔT is what makes the irreversibility because Q/T_hot for the hot reservoir is larger than Q/T_cool for the cool one, and net entropy is produced in the universe for that process, and since entropy can be made but not destroyed, you're "stuck." That's what we mean by irreversible: you make entropy so you're stuck with it.

The whole point about the direction of heat and the production of entropy is that the entropy loss of Q/T is less for the hot reservoir than the entropy gain Q/T for the cold. The point is that "heat," as a concept, demands a dS = δQ/T for every little δQ. The T's can all be different in your system, so long as there exists a defined T for every little δQ that enters or leaves a dinky control volume in your system, composed of a canonical ensemble of particles. I didn't say that there had to be any thermal equilibrium anywhere! Having a T does not imply thermal equilibrium! But you do need a T that applies to your δQ (a dinky flow, remember) for every place you keep track of a δQ, or else you cannot define a dS, and if you can't define a dS, you can't say what direction the energy is going to flow. The whole point of S is that it's a sort of index for how randomized energy has become in phase-space. You can have transfered energy for which S is zero-- that's work or potential or something, but not heat. The entropy cost dS for a bit of energy moved does not need to be anywhere near as high as E/T-- it can be anywhere between zero and dE/T. But TdS tells you how much of the energy is heat, and all the rest of it, you either know is work already, or (as in a heat engine) you're free to turn it into work if you can figure out how.

So, to recap, heat isn't just energy dE; it's a special type of degraded energy in motion, for which every bit of transfered energy dU or dE has a little T that goes with it to give it an entropy dE/T. That ability to calculate entropy for the dE added or subtracted, is what makes that transfered dE into a δQ, which is to say, into heat. IOW, it is that entropy that tags every bit of transfered thermal energy, that MAKES IT thermal energy (rather than work energy or rest mass energy or some other kind of godforsaken energy). I'm trying to explain in the lead what makes heat energy different from any other type of energy in joules, and this entropy accounting term dS = δQ/T is what does it. But you have to have that T. The T doesn't have to apply to the system (which have have a temperature field that varies in time and space all you like). But these T's DO need to apply to every bit of system that gains or loses thermal energy, or else by definition it's not thermal energy. Heat needs a δQ/T for where the δQ comes from, and another δQ/T for where it goes to. Of course they don't need to be equal. SBHarris 00:55, 25 April 2012 (UTC)

@Sbharris

• Wait! I didn't require in my lede definition that there be anything reversible about any heat transfer!...The point is that "heat," as a concept, demands a dS = δQ/T for every little δQ. I disagree. dS=dQ/T only for reversible processes. Since you used that relation, you did indeed assume reversibility. One example: the (irreversible) free expansion of a gas keeps E and T constant, so clearly ΔQ=0. But ΔS isn't zero since ΔV isn't. If on the other hand the gas expands by the same ΔV, but isothermally against a piston (while in contact with a reservoir at temp T), that is reversible, but in that case ΔQ isn't zero (it's equal to minus the work the gas does on the piston, which equals ΔS*T). In general, heat for irreversible processes is never equal to TdS - it's always strictly less than that.
• I didn't say that there had to be any thermal equilibrium anywhere! Having a T does not imply thermal equilibrium! I disagree. Strictly speaking if T is well-defined, you're in equilibrium.
• TdS tells you how much of the energy is heat No, it doesn't. That's falsified immediately by my example of the free expansion of a gas. Instead, it tells you how much energy would have been heat if the expansion was reversible.

It sounds like we might need to hash some of this out before we can come to a consensus on how to edit the article. In the meantime, can I suggest we stick to strictly verifiable edits, with modern, reliable sources? Waleswatcher (talk) 01:20, 25 April 2012 (UTC)

Having a T does imply thermal equilibrium, at east locally where that T applies. While this sort of an explanation can be used to illustrate what happens when heat can flow into a system, this cannot be used to define heat, because this is just a approximate picture, while the official definition of heat is rigorous and will als work when there isn't even approximately local thermal equilibrium. Count Iblis (talk) 01:20, 25 April 2012 (UTC)

Sbharris response

Clearly I should have qualified my dS as being the entropy change due solely to thermal interaction—that is, energy transfer due to a temperature difference. The lede now talks about “thermal interaction” as though we’re supposed to know what that term means. What it means is, that there’s a temperature difference, and that this energy flow of interest we call “heat” happens SOLELY due to that difference. I put that in, and you removed it. Why? It clarifies things a great deal.

I have no idea what the “official definition of heat” that Count Iblis is talking about, but I do know that the one in the lede now depends on an implicit idea of there being temperatures to cause these energy transfers called “heat” (that’s what “thermal process” MEANS, Count Iblis). So why cover the role of temperature up? Really, it can’t be ignored, much as you’d like to do it.

I do not like the idea that heat can be transferred by “friction” and viscosity, as the lede now says. Friction is a sort of mechanical work, done by a force applied through a distance. Right? Are we going to have a lede that says that heat can be transferred by mechanical work? Talk about confusing! And what the devil is “chemical dissipation”? I don’t mind being reverted if you come up with something better, but this is just pure laziness. And what’s in the lede now does not make much sense.

Perhaps indeed it’s gilding the lilly in the lede to note that such energy transfers that are indeed due to “thermal interaction” (forget friction) ALSO always transfer heat energies (dE) with characteristic entropies associated with them (dE/T) at whatever reservoir has the temperature T (which can be more than one reservoir in a thermal interaction). But this is yet another way of identifying the peculiar nature of the energy that is transferred as heat, and not transferred, or appearing, in some other way (like friction or compression or whatever). When heat is transferred by a temperature difference, it changes entropy by dE/T, and the T is different on each side of the energy transfer. Yes, that means entropy is different, but we said this was irreversible. That is WHY it is irreversible. A great many real heat transfer processes are irreversible for this precise reason, and reversible processes are an ideal used to calculate ideal maximal performances, as for heat engines. But real heat engines never come close to such ideals.

The lead now suggests that heat “transfers entropy” as though entropy were some thing that existed and that could be transferred, like energy. Of course that isn’t true. “Transfer” implies a conserved quantity, not one that increases on its own during the transport. (In the same way, we don’t speak of “photon transport” because photons are not conserved, and tend to multiply). Why imply that which is not true? When heat is transferred irreversibly (big thermal gradient) it is true that some entropy disappears HERE (dQ/T_hot) and some entropy is created THERE (dQ/T_cold), but since the dQ’s are the same and the T’s are different, there’s more entropy created in the cold reservoir than was destroyed in the hot one. For example, a bit of thermal energy dQ destined for the Earth leaving the Sun at 5800 K removes entropy dS = -dQ/5800. It doesn’t “transfer” entropy to the Earth at 300 K, but rather increases Earth’s entropy by dS = +dQ/300, which is a number a lot larger. Energy is transferred in this process, but entropy is greatly increased.

And no, the equation dS=dQ/T does NOT imply a reversible process. It does only if there is one T, but if there was only one T, heat wouldn’t flow in the first place. All real heat flows are irreversible to some extent. As in the paragraph above, dS=dQ/T perfectly well describes irreversible processes like the Sun heating the Earth, where there are quite different T’s. It is a generally true equation, so long T is well-defined and dS is solely from a thermal process (other ways of increasing entropy, like free gas expansion example, do not count here). But without a well-defined T we don’t have well-defined heat transfer anyway. How would you ever measure it anyway, since heat transfer cannot itself be measured (there is no instrument that measures heat). Think about that. To the extent that the lede pretends that temperature need not enter in as defined quantity, when we talk of heat, it is wrong.

“Well-defined” temperature means a local equilibrium (big enough to define T statistically and locally) but not necessarily a global one. If you take a metal tube and put one end in a hot reservoir at a high T and the other in a cold one at a low T, the temperature will vary in interesting ways while the system equilibrates (transient conduction) but it’s perfectly good physics to speak of temperatures along various points on the tube, even while these vary in time. The math is done for beginning engineering courses. Even after equilibrium is reached, the temperature fields then no longer vary in time, but they still do in space (there’s a nice spacially-dependent T gradient all along the tube, which does not vary in time). However, each of these temperatures makes sense, as it describes an equilibrium in a collection of atoms (an ensemble) which have thermally equilibrated canonically and thus one can speak of a temperature at that “point” even though you can’t be too fine-grained about how big your point is (it can’t be a Euclidian point, but only a very small region).

Don’t be dismissive about what is often a very nice approximation and an accurate one. Yes, it can break down—for example if we ran hypersonic thin turbulent gas down the tube, at some point we couldn’t speak of well-defined temperatures at points along the flow (or pressures, either). But slow the gas flow down, and at some point far from system equilibrium, we can talk about variations of pressure and temperature in such a flow. If they do it for gas around the re-entering spacecraft in simulations (and they do), you can’t dismiss it as being bad physics (the space shuttle worked the very first time, to my surprise in 1981). Why do we talk about heat engines in the lede when there’s barely enough room to define heat? Why do we talk about heat pumps when (as the lede admits) they really don’t pump heat? Why do we claim that latent heat is not a part of thermal energy, when many texts say it is, and when latent heat (as in steam turbine calculations) is a large part of heat transfer in engineering? And what about this sentence: “Heat can be measured with a calorimeter, or determined indirectly by calculations based on other quantities, relying for instance on the the first law of thermodynamics.” This implication (again) is that heat determination by calorimeter is somehow “direct,” not indirect, and somehow does NOT rely on calculations from the first law of thermodynamics. Er, this makes me wonder if everybody knows how a calorimeter actually works. FYI, they all use calibrations from the first law of thermo, and none of them actually measure heat. They measure temperature and calculate heat. SBHarris 04:31, 25 April 2012 (UTC)

Sbharris, thanks for the response. I'll address a few of your comments, but my general approach is to avoid long discussions on talk pages unless absolutely necessary. Unfortunately some of what you are saying contradicts or is in tension with the standard textbooks on thermodynamcs (I'll give some examples below). Per wiki policy, it therefore cannot go into the article regardless of its correctness.

• Clearly I should have qualified my dS as being the entropy change due solely to thermal interaction—that is, energy transfer due to a temperature difference. That would still be incorrect, as my example of the isothermal expansion of a gas against a piston shows. There is never a temperature difference, and yet the heat exchange is macroscopic.
• And no, the equation dS=dQ/T does NOT imply a reversible process. I'm sorry, but you're incorrect. See any text on thermal physics, for example Kittel and Kroemer Chapter 8 eqs. (1) and (29).
• It does only if there is one T, but if there was only one T, heat wouldn’t flow in the first place. Again, falsified by the example of isothermal gas expansion. Moreover, if there is more than one T, the process cannot be reversible.
• Why do we talk about heat engines in the lede when there’s barely enough room to... The lead should summarize the article. Heat engines are in the article. Discussing the definition of heat in technical detail doesn't belong there.

After reading several of your comments, can I suggest you read (or re-read) Chapter 8 of Kittel and Kroemer? Waleswatcher (talk) 12:32, 25 April 2012 (UTC)

One other quick comment. Your central claim - that heat can only flow when there's a temperature difference - isn't really wrong. Even in my isothermal expansion example, it's only in a limit that it's really isothermal. But what I think you don't appreciate that limit is the reversible limit, and it's only in that limit that dQ=T*dS. It's also the most important limit in thermodynamics. Waleswatcher (talk) 13:45, 25 April 2012 (UTC)

Of course my claim that heat can only flow with a ∆T difference "isn't wrong." Rather, it's your counter-idea of a heat flow with no T difference which is (strictly speaking) always wrong. But that is the limiting case for processes taking an infinite amount of time (like your isothermal expansion). In a real isothermal expansion, there would be a small T difference (according to how fast you did the expansion), and while the system would approach irreversiblity and dS = 0 if the process were very slow, it wouldn't quite get there because the process cannot be infinitely slow or it wouldn't happen at all. To that extent, all real processes are partly irreversible, just as as all heat flows are also irreversible (in all real heat transfer, dS >0). Heat flow is reversible only in idealistic thermo texts where they pretend there's only one T to deal with, but in reality there are always two T's.

Now, I don't mind when texts restrict themselves to this unrealizable ideal, as yours does at the beginning of chapter 8. But this text does this by free choice by restricting itself to ideal processes, not by physical necessity. They pretend that all heats come out of reservoirs reversibly (dS = 0) with no T gradients, and they handle T gradients when they must (as in the heat engine) by pretending that heat comes out of the hot reservoir reversibly with dS = 0 and enters the cold reservoir reversibly with dS = 0 also. Of course this means some heat disappears and is converted at 100% efficiency to work, so the whole cycle is reversible, also (again dS = 0 for a perfectly efficient heat engine). But no heat engine is perfectly reversible. In a heat engine with 0% efficiency and no work comes out (where heat is merely conducted from hot to cold and no work is produced), the equations dQ/T(hot) and dQ/T(cold) still are perfectly valid. It's just that now dS(hot) is not the same as dS(cold), so ∆S >0, and by definition this is not reversible. I can only see most of chapter 8 of Kittel and Kroemer on line (not all of it), but they say they discuss irreversible heat transfer in chapter 2, so why don't you look there and tell me what they say? In their intro, they certainly say that when any energy U leaves a reservoir at temp T, it "transfers" entropy U/T out of the reservoir, and they don't put in any qualifiers there-- nor should they. For it does not matter what happens to the heat after that, or if it came out "reversibly" or not (or nearly)-- the entropy change for where it originated is still U/T. In any case, don't let your "important limit" confuse you as to reality.

If you want a slide from Thermo 10.2, look at the slide Loss of available energy in irreversible heat transfer here: [1]. Notice the old ∆S = ∆Q/T? It's still there for each reservoir (which in this case are so large that T doesn't change), even though the process is deliberately very much rreversible here. They just put in different T's. SBHarris 23:12, 25 April 2012 (UTC)

when any energy U leaves a reservoir at temp T, it "transfers" entropy U/T out of the reservoir, and they don't put in any qualifiers there-- nor should they Actually, they qualify that in the paragraph immediately below that one, to reversible processes. I've already provided you with a reliable source that states explicitly that you are wrong - that dS=dQ/T only for reversible processes, and I've given you an example of an irreversible process where dS>dQ/T. There's no point in further discussion until you either acknowledge your error, or find a reliable source that contradicts me. Thanks. Waleswatcher (talk) 23:42, 25 April 2012 (UTC)

Here it is, in the very first text I looked at on line, where heat is being transfered irreversibly and dS > 0. [2]. I can embarass you with more and more of this, or else you can just admit that you're wrong. You won't learn a damn thing unless you do. SBHarris 23:57, 25 April 2012 (UTC)

There's nothing on that page that establishes what you asserted. In fact, it's another example that proves you wrong. The equation there shows that entropy gets generated in that process, which means that dQ<TdS (for any given part of the system, or the whole thing), precisely as I told you is always the case for an irreversible process. Care to try again? (Of course that would be absurd, since, among many other sources, Kittel and Kroemer prove this and write it explicitly in equation (29) of Chapter 8.) Waleswatcher (talk) 02:09, 26 April 2012 (UTC)

Man, did you even read the page? The generated entropy S_gen results from two unequal dS terms. In irreversible heat conduction with a T gap, the two unequal dS's consist of one dS_hot for the hot reservoir, and another larger dS_cold for the cold reservoir, and thus S_gen = dS_cold - dS_hot. There are also two T's explicitly written out (again, one for the hot and one for the cold). There is only one dQ because this is simple heat transfer (no work generated) and Q is conserved, so dQ's magnitude is the same for each reservoir (you could have a sign change, which we will ignore). So dQ = T_hotdS_hot = T_colddS_cold. There are no inequalities here. Of course dS_cold > dS_hot so entropy is being generated (more is created in the cold reservoir than was destroyed in the hot). But the only way to get an equation where dQ<TdS is if you cross terms and use the larger of the two T and two dS terms. So dQ < T_hotdS_cold (!) But that's screwy, since why would you use the entropy change from one reservoir and the temp from a different one? If you want to play that trick, it is also the case that dQ > T_colddS_hot. So you can make dQ less than, or greater than, any TdS if you are allowed to cherrypick which pair of T and dS values you like from this problem. I don't know which ones you had in mind. The natural ones gives you the equalities I have noted.

Finally, I don't know what you think Kittle and Kroemer prove in equation 29, but I think this is a treatment of heat engines. The only way dQ can be less than an appropriately chosen TdS (where each variable is from the same reservoir) is if you choose dQ_hot = T_hot and dS_hot, and then you don't have simple conduction but heat conversion, so that some of the Q is then converted to work, so that when the diminished dQ_cold (now less than T_hotdS_hot since some Q has disappeared into work) reaches the other reservoir, there is now the same amount of dS_cold as dS_hot, instead of a lot more entropy in the cold (entropy generation). Equal entropy changes must happen in a reversible perfectly efficient heat engine where dS_hot = dS_cold (the case I believe is treated in equation 29 for reversible heat engines but I cannot see the preceeding pages). However, it most certainly does NOT happen in simple irreversible heat flow and nobody proves that it does happen. We just proved that it does not happen. Pick the correct reservoir and conserve Q, and you never have an inequality, even in irreversible processes. That's because one dS is not the same as the other dS, in irreversible processes. SBHarris 04:51, 26 April 2012 (UTC)

What's dQ for the middle region (in the problem analyzed in your source), Sbharris? It's dQ=0. What's dS? It's given by that equation, and it's >0. So this example (like all others) proves you wrong: dQ<T*dS for any irreversible process. That by the way is a direct consequence of the 2nd law. If dQ=T*dS everywhere in some process, the total delta S=0, i.e., the process is irreversible. In any case, this discussion (as anticipated) is pointless. Waleswatcher (talk) 10:30, 26 April 2012 (UTC)

It's certainly pointless if you refuse to read what I write and refuse to read my cite, but perhaps somebody reading along will learn something. You just pick whatever the hell T and S you like from the system (when there are 4 of these combinations) to make your statement true, but I can pick any other pair, including the natural ones, and make it false. In that example dQ > TdS if you pick T(cold) and dS(hot), and dQ < TdS only if you (perversely) pick T(hot) and dS(cold). What makes you think you get to chose the last way, as you did? You continue to write as if there were only one value of T in these situations. As I noted, dQ = TdS if you correctly pick the T and dS that are associated with each other, that is for T(cold)dS(cold) = heat entering cold reservoir, and T(hot)dS(hot) = heat leaving hot reservoir. Thus, for 3 out of 4 combinations of those variables, including the two correct combinations, your statement is incorrect.

By the way, I find on my shelf also a copy of Reif's 1965 hardback Statisical and Thermal Physics (I guess this was THE thermo text then), and he also treats irreversible thermal exchanges, as for example when heat enters or leaves an ideal thermal reservoir where the temperature is not changed by the loss. This can be slice of lemon in a cup of tea (which is then the reservoir for the lemon), or the glass of tea cooling (or warming) in a room (where the room is the reservoir). These are the examples in Reif (chap 3 sec 6, page 107). For heat loss or gain ∆Q, the change in heat for the reservoir is T∆S. So ∆Q = T δq not < T∆S. Yet, of course, this is an irreversible process if you're heating a smaller object which has a changing temperature that approaches that of the reservoir. The smaller object absorbs the same ∆Q the room loses but there is no single T you can use to calculate the tea's total entropy change ∆S (which will of course be larger than the room's). However, if you heat (or cool) it slowly enough so that there are a series of "quasi-static" values for T in the small non-reservoir object for each increment of heat δq, then it is still true that for each of these bits of heat dS=δq/T (even in this irreversible process). THEN you can integrate through all these quasistatic (i.e., well-defined) temperatures that the non-reservoir goes through, to get a total nonreservoir ∆S=∫δq/T where it is understood that you can't heat or change T too fast (see Reif p. 118 and 142). If you heat too fast, this integration cannot be done because you lose the well defined 1/T that must act as integrating factor to convert the inexact differential δq to the exact one dS. It is typical in Reif that wherever there is no well-defined T, that the only way to calculate ∆Q is by use of the first law and energy conservation. Here, work is calculated and if necessary subtracted, from internal energy changes, or else simply calculated from "heat conservation", as here, if no work is involved. Anyway, you will notice the lack of inequalities in all of the above, even though the process is manifestly irreversible (of course, system entropy increases when a glass of tea warms or cools in a room). SBHarris 19:42, 26 April 2012 (UTC)

The smaller object absorbs the same ∆Q the room loses but there is no single T you can use to calculate the tea's total entropy change ∆S In other words, ∆S is not equal to ∆Q/T. It is greater than that, due to the 2nd law. Do you understand yet? Waleswatcher (talk) 02:52, 27 April 2012 (UTC)

Yes, ∆S(cup) > ∆Q/T (room), assuming the room is hot and the cup is cool. But ∆S(cup) < ∆Q/T (room) if the cup of tea is hot and the room is cool. The inequality points in whatever direction you like, depending on initial conditions for this particular irreversible process. But even in this case, ∆S(room) = ∆Q/T(room) for this same process. No inequality. Thus, what I'm objecting to here is you simply writing down an equation like δQ <TdS and assuming it holds generally for any irreversible situation. It only holds if you carefully specify which δQ, T and dS you're talking about in the irreversible process. In this case, it depended on whether the reservoir supplied or absorbed the heat, but if you have two reservoirs at two different static T's, it's completely general that you can choose the inequality in either direction you like by choosing which ∆S and which T, and that there is no inequality if you only look at what happens at each reservoir in isolation. The equation you wrote down is not generally true. If you pick ∆S from your cool thing and T from your hot thing, and transfer heat dq, it is true. But only then. Pick ∆S from the hot thing and T from the cool thing and δQ >TdS. Pick all Q, T and S from the same thing, and δQ = TdS. Do YOU understand, yet? SBHarris 04:16, 27 April 2012 (UTC)

Note that there are signs issues here. ∆S(cup) and ∆Q(cup) are negative. So if ∆S(cup) = ∆Q(cup)/T(cup), then it is in fact true to say that ∆S(cup) > ∆Q(cup)/T(room), because it is less negative.

Haven't read the discussion (sorry), so I'm not going to say what (if anything) the relevance of this is; but I just saw the diff and thought I'd jump in. Jheald (talk) 10:51, 27 April 2012 (UTC)

If we adopt your sign convension, you can reverse the inequality by simply reversing the temperatures in cup and room to opposite to what you imagined to begin with. There's no getting away from the fact that this sign points in whatever direction you like, if you insist on mixing up entropy changes due to heat transfer with other than the temperatures associated WITH those entropy changes, in the same reservoir where the changes take place. But if you keep the value of the entropy change with the same temperature at which the entropy change occured, it's always the case that dS = δQ/T and thus δQ = TdS. SBHarris 20:38, 27 April 2012 (UTC)

Well of course the inequality reverses if you switch the temperatures of the room and the cup. It's not a bug, it's a feature. If the room is hotter than the cup, then energy moving from the (cold) cup to the (hot) room would be associated with a net fall in entropy. The entropy increase in the room does not compensate for the entropy decrease in the cup.

But it's a reasonably well-known physical proposition that such energy transfers, which would invert the inequality, do not in fact happen (at least not for quantities of energy above the level of the random thermodynamic fluctuations in the macroscopic variables). Jheald (talk) 22:05, 27 April 2012 (UTC)

There are no inequalities at either reservoir if the changes there are quasistatic. SBHarris' analysis looks to be correct in this respect, however it does lead to a paradox, i.e. one can raise the question: "how can the total entropy increase if we only have locally reversible processes?" The answer is perhaps a bit subtle, it is given in the book by Reif, in Section 4.5 on page 143 in example 1.

Basically, the important point here is that the equation dS = dQ/T is only valid for quasistatic changes, but that means that the system must exchange the heat of dQ with a reservoir that must be at the same temperature. When you approach that quasistatic limit closer and closer, you consider heat reservoirs that are at a temperature that differ smaller and smaller from T, so you could say that the temperature of the reservoir must be T + dT as Reif says in that example at every stage of the process.

Then the total entropy change of the cup of tea, the room and the reservoir in contact with the cup of tea and the reservoir in cntact woth the room is zero, but the entropy of the cup of tea and the room added together has increased as computed above. In reality, the reservoirs aren't there, and the total entropy has increased. What this points to is that one could have extracted a certain amount of work from this processes which instead has been left to dissipate. So, when the hot cup of tea cools, the transport of heat to the room happens via processes that are not immediately fully thermalized, e.g. there is macroscopic motion in the form of turbulent air flow which could in theory drive miniature wind turbines etc. etc.

The total entropy only really increases in the end, because in end we can no longer keep track of how the turbulent air flow and other macroscopic processes, got distributed over ever more microscopic degrees of freedom, and we can describe the final state statistically as one of thermal equilibrium where all the accessible states are now equally likely. Count Iblis (talk) 17:34, 27 April 2012 (UTC)

@Sbharris: The inequality points in whatever direction you like If you forget a minus sign or violate the 2nd law of thermodynamics, maybe. If you randomly combine entropies of one object with temperatures of some other, perhaps. But if you do it correctly, no. Waleswatcher (talk) 17:46, 27 April 2012 (UTC)

As Iblis points out above, if you combine the constant temperature of one reservoir with the entropy change of that same reservoir, and the heat that flows into (or out of) that same reservoir, there is never an inequality at all. SBHarris 20:38, 27 April 2012 (UTC)

response 5 to objection

I can only agree with Count Iblis and Waleswatcher. These revisions by Sbharris do not improve an article that is already in a dire state. --Damorbel (talk) 06:40, 25 April 2012 (UTC)

response 3 to objection

Waleswatcher, I agree with you that SBHarris' edit, as it was posted, was too wordy for the lead. Also I would reject his idea of "effective temperature-difference".

While it is true that the present edit is almost verbatim from Reif and from Kittel & Kroemer, almost so is not exactly so, and in this case near enough is not good enough. There is, at least as Count Iblis reads it, a contradiction hidden in the use of those two references like that, as I explain below to Count Iblis.

Reif is cited as to his pages 67 and 73. He is also implicitly assuming the temperature throughout, and explicitly in his Example in the grey box in the middle of page 67: "Suppose that a bottle of beer is removed from a refrigerator and placed in the trunk of a car, ..." It would be ludicrous to suggest that here Reif is imagining that his reader will interpret this to refer to physical situations so far from thermodynamic equilibrium that temperature cannot be defined. He is obviously referring to situations when temperature is defined. "Refrigerator", "the beer tastes less good"; these are not so far from thermodynamic equilibrium that temperature cannot be defined, and Reif gives not the least hint that it might be so. Reif goes on on page 68 to be more explicit. He defines his adiabatic envelopes in terms of systems "initially in internal equilibrium", and does not hint at the possibility of undefined temperature. In the caption of his Fig. 2.7.1 he writes: "If the partition is not adiabatic, the gas pressures will, in general, change in time until they attain mutually compatible values in the final equilibrium." There is no hint here that Reif intends to deal with situations for which pressure is not defined. But situations in which pressure is not defined can easily occur far-from thermodynamic equilibrium problems in which temperature is not defined. Reif is not referring to this, but Count Iblis wants to make out that Reif's definitions can deal with it. That is just reading things into Reif that are far from his intentions. On page 73, Reif shows a picture of a cylinder with a piston. The piston is clamped in position. This is not a story that remotely imagines physics in which temperature cannot be defined. On page 75 indeed Reif says he has been considering quite general processes, but he does not provide any specific justification for reading that as referring to situations in which temperature cannot be defined. He goes on immediately to talk about quasi-static processes, nearly as far from such situations as one can get. He talks on page 76 about "generalized forces", things that one encounters in classical non-equilibrium thermodynamics. Classical non-equilibrium thermodynamics is all about processes for which temperature can be defined.Chjoaygame (talk) 08:33, 25 April 2012 (UTC)

So it remains that the "no admission of temperature" doctrine is, on your criteria, "unequivocally original research". The writers you cite never for a moment imagine that anyone would read them to mean that temperature is not physically defined in the bodies they refer to, Kittel & Kroemer explicitly so, Reif implicitly so. Reif is putting a purely logical or mathematical case that one can calculate amount of heat transferred without explicit reference to the existence of temperature, but the basis of that case is in Carathéodory 1909 (relied upon by Born 1921) who actually shows that absolute temperature can be derived from his "non-deformation" variable, which exists a priori for him, and prior to any suggestion about heat, which in fact eventually he does not actually make. The "no admission of temperature" doctrine is a misreading of the original texts, unimagined by the original writers, and so not denied explicitly by them. But what they didn't imagine is imagined for them by the fanatical reading advocated by Count Iblis and perhaps by other editors who still lurk unseen. The Wikipedia should not rely on fanatical misreadings, not even if Count Iblis calls them "official".

As for the "technical" point. Either there is an infinitesimal temperature difference that is considered to go to zero in the mathematical limit, or heat does not flow even infinitesimally slowly. The limit exists mathematically but not physically. It is an example of a sequence of points belonging to a certain set, with a limit point that does not belong to that set. The "technical" point is verbalistic but unphysical. Here I am just re-stating what SBHarris has said above.

You write: "Strictly speaking, if T is well-defined, you're in equilibrium." Yes, in thermal equilibrium which is a relation between two systems. Only one of the two systems has to be in thermodynamic equilibrium in itself (the thermometer) to define the temperature strictly as you desire, while the system of interest is not required to be in thermodynamic equilibrium, but is allowed to have steady flow, in thermal connection across a diabatic partition with the thermometer.Chjoaygame (talk) 04:31, 25 April 2012 (UTC)

response 4 to objection

Count Iblis, you would do well as a bureaucrat, concerned with the verbal appearance of "official" definitions. But this is about science here, where we don't kow-tow to "official findings".

The two present "official" (as you call them) sources contradict each other, if you want to read Reif as a fanatical "no admission of temperature" man. Kittel & Kroemer speak of "thermal contact with a reservoir", and later on the same page explicitly admit that the reservoir has a temperature τ, thus contradicting the fanatical idea that temperature is not part of the physical situation. The difference is really between a purely mathematical statement and a physical statement. The absence of temperature from the "official" definition is purely verbal; the mathematical formula refers to an axiomatic set-up in which temperature is defined, although the notation suppresses the functional dependence. The internal energy of the Born formula is defined as a function of entropy and volume, which entails the existence of temperature. An axiomatic system cannot rightly be physically interpreted piecemeal; all parts of the axiomatic system are involved in its right physical interpretation. Only a bureaucrat would try to make a physical interpretation of one item out of its full axiomatic context. We are talking about physics here.

You say that the "official" definition will work even when there isn't a temperature, but you haven't even tried to give a trace of evidence or argument or source for that, and nowhere in the literature is there reason given to believe it. It is just a fanatical verbalistic reading of a mathematical formula without regard to the physical meaning of the formula. There is nothing in the real literature that explicitly says that you can define work when temperature is not defined; that is just a bureaucrat's misreading of a student text. And there is plenty to say that there are physical situations when work cannot be defined, as I have noted on this page and as you have failed to reply to.

You want it both ways: sometimes you admit quasi-static processes, which are not physically real, and still not strictly of exactly equal temperatures on either side of the partition, so as to make the heat flow, when you want to say that heat flows reversibly; other times, you insist that there is no temperature outside strict thermodynamic equilibrium, when no flow is permitted. You fail to make explicit recognition of the case steady state case of thermodynamic equilibrium on one side of a diathermal partition (in the thermometer) while there is steady flow on the other side (in the system of interest), with thermal equilibrium across the partition.

It is all very well to demand explicit reliable source statements for the proposition that where there is heat there is temperature, but with that attitude you should also be offering explicit reliable source statments for the proposition that where there is no temperature there is always still work, which is your position.

Your argument above that two systems with different temperatures and heat passing from one to the other is a situation when temperature is not defined is worthy of the finest tradition of bureaucracy. We are here talking about non-equilibrium situations, as is implied by your concern for the general case, where one will consider the possibility of local temperature.

We are here talking about the general case. In cases of thermodynamic equilibrium, temperature is always defined, though it doesn't have to appear explicitly in every formula. What is being asserted by Count Iblis is that there are cases in which temparature is not definable but work is. It is inappropriate to mix up accounts (a) of simple systems in thermodynamic equilibrium, which are in classical texts said to be internally homogeneous and which have zero fluxes, with (b) of general systems not in thermodynamic equilibrium which are not in general homogeneous and for the present problem are not even required to have local temperatures and in general have non-zero fluxes.

You talk about systems that are not in even approximately local thermodynamic equilibrium. But in such cases, there is no reason to suppose that a hydrodynamic description is possible, such as would be needed for a definition of local pressure and thus of work. You don't even try to offer an argument for your assertion.

It becomes clearer and clearer that you have not mounted any case at all that you can always define work transfer for the relevant physical situations, but are just relying on unsupported assertion and assumption that a fanatical reading of a student text is "correct" and "official". What "official"?Chjoaygame (talk) 04:31, 25 April 2012 (UTC)

point of view of F. Reif 1965

Definition of heat and work are given in section 2.8, it is instructive to start reading from section 2.6 and onward. What Reif does is to consider some general system described by some Hamiltonian, which contains some number of external parameters x1, x2,,...,xn (e.g. volume, magnetic and electric fields etc. etc.). Then the energy levels of the system Er will be functions of the external parameters x1, x2,....,xn, so we can write this as Er(x1,x2,...,xn).

The macrostate of a system is then defined by specifying the external variables and other additional conditions; in case of an isolated system that other condition can be the total energy, which is then conserved in that case. Since physical quantities will depend on the precise microstate, Reif considers ensembles of systems that are in the same macrostate, but each member of the ensemble can be in any one of the possible microstate correspondng to that macrostate.

Definition of purely thermal interaction. This is any arbitrary interaction between two systems during which all external parameters are fixed. In this case the energy levels of the systems remain fixed. The energy transferred between the systems when it evolves from one to another macrostate will depend on the detailed change in the microstate.

The transfered heat in a purely thermal interaction is defined as the ensemble average of the transferred energy between the systems. Ref explains that since the external parameters do not change in this process, the energy levels do not change, and that therefore mean energy change is due to the change in the relative number of systems in the ensemble which are distributed over the fixed energy levels.

Then, the definition of a purely mechanical interaction. Reif considers thermally insulated systems that can only interact by changing ech other's external parameters. This is called "macroscopic work". One again has to define this by considering ensemble avarages, because for individual systems the energy does not change by the same amount when the external parametes are changed in the same manner.

Next Reif looks at general interactions, which is a combination of a thermal and mechanical interaction as defined above. He writes down the First Law of thermodynamics, but this is then to be interpreted as the definition of heat absorbed by a system (as stated below eq. 2.8.2).

Note that none of this assumes thermal equilibrium, nor quasistatic processes. In case of mechanical interactions, he explicitely leaves open the possibility of the system jumping from one energy level to another.

He then goes on to describe quasi-static processes, the infinitesimal work done in such a process as a result of infinitesimal change in an external parameter x of the form dW = X dx, and X is then the generalized force, which is given by the average of minus the partial derivative of Er w.r.t. x, because in the quasistatic limit, the system stays in the same energy level. The change in energy is due to the energy of that energy level changing.

Count Iblis (talk) 20:52, 25 April 2012 (UTC)

COMMENT

Yes, I see that you put all thatinto the wiki on Fundamental thermodynamic relation in 2009. That was a lot of LaTeX work-- after all that, why were you so lazy as to fail to put in Reif as your source for it all? ;) These ensemble averages of energy in canonical systems are related to the temperatures of those systems, and so there is no getting away from having temprature as a well-defined concept here in heat transfer, even if you define heat as some change in the summed energies of these just-so distributions, while managing to avoid talking about temperature. These systems all have a temperature, if they are canonical ensembles. That's part of the definition of such a thing. And here's the relation you stuck into the above-mentioned article, yourself. See the T? SBHarris 22:58, 25 April 2012 (UTC)

${\frac {1}{kT}}\equiv \beta \equiv {\frac {d\log \left[\Omega \left(E\right)\right]}{dE}}\,$

This definition doesn't work for the general case, because not all of the $\Omega (E)$ accessible states are necessarily equally likely, the system isn't assumed to be in equilibrium. Of course, you can still write down the entropy using Shannon's formula, and then define temperature using the derivative of S w.r.t. E. However, regardless of this, your logic about heat flow would be the opposite of Reif's. Heat flows due to the dynamics of the system being such that the number of all accessible states are all equally likely to be reached eventually, so the entropy increases and you then approach a final equilibrium state where $\Omega (E)$ for the combined system is a maximum. You can then define temperature based on the fact that $\Omega (E)$ becomes maximal in thermal equilibrium. This is what Reif does.

To tackle the non-equilibrium problem of how systems reach equilibrium, you don't gain much more than the picture sketched by Reif in the intorductory chapters, by merely introducing temperature. If you read the chapters in non-equilibrium problems, you'll see that you need to include more about the real dynamics of the system.

Consider e.g. thermal conduction in an ideal gas. In section 14.7 of Reif, it is explaind that while to a first approximation, you can write down the distribution function corresponding to local thermal equilibrium (i.e. a Maxwell distribution with position dependent parameters), but this will not satisfy the Boltzmann transport equation. Collisions will have no effect on the distribution function, precisely because they are local and the distribution function describes local equilibrium. However, because the paramters depend on position, there is now a nonzero "convective" time derivative, so you don't have a distribution function that correctly describes a (steady state) nonequilibrium situation where heat flows through the gas, no matter how small the heat flux is.

You can only describe this situation correctly to leading order (where there is net heat flow), when you solve for the small departure from local thermal equilibrium. This then yields the net heat flux as the temperature gradient times a constant, the thermal conduction coefficient, which is then expressed in terms of the differential cross section of the molecules.

Then the picture you get from studying Reif's book, is that heat flow is associated with systems not being in thermal equilibrium. You can say that this in turn is associated with temperatures not being equal, but that doesn't capture this whole issue correctly, because temperature then also becomes only a quantity that only approximately describes the situation, and the departure from it being an exact description (even in a local sense) is what actually causes heat flow. Count Iblis (talk) 01:41, 26 April 2012 (UTC)

For our article, we are discussing a proposal that heat can be defined by a work calculation when temperature cannot be defined. The question here is not how to define temperature. Neither is the question here how to calculate heat flux given the temperature distribution. The question here is whether one can define work for processes for which temperature cannot be defined. I do not see the above comment by Count Iblis tackling this question. This is consistent with my reading that Reif does not tackle this question.Chjoaygame (talk) 03:41, 26 April 2012 (UTC)

No, as is explained in detail in the book by Reif (as I pointed out in my first section on the POV of Reif), Reif defines heat for general processes where temperature is not defined. If you were to argue that Reif could ahve defined temperature for those cases also, then you are actually saying that you can always define temperature (which is more or less what is discussed in ths subsection started by SBHarris). Count Iblis (talk) 15:20, 26 April 2012 (UTC)

sources indicated by Reif 1965

On pages 631–635 Reif gives a bibliography.

On page 83 Reif lists some suggestions for supplementary reading, as follows:

Statistical formulation

R.C. Tolman: "The Principles of Statistical Mechanics," chaps. 3 and 9, Oxford University Press, Oxford, 1938. (This book is a classic in the field of statistical mechanics and is entirely devoted to a careful exposition of fundamental ideas. The chapters cited discuss ensembles of systems and the fundamental statistical postulate in classical and quantum mechanics, respectively.)

Work and heat—macroscopic discussion

M.W. Zemansky: "Heat and Thermodynamics," 4th ed, chaps. 3 and 4, McGraw–Hill Book Company, New York 1957.

H.B. Callen: "Thermodynamics," secs, 1.1–1.7, John Wiley & Sons, inc., New York, 1960. (The analogy mentioned on pp. 19 and 20 is particularly instructive.)

The Callen reference is to the first edition of Callen 1985 mentioned above.Chjoaygame (talk) 02:52, 26 April 2012 (UTC)

material from Reif 1965

On page 123, Reif writes: "Note again that the four laws are completely macroscopic in content. We have introduced three quantities (Ē, S, and T) which are asserted to be defined for each macrostate of the system, ..."

As I read it, this settles the question of whether Reif intends to discuss physical situations in which temperature is not definable. He does not.Chjoaygame (talk) 03:00, 26 April 2012 (UTC)

He says this only in the context of the 4 thermodynamic laws and there temperature is assumed to be defined for macrostates. Part of the book is about such situations, but that doesn't mean that he has made the definition of heat conditional on temperature being defined. That he hasn't is clear from Chapter 2. Count Iblis (talk) 03:12, 26 April 2012 (UTC)

We are here considering the possibility of definitions of heat transfer that may be alternative to Reif's, not relying on a proposal that Reif's definition is invalid. Thus the question here is not necessarily to be answered just by looking at Reif's definition of heat transfer. If Reif's definition is not as general as you think it is, that is a reason for looking for another definition. But there are other reasons for looking for another definition, other points of view.

The question here is not whether Reif has made the definition explicitly conditional on temperature being defined. It is true that Reif does not make his definition of heat explicitly dependent on the definition of temperature; but that does not answer the present question. A question here is whether his definition in terms of work will do the job of defining heat transfer when temperature cannot be defined. You are extrapolating in your mind to assume that Reif intends to refer to situations in which work can be defined but temperature cannot. Reif does not discuss such situations, and there is no reason to suppose that he intends to refer to them.

But reading Chapter 2, one finds on page 66: "In describing a macroscopic system it is, in general, possible to specify some macroscopically measurable independent parameters x₁, x₂, ... , x_n which are known to affect the equations of motion (i.e., to appear in the Hamiltonian) of this system." In the Carathéodory story, these are also called deformation parameters. They do not fully define the state of the system, and another non-deformation parameter, which may be denoted x₀, is always needed. This parameter may be for example the internal energy, or it may be the empirical temperature, of the system. Continuing in this section, on page 68, Reif, as cited by the article, writes: "Since the external parameters do not change in a purely thermal interaction, the energy levels of neither system are in any way affected." It follows that the thermal change must be indicated by a change of the non-deformation parameter. Without the non-deformation parameter, the story does not work. Reif refers to the relevant information in the non-deformation parameter in terms of its appearance in "the relative number of systems in the ensemble which are distributed of the fixed energy levels (see Fig. 2.7.3a and b)." This is referring to temperature implicitly, though it is not explicitly saying that temperature can or cannot be defined. To make your case, you need from Reif a statement that work can be defined, and thereby heat, when temperature cannot be defined. Reif makes no such statement.

The question here is not how Reif defines heat transfer. It is whether heat transfer makes sense in situations when temperature cannot be defined.Chjoaygame (talk) 04:23, 26 April 2012 (UTC)

Count Iblis writes above: "He [Reif] says this only in the context of the 4 thermodynamic laws and there temperature is assumed to be defined for macrostates. Part of the book is about such situations, ..."

There isn't much that thermodynamics has to say that isn't in the context of the four laws. Count Iblis' statement here seems to suggest that there is significant else about heat transfer that is said by thermodynamics or by Reif, but Count Iblis doesn't say exactly what. Perhaps he thinks that thermodynamics or Reif says something significant about heat transfer that is not covered by the four laws?

No one here is denying that heat transfer can be defined validly without explicit mention of temperature. What is at stake here is the idea of the crocodile that the only valid or useful definitions of heat transfer must avoid mention of temperature. One way to establish that idea of the crocodile would be for it to show that heat transfer can be defined validly when temperature cannot be defined. It does not establish that idea of the crocodile to show that heat transfer can be defined validly when temperature is not explicitly mentioned.Chjoaygame (talk) 06:15, 26 April 2012 (UTC)

You assert that:

"Reif refers to the relevant information in the non-deformation parameter in terms of its appearance in "the relative number of systems in the ensemble which are distributed of the fixed energy levels (see Fig. 2.7.3a and b)." This is referring to temperature implicitly, though it is not explicitly saying that temperature can or cannot be defined."

And I call bullshit on that, he does not even implicitely refer to temperature. He consideres the most general closed system you can imagine and defines heat and work for that. If this implicitely defines temperature, you have to come up with reliable references on definition of temperature for such cases, and also show how it is so very relevant for the definition of heat to merit incusion in the very definition of heat.

You assert:

"To make your case, you need from Reif a statement that work can be defined, and thereby heat, when temperature cannot be defined. Reif makes no such statement."

No I don't, because it all follows from the context that Reif considers, i.e. general processes completely out of thermal equilibrium that are not even quasistatic, and in his writing he gives plenty of explanations about the definition he first gives being for completely general processes, and when he specializes to quasi-static processes and defines work for that, he gives plenty of explanations about that too in the text. Count Iblis (talk) 15:32, 26 April 2012 (UTC)

You write that I am talking bullshit where I say "This is referring to temperature implicitly." I will accept that I was writing very loosely. I had in mind that temperature being defined means that "the relative number of systems which are distributed of [typo for 'over'] the fixed energy levels" is defined. And that a reference to that relative number implies a hint at temperature. I accept this was loose and practically uninformative talk by me.

You write here, in your last paragraph: "... general processes completely out of thermal equilibrium that are not even quasistatic, and in his writing he gives plenty of explanations about the definition he first gives being for completely general processes."

You are referring here, I think, specifically to Sections 2.8 and 2.9 of Reif 1965. I will assume that this is the focus of your comment.

Section 2.8 indeed talks about a "most general interaction". I read it, however, as a formal programmatic sketch, not a prescription for a definite calculation. It gives no hint of how the complete departure from thermal equilibrium of the general system will be specified, and no hint of how the work will be calculated. Reif here does not say how to calculate the work. There is no hint of an attempt to define generalized forces such as would be needed for a definite calculation of the work. I say that this is consistent with the fact that Section 2.8 gives no hint of how the temperature is to be defined for it.

Section 2.9 is quite different. It goes to a special case, in which the calculation of the work can indeed be done "by integration" (as noted at the bottom of page 75), because the generalized forces are defined as a consequence of the quasi-static assumption. In this special case, the temperatures are also definable.

Thus I say that these two sections bear out my claims. Sometimes work cannot be calculated, and in such cases also it is likely that temperature cannot be defined. In the contrary case, when work can be calculated, the temperatures are definable.Chjoaygame (talk) 19:57, 26 April 2012 (UTC)

It's in Section 2.7 and further. What Reif says here is that you have some system that has energy levels Er that depend on the external parameters. Then, if you change the external parameters in some specified way, and you start with an ensemble of systems, that ensemble will evolve to a new ensemble, the change in mean value of the energy of the ensemble will be fixed due to the laws of physics. Work can still be calculated, even if the changes are not quasistatic (i.e. when the systems can jump from one energy level r to another energy level), because the probabilities of such jumps are (in princple) calculable using the Schrödinger equation. He doesn't mention this last fact explicitely, because this should be self-evident (I'll explain below).

Then in the next section 2.8, in case of both thermal and mechanical interaction, he simply presents the First Law of thermodynamics as defining heat. The change in external parameters alone would lead to some change in energy, the rest is the heat absorbed by the system.

So, I agree that Reif isn't explicit about how to compute work when it isn't due to quasistatic change, but it should be clear that it is well defined in principle when the way the external parameters are changed is specified. He assumes that it is on page 70 and further. What he doesn't mention explicitely is the following (which is self-evident for readers familiar with quantum mechanics, which is why he doesn't elaborate on it). He has mentioned that the system is defined by the Hamiltonian and the external parametes, but then the Schrödinger equation i hbar d|psi>/dt = H|psi> with initial condition

|psi(0)> = |r>, being the energy level r, will upon integration and the way H depends on time (H depends on the external parameters which depend on time) yield a superposition of the new energy levels of the final state Hamiltonian. And then the probabilities are the squares of the absolute values of the components of that superposition.

So, given some ensemble with a distribution over the energy levels, you know (in principle) what the new distribution over the new energy levels will be, given some specification of how the external parameters are changed. Therefore the change in means value of the ensemble is fixed (in principle). Work en heat are thus defined in this framework (in princple). That doesn't mean that you cannot somehow define a temperature for the systems before and after such an interactions, though.

What I take from the way the topic is presented in Reif is that regardless of whether or not you can define temperature in general, you don't need to do so to define work and heat. Count Iblis (talk) 20:57, 26 April 2012 (UTC)

As I noted above, I found a 1965 copy of Reif on my shelf (one of many severe consequences of garage sales and bibliophilia-- long story) and I've been reading it. And I'm beginning to see your point that temperature is not strictly necessary for a process in which entropy increases, and it is entropy increase that drives heat flow, which is to say, heat. Reif does indeed focus on entropy S (as defined in Bolzmannian fashion as S = klogΩ, where Ω is number of microstates per macrostate). And he basically points out that what makes heat flow is entropy increase (it flows in the direction that increases number of microstates for the energy available), and only stops when entropy is maximized for the energy available in the system. For Reif, "entropy" is just a handy way to talk about logΩ. And as you noted, although there are many situations where there are defined T's, and even quasi-statically defined T's while T is changing, in all those cases T is just dE/dS, which have the usual definitions of E and S, and it's not fundamental since there are other situations in which T cannot defined, and yet in those circumstances, heat flows to increase entropy (and logΩ) anyway. So temperature points the way to heat flow when it exists, but it may not exist and yet heat flow may still occur in ways that maximize entropy. Got it. At the end of such a process, or at points along the way, there may well exist a definable T, but not at all of them. You can always define S, but not always T.

As we've noted, where there's a T we can always calculate a δQ as dS/T (Waleswatcher is totally wrong about that), but when there is not a T we are left with the old trick of resorting to the first law of thermo and defining Q as any internal energy change that isn't work, which we can define in a force x distance type way. Or, if we have a heat flow and no work, and we have a well-defined T in one place, we can still compute an SdT there and that's the δQ heat added to part of the system where things are too mixed up or changing too fast to define T (with no work done, the conservation of energy gives you a sort of conservation of heat).

The problem with all this is that it leaves us having to be too glib with the reader in the lede. If we say that heat is the flow of energy that causes any energy change in a system that isn't due to thermo work, it leaves us (as I complain above) with a severe problem in defining thermo work that isn't circular. Even Reif has to admit that there are types of chemical potential work that count as thermo work that don't fit his general "XdX" were x is a distance and X the force-type-congugate. Our only alternative is rather technical: heat is that part of the energy flow in systems that is directed toward increasing entropy. Temperature is an intuitive concept for people but entropy is not. Perhaps we can add that heat is energy flow associated with temperature gradients in places where temperatures can be defined, but that heat flows also occasionally occur in nature in places where entropy increases due to the heat flow, but temperature cannot be defined. That leaves us wondering if we should define entropy in the lede. A microscopic definition of entropy and thus heat is going to be pretty hard to start off with. SBHarris 23:05, 26 April 2012 (UTC)

Count Iblis, I can agree with you about two things: (1) "I agree that Reif isn't explicit about how to compute work when it isn't due to quasistatic change, ..." and (2) when you write "What he doesn't mention explicitely is the following (which is self-evident for readers familiar with quantum mechanics, which is why he doesn't elaborate on it)," you mean that you are reading into Reif things he doesn't say.

In my book that makes you an original researcher.

I will repeat what I wrote above:

"•Heat is about moles not molecules. Count Iblis is trying to muddle the questions by trying to make it about molecules. I suppose this may be because of the influence of that angel of muddle, Reif.

"•Mere talk of molecules will not solve the present problem."

Looking at these just above comments of Count Iblis and SBHarris, I am led to think that further discussion here and now would be futile.Chjoaygame (talk) 01:06, 27 April 2012 (UTC)

Actually, if you just read page 70 and 71 and forget my explanations, then you'll see that Reif explicitely talks about mechanical work when the change in the parameters is not quasistatic. So, there are transitions between energy levels, saying that due to these transitions this can be quite complicated. But then he says that, nevertheless, this can be readily measured on page 71. He considers two systems A and A' doing work on each other, A' is a simple system allwing you to compute the work easily using force tomes displacement, and then the work performed by A is minus the work performed by A'.

So, not only is this all theoretically well defined, it is also experimentally accessible, according to Reif. He illustrates this using a few figures. E.g. figure 2.7.5. on page 72 shows a vessel containing a liquid and a paddle wheel. A falling weight can perform work by rotating the paddle wheel. Then A' is the system consisting of the weight and the Earth, the potential energy change here is readily measured from the external paramter which is the height of the weight. System A here is the water and the paddle wheel, the work done by this system is then minus the work done by system A'.

But note that system A here is an extremely complicated system. The external parameter is the orientation of the paddle wheel. A rapid change in this affects the system A in an extremely complicated way, by causing turbulent motion of the water. Count Iblis (talk) 02:02, 27 April 2012 (UTC)

As I read you, you intend to calculate the work done on the system by the fall of the weight. Nice pictures of this kind of experiment are to be found in many books. It is Joule's experiment to measure the ratio of quantity of heat produced to quantity of work supplied. The quantity of heat is measured by the temperature change of the water. The temperatures are definable on more or less the same time scale as is the work. This is not the kind of problem that worries us here.

The problem of interest here is the case in which one wants to follow the temperature change closely. If one can't do that, it is likely that one will have difficulty following the work transfer as well.

With all respect, I have the impression that you are not interested in non-equilibrium thermodynamics. That is the setting in which I am thinking. In non-equilibrium thermodynamics, one can often do a fair job using a thermometer with a rapid response, and can also calculate the work. But eventually one runs into problems where it is not feasible to define temperature. I am saying that in such problems, one will most likely have problems following the rapid transfer of energy as work as well.

Conceptually, there are problems in defining work in general for non-equilibrium processes. And problems in defining heat transfer in general. I have given some references to these above. I am not about to try to deal with them in the article at this stage.

It is a matter of sorting out what one really means by heat. At a first level, heat is what is transported through a thermal conductor, driven by temperature gradient, as in the Fourier law. That is even how Reif introduces it. Also, at a first level, heat is what is transported by thermal radiation. An alternative conception, raised by SBHarris just above, is that heat is not driven by temperature gradient, but is driven by a tendency for entropy to grow. I don't feel I have a good handle on this latter conception. It doesn't attract me, it doesn't feel as if it really makes sense; but perhaps it might grow on me. For it, one might encounter the gradient not of the temperature, but of the reciprocal of the temperature. I am not proposing to try to bring this into our discussion at this stage, if ever.

No one doubts but that the Carathéodory-Born definition is theoretically valid and theoretically clever. But it gives no hint of the physical meaning of heat. Carathéodory himself doesn't even mention heat in his own story; but his system defines temperature as a derivative of the second law of thermodynamics. His only mention of heat in the 1909 paper is in the introduction in which he outlines the classical approach and says he intends to do it afresh without taking heat as a presupposition.

Likewise, no one doubts but that statistical mechanics can do wonders and is very clever. But it remains explanatory of the phenomena, which have to be considered in their own right, as Buchdahl 1966 says (and as every real thermodynamic text says). No one doubts but that quantum mechanics is very clever. But, with all respect, it is hardly relevant to the present problems. Boltzmann and Gibbs did the heavy lifting.

I have the strong impression that you feel that the phenomenological approach is for fools and ignoramuses. Ignorant fools such as Maxwell and Planck and Prigogine. You are dismissive of the idea that there are problems defining work. While you are so dismissive of those problems, I don't see you coming to grips with them. Reif 1965 is not about to discuss them; they are way outside the purview of his book; he mentions them briefly in paragraph c on page 3.Chjoaygame (talk) 03:31, 27 April 2012 (UTC)

You wrote "With all respect, I have the impression that you are not interested in non-equilibrium thermodynamics." I am interested in that, and note that quite a few chapters of the book by Reif are devoted to this. However, one has to note that in case of approximate local thermal equilibrium where there is a temperature gradient (in approximate sense where you ignore deviations from local termal equilibrium), the heat flow and the deviation from local thermal equilibrium are two sides of the same coin. Perhaps best to start a new section on this talk page to discuss this in detail from first principles. Count Iblis (talk) 15:23, 27 April 2012 (UTC)

Conclusions

I like to draw some conclusions, based on the discussions so far.

I accept that some sources imply definability of temperature in case of heat flow, such that heat flows from high to low temperatures, while others do not make such statements. To make progresson this point regarding how to mention this in our article, its's best to discuss this from first principles (those principles taken from reliable sources, of course, and used appropriately as is done in those textbooks).

The issue then arises about how to describe heat flow, if we also in some way mention temperature. I think it is totally wrong to imply that heat flows because of a temperature difference, that's not at all how many reliable sources explain this. Rather they will define temperature such that the notion of temperature will be such that heat flows from high to low temperature (at least in those cases where it is defined in those sources). Before temperature is introduced, plenty of explanations involving number of accessible states all being equally probable a priori are given, temperature is defined later, partially based on this.

Heat flow is thus (according to may reliable sources) a spontaneous stochastic effect, and we can also note that textbooks such as Reif will go into details about the statistical nature, mentioning also statistical fluctuations and requiring heat to be defined only after averaging over ensembles. Count Iblis (talk) 16:14, 26 April 2012 (UTC)

See my comment to Damorbel at the end. I now have questions again about whether heat is GOING to flow in any kind of definable way (meaning in one direction and not back and forth in microamounts) unless you have some "quasi-static" temp difference, which you could measure with a (very fast) thermometer at both ends. Instead, are we really going to possit that heat sometimes flows in order to maximize entropy in some tricky and rapid way such that you can never catch T differences with any kind of thermometer? Which is to say, never at any point in the process measure an effective temperature, with any kind of thermometer? Is what you measure with a thermometer DIFFERENT from what you calculate as dE/dS? = k (dE/dln(states)?

I suppose what I'm asking is, if enough heat flows that you can see it as an internal energy difference (change) in the service of entropy-increase, should you not be able to see that process with an ideal and very fast thermometer? SBHarris 21:33, 27 April 2012 (UTC)

why the definition of heat matters

Thermodynamics works on the principle that there is only one kind of heat. But it has two faces. One face is that heat is the energy transfer that must be regarded as due to random elementary processes because the macroscopic scale can't deal with them. The other face is that heat is the energy transfer that my current theory of macroscopic physics can't account for as work. The difference arises from the possibility, God forbid, that there might be something in nature that my current theory of macroscopic physics should account for on the macroscopic scale but doesn't. Oh, no! That can't be so, I know everything! The Carathéodory approach simply assumes that my current theory of macroscopic physics can account for all that occurs on the macroscopic scale.

Mathematics is not physics. It is an aid to physics. A mathematical theory is about what appears in its axioms. It doesn't think about what doesn't appear in its axioms. Physics is very much about what doesn't appear in its axioms, but might do so if more were known. Defining heat as a residual is the mathematical way to make the axioms cover everything. Defining heat as due to temperature is the physical way to use thermodynamics to reveal what doesn't appear in the physical axioms. The aim of mathematics is to be right. The aim of thermodynamics is to be wrong.Chjoaygame (talk) 16:12, 27 April 2012 (UTC)

Chjoaygame, you write "One face is that heat is the energy transfer". The definition that approximates to 'heat is energy in transfer due to difference in temperature....' is not really sustainable, basically because of the 'temperature difference' part. What happens when the difference disappear, does this mean there is no heat anymore? And before the temperature difference disappears, is the system described not in disequilibrium because of the still existing temperature difference? --Damorbel (talk) 20:00, 27 April 2012 (UTC)

Certainly when all temperature differences disappear there will be no more heat = heat flow. The question is whether there is heat flow in situations where one cannot define temperatures, as for example in a flow of gas where all the molecules are moving at very nearly the same speed, and do not have a Maxwell-Bolzmann distribution. Clearly such a flow would transfer heat to a pipe holding it (or get heat back from the pipe) depending on the speed of the gas and the temperature of the pipe (which could be well-defined). So the question is how to look at such situations, thermodynamically.

This has been puzzling me while reading Reif and one possible solution I see is the the instrumentalist approach that Reif, as a theorist, is naturally loathe to admit. The instrumentalist approach is to say that temperature is definable for systems of more than 2 particles, when you can stick a tiny little thermometer into such systems, and MEASURE the temperature (and the temperature is quasi-stable). Thus we define temperature not by some complicated statistical thermdynamic equation, but by what the tiny thermometer reads, so long as the temperature is measurable quickly enough. YOu could stick that tiny thermometer into that gas flow, for example, and read temperatures in various places, and those would BE the termperatures. Then the second law guarantees that if your thermometer is in equilibrium thermally with system A, then system A will act as though it has that same temperature whenever it comes into themal contact with system B. Thus temperature is a reproducible propery, and a system with a quasi-stable temp cannot pretend it has one temperature to your thermometer, then act as though it has some other temperature in some other thermodynamic situation. The upshot of the instrumentalist approach is that while we cannot always calculate a dE/dS for a system, we can always take its temperature directly with a thermometer, and when we do, we can always guarantee that the heat will flow in the direction of the temperature difference if we put it in thermal contact with some thermal reservoir with some other temperature. We can calculate heat flows as dQ = dS/T in such situations, since in all of them T is the quasistable T demanded by Reif. If T is not quasistable enough to say what T is, then the question them becomes, what is it that our thermometer reads? And the answer is that it reads various numbers up and down, or it has hysteresis and reads some number which is wrong, and so the heat flows are in one direction or another, or not what our our thermometer promised, and the idea of heat still makes no sense. So maybe heat must be connected with a quasi-stable temp difference, after all. I'm convinced of one thing on Mondays, Wednesdays and Fridays, and the other on Tuesdays, Thursdays and Saturdays. On Sundays I'm agnostic. SBHarris 21:18, 27 April 2012 (UTC)

point of view of Landau & Lifshitz 1938

I refer to Landau, L., Lifshitz, E. (1938), translated by D. Schoenberg, Oxford University Press, London. This work is recommended by Buchdahl 1966. The 1963 edition of this work is recommended by Reif 1965 on page 126. The 1980 edition is recommended by Callen 1985 on page 486. Landau & Lifshitz 1938 would not cut it as Wikipedia editors because they give no references at all, no reliable sources; shocking!

Landau and Lifshitz 1938 start with a general view of statistical mechanics, introducing the quantities of internal energy and entropy for closed systems. They go on to Chapter III, 'The Thermodynamic Functions'. It starts with section 9, 'Temperature'. They consider a closed system in statistical equilibrium, and define its temperature. In section 12 they define the pressure of the closed system in thermodynamic equilibrium as a thermodynamic variable. In section 13 they introduce the ideas of work and heat. They define quantity of heat for an infinitesimal increment in a quasi-static process in terms of the temperature T and the increment of entropy. They say about heat: "In the general case, however, a body which is not thermally isolated may also receive energy from (or lose energy to) other bodies directly, which is not associated with a change of external conditions. This part of the energy is called the heat received or given up by the body." They make hardly any reference to non-equilibrium problems.

From this I infer that Landau & Lifshitz 1938 presume temperature to be defined before they mention the notion of heat, and they define quantity of heat in terms of temperature.

I observe that they make hardly any reference to non-equilibrium problems. From this I infer that, while they do not explicitly deny that it can be done, they do not consider the problem of defining heat or work when temperature cannot be defined. From this I would say that anyone who wants to talk in a Wikipedia article about the definition of work when temperature cannot be defined has a burden of obligation to provide explicit reliable sources.Chjoaygame (talk) 05:03, 28 April 2012 (UTC)

Such references have been provided, e.g. Reif. Also, you are not analyzing what the books you write about say in good faith. You quote selectively, and give your own spin on it, which is introduced by "From this I infer that...". You even managed to draw the conclusion that Reif defines work in such a way that requires temperature to be defined. Why not simply state how they define things by sticking to what they say?

I seem to vaguely remember from look in into Landau & Lifshitz 20 years ago, that the way define temperature is not the same as how most other sources define it. They have an exercise where you are supposed to compute fluctuations in the temperature, while accoding to the standard definition of temeprature, the temperaturee is constant while you have fluctuations in the internal energy. So, the notion of temperature is presumably different in this book than in most other sources, but I could be wrong bout this...

So, you are not doing what I suggested, i.e. analyze how some particular books treat the subject indepth, from their perspective. When I asked a question about how free expansion is described from the persective of one of the books you mentioned above, and also for all the other books, you simply refused to engage. Now, I'm not sure abut that particular book (I don't have a copy of that book), but surely at least one of the books (perhaps Kittel?) does treat the free expansion experiment...

Count Iblis (talk) 15:57, 28 April 2012 (UTC)

Dear Count Iblis, thank you for your above comment.

You make several pejorative criticisms of what I have written above: "not ... in good faith", "own spin". For the moment, I do not think it useful for me to directly discuss those criticisms. I prefer at present to continue to talk about the subject matter.

Moreover, you make several charges against me: that I am not doing what you suggested, that I simply refused to engage. It seems that you feel I should obey your suggestions, and supply you with details of books, such as for example as to what you "seem vaguely to remember from look into Landau& Lifshitz 20 years ago".

You are proposing to narrow the subject matter, at present, to Reif 1965. I do not think that a good policy, but for the sake of your feelings, for the immediate moment I will accept it. The following is rather tedious and will probably be of interest to very few if any. But I do not see how to counter your comments without it. My summary of it in a nutshell is marked below by a dot point.

From my point of view, the question is about how to define work when temperature cannot be defined. As I read you, you believe that Reif tells how to do that. Your reason for that belief is that his definition of work makes no explicit statement about whether it refers to the possibility or impossibility of defining temperature, but rather it claims to be perfectly general. From that claim of perfect generality, you infer that Reif's account covers the case in which temperature cannot be defined.

Contrary to that, I have proposed that Reif does not actually tell how to define work in the perfectly general case. My argument is based on carefully reading Reif. I do not seem to know at present how to find a searchable copy, and so I will have to read by hand and eye a paper-and-ink hard copy. I will look for occurrences of the word 'work', and report here my findings, particularly noting positive instances that seem to tell how to calculate quantity of work (negative instances I will often leave uncommented).

(1) page vii: "The history of ideas concerned with heat, work, and the kinetic theory of matter is interesting, ..."

(2) page xii: "Quasi-static work done by pressure"

(3) page xii: "Work and internal energy"

Chapter 1 is about statistical methods. I skimmed it without finding any occurrence of the word 'work'. Perhaps I missed something.

I skimmed sections 2·0 to 2·5 without finding the word. Perhaps I missed something.

Section 2·6 I read more carefully. No occurrence detected.

Section 2·7

(4) page 69: "When two systems are thermally insulated, they are still capable in interacting with each other through changes in their respective external parameters. This represents the second kind of simple macroscopic interaction, the case of purely "mechanical interaction." The systems are then said to exchange energy by doing "macroscopic work" on each other. There follows a grey box with an example in which a net amount of work is calculated, for a change of state between two equilibrium states. Then the text tells about the corresponding calculation for the statistical description.

(5) page 70: "Whenever we use the term “work” without further qualifications, we shall be referring to the macroscopic work just defined." Then "i.e. the work done by one system must be equal to the work done on the other system." Then in the caption to Fig. 2·7·3: "Schematic illustration of heat and work." The rest of the caption talks about initial and final equilibrium situations.

(6) page 71: "Macroscopic work is, nevertheless, a quantity which can be readily measured experimentally." And: "Then the mean work W′ done by A′ on A is immediately obtained as the product of a mean force multiplied by the corresponding displacement: by (2·7·3), the work done by A is then given by W = −W′."

(7) page 72: in the top grey box: "does an amount of work W = w(s_f − s_i) on the system A′." and in the middle grey box: "this is then also the work done on the system A consisting of the paddle wheel and the liquid." In the caption in that box: "The falling weight can perform work on the system by rotating the paddle wheel." In the bottom box: "Hence the battery does an amount of work qV on the system A ..." And in the caption: "The battery can perform electrical work on the system by sending current through the resistor."

Section 2·8

(8) page 73: "Let Δ_xĒ = W denote the increase of its mean energy calculable from the change in external parameters (i.e. due to the macroscopic work W done on the system.)"

With all respect, this is getting a bit tedious, and I will omit some material at this point; I think it reasonable to ask the reader who thinks this is a spin by me to actually find the text for himself. There is more in this section. In particular it talks about infinitesimal changes, which are rather relevant here: "If one contemplates infinitesimal changes, the small increment of mean energy resulting from the interaction can be written as the differential dĒ. The infinitesimal amount of work done by the system in the process will be denoted by đW; ..." In the second grey box: "It does not designate any difference between works."

Sections 2·9 and 2·10 are about quasi-static processes. I think we are agreed that temperature is defined for them, so I will spare us the detail here.

Section 2·10 is about exact and "inexact" differentials, and again I hope we may be spared the details.

I give up the literal presentation at this point, and ask the reader to check the rest for himself.

• In a nutshell, Reif says on page 70: "Whenever we use the term “work” without further qualifications, we shall be referring to the macroscopic work just defined." That covers it all. It refers to work as an increment between two equilibrium states. For equilibrium states, temperature is definable. There is no hint here that Reif intends to define work for cases when temperature is not definable. You would like to read into what he says that he intends here to define work for cases when temperature is not definable. I say that reading by you would be an utterly mistaken imputation and would be some kind of synthesis.Chjoaygame (talk) 19:23, 28 April 2012 (UTC)Chjoaygame (talk) 23:15, 28 April 2012 (UTC)

Dear Count Iblis, did I go to all that trouble to do exactly as you demanded and examine Reif letter by letter, only to find that you do not make a direct response to my efforts? Instead, you start a new thread that makes only one explicit reference to Reif, one that does not come near addressing the contents of my efforts to obey your instructions to the letter, but instead intends to "discuss here this issue raised by SBHarris above in more detail".Chjoaygame (talk) 23:27, 28 April 2012 (UTC)

Reif on page 70 makes a statement about completely general changes of the external parameters. You may be able to define temperature at the start of the change and after the change, but not necessarily during the change. Take e.g. a free expansion experiment, where the volume is suddenly increased. Reif does consider the free expansion experiment and concludes that Q = W = 0 based on his definition. Clearly that should settle the matter as far as Reif is concerned.

If other books set up things different, then we should also include that in this article, but we do need to read about about how they set up things in full detail here, and not some argument that they intent to do this or that based on a few selective quotes, because that kind or reasoning by you was used to let Reif say something completely different than what he actually says in his book. Count Iblis (talk) 23:44, 28 April 2012 (UTC)

Thank you for this response.

You rightly say that during the process, it may be impossible to define the temperature. We can agree about that. What is being asked of you is, in the case when it is impossible to define the temperature during the process, that you say how to define the work during the process. Your contention has been that you can always define the work even when you cannot define the temperature. To define the work during the process, you need both the pressure and the volume to be defined during the process. If the process is such that during it the temperature cannot be defined, then there is in general no reason to suppose that during it both the pressure and the volume can be defined. To make your case, you would need to show that there is always a way of defining both the pressure and the volume during the process including when the temperature cannot be defined. You have not so far offered the slightest argument to show that. I have produced an explicit statement to the contrary from a reliable source, Glansdorff & Prigogine 1971, page 15: "A continuum hydrodynamic description is then impossible." (Ilya Prigogine won a Nobel Prize for his work precisely in this area.)

It is not reasonable that you ask your opponent to define the temperature for the infinite continuum of intermediate states throughout the process but indulge yourself by defining the work only for the single one-step difference between the two equilibrium states that define the process, the initial and the final states. That would be to ask your opponent to provide infinitely more information than you can, but make out that you are providing the same amount. Up to now, you have been doing just this. No, you are being asked to define the work on the same basis as the temperature is to be defined. If the temperature is to be defined as a continuous function of time, then so is the work to be defined, to make your case. This can be more rigorously formulated in various forms of time-dependent non-equilibrium thermodynamics, but I think what I have just written here makes the point clearly enough.

The reason Reif 1965 confines his detailed prescription for calculating the work to the quasi-static process of Section 2·9 is precisely that such a process offers a definite way to define the presssures that he needs, so that "the macroscopic work ... can then be defined by integration". You are claiming that he does much more, and I say that he explicitly says on page 70 that he won't try to do so: "Whenever we use the term “work” without further qualifications, we shall be referring to the macroscopic work just defined."Chjoaygame (talk) 01:21, 29 April 2012 (UTC)

You assert that: "To define the work during the process, you need the pressure to be defined during the process." I disagree here. The definition acording to Reif on page 70 is rigorous, but it doesn't involve generalized forces. That a continuum hydrodynamic picture may not exist is presumably correct for general procresses, but that's neither here nor there.

You assert: "...and I say that he explicitly says on page 70 that he won't try to do so: "Whenever we use the term “work” without further qualifications, we shall be referring to the macroscopic work just defined.""

No, that's not what he means, he refers to the definition of work he just gave and he builds on that on page 70 and further, where he explicitely considers non-quasistatic changes. Count Iblis (talk) 01:44, 29 April 2012 (UTC)

Dear Count Iblis, your above reply doesn't deal with the physics that I have pointed out in my above comment. Reif makes no attempt to deal with the time-courses of the pressure and volume during the process; he refers only to the initial and final equilibrium states; as you say, it doesn't refer to generalized forces. But they are needed for the calculation for a continuous process description, as is evident in his use of the quasi-static process for his only explicit example of how to do the calculation. I don't think your reply accurately deals with what Reif says.

This disagreement is going far enough to make me say that Reif expresses himself so sloppily that he is not a reliable source for this purpose. You say above that your Professor thought Reif was lacking in rigour: "(he didn't like Reif because of his lack of rigor)". It seems he was right. On your interpretation of Reif, he would contradict the view of the other reference, Kittel & Kroemer 1980, who explicitly say that the reservoir has a temperature τ. I think Reif does not intend to be read as you read him, and that he does not intend to contradict Kittel & Kroemer 1980, but either way, his clarity of expression is now, on a charitable view, in serious doubt. Not a good recommendation for an intended source.Chjoaygame (talk) 02:21, 29 April 2012 (UTC)