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definition of heat; fear of a crocodile

SBHarris writes: "Heat is that energy that flows spontaneously from one place to another as a result of a difference in temperature between one place and another."

I think this rightly expresses one of the main senses, indeed the leading sense, of heat in physics. There is another, that heat can be produced within a system by dissipative degradation of chemical potential energy or by dissipation of kinetic energy of bulk flow by viscosity in a fluid or by friction between solid and another material; these mechanisms can raise the temperature of material without external work being done on the material and without heat being transferred into it; and they are irreversible. These usages for heat production by dissipation are not as rigorously supported by authorities as is the transfer usage pointed out by SBHarris, but I think they are well enough supported to get a place in the heat team, though not as captain.

Added note: The above orange comment was merely intended as a parenthetic remark; it was nearly irrelevant and was not related to my fear of the crocodile. I would have done better to make this parenthetic remark elsewhere. The usage of 'heat production' referred to in the parenthetic remark is a not a primary usage of the term of art 'heat'; it is a slip towards ordinary language usage that happens in ways that people don't expect to lead to general statements about amount of heat transferred; I would list it under the heading 'other usages'. It was a mistake for me to mention it here.Chjoaygame (talk) 11:04, 21 April 2012 (UTC)

I think there is a body of opinion, or one might say doctrine or even dogma, that has not said much in this present exchange, that would say that my above comments are wrong I am wrong to support the above definition proposed by SBHarris: "Heat is that energy that flows spontaneously from one place to another as a result of a difference in temperature between one place and another." This body of opinion is perhaps nearly silent right now, but I think it lurks like a crocodile under the water near us. It insists that heat be defined only for transfer of energy and that the amount of it be defined only as a residual from work-mediated transfer, calculated through the law of conservation of energy, without mention of temperature. This doctrine is derived from the Carathéodory 1909 paper that was given a big imprimatur by Born in 1921. According to L.A. Turner (1962), Simplification of Carathéodory's treatment of thermodynamics, Am. J. Phys.. 30: 781–786, on page 781: "Many physicists, however, have found the mathematics [of Carathéodory] to be difficult. ... Buchdahl⁵ has given alternative proofs of Carathéodory's theorem but these proofs also are fairly involved. The mathematical difficulties have stood in the way of proper appreciation and assimilation of Carathéodory's contribution to the subject." Of course Turner and all those physicists are silly ignorant old fools and we clever Wikipedia editors and readers have no problems with the mathematics. We have all read, marked, learnt, inwardly digested, and written on our hearts with letters of fire and gold the contents of Carathéodory's 1909 paper or of Buchdahl's 1996 monograph on the subject; the widely cited text of Callen does something not too different from Carathéodory; so does volume 1 edited by W. Jost (1971) of the nine-volume treatise of Eyring, Henderson & Jost; and I get the impression that many current student texts do it too. That's part of the reason we have no worries about insisting that the Carathéodory way is the only "correct" one.

But even Buchdahl (in The Concepts of Classical Thermodynamics, Cambridge University Press 1966) restricts his theory to the kinds of system considered in classical thermodynamics, for which, at thermodynamic equilibrium, temperature is defined, and he makes essential use of processes that can go so slowly as to be considered quasi-static and (quasi-)reversible, for which temperature is again quasi-defined. Under these conditions, one can always state the first law of thermdynamics without explicitly mentioning temperature. But a system of axioms should be read as a whole, and it is not reasonable to tear out the statement of the first law from its full axiomatic context. In its axiomatic context, the statement has implicit, though not explicit, dependence on the existence of temperature.

The argument might be mounted, in favour of an extreme insistence on the said doctrine, that work can be always be defined, for all processes, even outside the usual thermodynamic axiom systems, and that that heat therefore can also be so defined. I have not seen this argument actually explicitly presented. I think it might have difficulties. The integration needs definition, for example, of $P\ dV/dt$ for every process. One might make a machine that would controlledly determine $dV/dt$ for every process, but the system then gets to determine whether one can define also $P\$ as a function of time for the process. I am not too clear about how this might be done for naughty processes for which temperature could not be defined. The difficulty seems greater for open systems; experts have various ways of dealing with the definition of heat for open systems in which local temperature is defined and diffusion is allowed. One might consider a diversity of processes with externally mechanically controlled volume that involve ordinary matter, electromagnetic radiation, and neutrinos, the three kinds significantly working on different time scales. One has three pressure meters, one for each of the three kinds. Remembering Maxwell's maxim that there is only one kind of heat, how should one weight the contributions of the three meters to the overall "pressure" reading to calculate the work?Chjoaygame (talk) 11:13, 20 April 2012 (UTC) Our dogmatists might have an answer to this, and now would be a good time for them to come up with it if they do.

Just as a matter of detail, Carathéodory 1909 himself does not even define heat in his own terms, although his systems have temperatures.

If the true generality of the dogma can be established even when temperature cannot be defined, then perhaps we would have to agree that its definition of heat might be sustained in the absence of temperature.

But I think the point of view that takes it that heat and temperature are essentially coherent concepts, as above proposed by SBHarris, deserves a run as a valid point of view also. I have an idea that the crocodile will not allow that; it seems to me that we have just seen an instance of this.

I mentioned this problem long ago on this page, expressing then my fear that I would be shot at dawn every morning for a year if I tried to post it in the article.

Perhaps this crocodile is a mere figment of my perfervid and comprehensibility-eschewing imagination and does not really exist. If it does exist, let's hope it expresses its views on this question here and now. Perhaps it is not really a crocodile, but a beneficent water-spirit after all?Chjoaygame (talk) 21:12, 19 April 2012 (UTC)

Chjoaygame, you write "....then perhaps we would have to agree that its definition of heat might be sustained in the absence of temperature." Do not forget that a single temperature can only be assigned to a thermal (heat) system when it is in equilibrium. A thermal system may well have two or more parts each with its own temperature, these various parts will of course, because of the temperature difference(s) between them, exchange thermal energy until they all have the same temperature. The point being, of course, that it may be possible to identify different temperatures in one thermal system. --Damorbel (talk) 08:07, 21 April 2012 (UTC)

In thermo, heat is defined as heat flow due to a temperature difference, period. In physics and chem, it's defined as heat flow PLUS all that energy in a system that contributes to its temperature, and that must be extracted by a temp difference, since it's been thermalized (and now has maximal entropy). All other definitions of heat are colloquial and nonscientific. SBHarris 23:25, 20 April 2012 (UTC)

Does this "heat is defined as heat flow" definition 1/ support the kinetic theory of heat? And 2/ how does your definition explain other aspects of kinetic theory such as pressure (in gases) and the speed of sound? --Damorbel (talk) 06:24, 21 April 2012 (UTC)

Please see above some coloured remarks and modifications of my initial version of this comment.

The crocodile of my fears has not spoken here so far. Perhaps it is now only a memory from the past and is no longer lurking in the actual present.Chjoaygame (talk) 11:04, 21 April 2012 (UTC)

To put it in a nutshell, the crocodile that I fear is the idea that heat can be defined without reference, explicit or implicit, to temperature, that is to say, that heat can be defined in situations when temperature cannot be defined.Chjoaygame (talk) 12:55, 21 April 2012 (UTC)

It seems that Waleswatcher has shot the crocodile with nary a peep from it. Well done him. It seems he has just blown away the Carathéodory-Born tradition with a keystroke, on the grounds that it "sounds like original research/improper synthesis" by a Wikipedia editor and "was uncited". It seems that one has to cite support for every word to satisfy Waleswatcher if he isn't familiar with something. No need for him to waste his valuable time on the talk page (just a long posting-comment is enough for a superior being like him), or on reading the puny references that are given by other editors, who of course are ignorant compared with him.Chjoaygame (talk) 23:10, 21 April 2012 (UTC)

Comment A

I agree with Chjoaygame, but I would drop the requirement of being able to define temperature, quasistatic changes are enough. Let me explain. Suppose first that we do have a thermodynamic description, say you are given a PV diagriam, and all you know is that the system has visited some points on that diagram, i.e. all you know is that the system was in thermal equilibrium at the times it was at those points, and it's thermodynamic state was spcified by those points.

Then you can then only define heat and work when the system evolves quasistatically from one state to another state. You can see that in several ways, e.g. the free expansion of a gas where the volume is increased infinitesimally. In both the initial and final states, we have thermal equilibrium, pressure and volume are well defined, yet the work done by the gas is not P dV.

Another way to see this is to invoke the well known path dependency of heat and work. Note that quasi-static means that the changes from one state to another happen so slowly that you can ignore that the system is not in thermal equilibrium, computations based on this assumption become exact in the limit that the changes happen infinitely slowly. Then, consider an infinitesimal change where the in the initial and final state the system is in thermal equilibrium, but the change from these two states proceeds via non-equilibrium within the system, which can be described thermodynamically by chopping te system up in two parts, each is in thermal equilibrium but there is no mutual thermal equilibrium.

Mutual thermal equilibrium exists only in the intial and final state. Then, work and heat can still be computed using thermodynamics, but path dependence means that it doesn't just depend in the initial and final states.

But all this doesn't stop one from defining heat and work for a general system when the changes are qusistatic. I'll have to re-read Reif, but I think what he does is similar to the following. We assume that the system has some probability pi of being in some energy eigenstate |i> with energy Ei. The change in the expectation value of the system's energy due to an infinitesimal change in the system's external parameters has wo contributions, one comes from the change in the system's energy eigenvalues and one comes from the change in the probabilities.

In case of quasistatic changes, the latter is not due to the change in te external parameters. This follows from the adiabatic theorem of quantum mechanics, in the limit where the parameters are changed infinitely slowly, the system will stay in the same |i>, but |i> depends on the system's parameters, made explicit we can denote the states as |i, value of the parameters>, the probability that the system will jump to aother value of i will tend to zero in the limit of infinitely slow changes. Then the former contribution is., by definition, the sum of the change in parameters times the respective generalized forces, which is the work done by the system, the latter contribution is then what is left when this is taken into account, which can be defned as heat.

This also fits in nicely with entropy change of the system, if the probablities pi don't change, the system stays in whatever state |i> it wasin, then everything is reversible. The states |i> depend on the value of the external parameters so if you change te paraemeters back to what it was, you restore the system's microstate. But in case of a rapid change, or when heat is transferred to the system, the system will jump and the value of i will change, and then you get irreversible change.

Just characterizing a system using the probabilities pi is thus enough to define heat and work in case of quasistatic change, but the system is then described by the huge number of independent parameters pi. In thermal equilibrium, the pi are themselves parametrized by only a few parameters. E.g. for isolated systems in thermal equilibrium, pi is constant within a narrow range in case, we call this the microcanonical ensemble description, or pi = exp[-Ei/(kT)]/Z in case of a system in contact with a heat reservoir at temperature T, this is the canonical ensemble description, etc. etc. Count Iblis (talk) 16:43, 21 April 2012 (UTC)

response A3

Count Iblis, can you comment further on this?

the latter contribution is then what is left when this is taken into account, which can be defned as heat.

This also fits in nicely with entropy change of the system, if the probablities pi don't change, the system stays in whatever state |i> it wasin, then everything is reversible. The states |i> depend on the value of the external parameters so if you change te paraemeters back to what it was, you restore the system's microstate. But in case of a rapid change, or when heat is transferred to the system, the system will jump and the value of i will change, and then you get irreversible change.

I don't see how that's true. A sudden change indeed changes the pis (I agreed with everything you said up to that point). But it's not exactly true that it's irreversible, nor does it necessarily change the entropy. A classic problem in QM is to start with the ground state of a harmonic oscillator, and then suddenly change the frequency. The wavefunction doesn't have time to change, but expressed in the basis of the new eigenstates it indeed isn't the ground state anymore, so the pis have changed. But the entropy hasn't, because the new state is still pure and so still has zero von Neumann entropy, and it's also reversible at least in the sense that if you suddenly change the frequency back after a very short time, the system goes back to its ground state.

I suppose it's true, however, that if you wait a while and THEN change the frequency back, you will NOT go back to the ground state (unlike the case of an adiatbatic change, where you always remain in the ground state). Is that the point? But if so, I'm still puzzled why the entropy doesn't change. Thanks in advance. Waleswatcher (talk) 17:23, 22 April 2012 (UTC)

In short, I see two aspects of the issue you raise. One is the problem of dealing with completely isolated systems, which is still a point of debate today. Another one is dealing with the problem at hand in a moe practical way. To start with the latter, if we have some macroscopic system isntead of a single harmonic oscilator, the system would decohere very fast. Even if we keep the system isolated in a thermoynamic sense, the Hamiltonian that describes the system would contain interaction terms of the system to the environmment. If we assume some simple toy model where all these itneractions commute with the Hamiltoinian, then you get what you want: the off diagonal terms of the density matrix radidly go to zero and the von Neumann entropy becomes the Shannon entropy in terms of the new Pis, so the entropy will have increased.

However, there is still a theoretical problem in case of a perfectly isolated system. The time evolution is unitary, and therefore the entropy shouldn't change. This issue shouldn't be dismissed to easily, the entire universe can be considered to be a closed system that evolves in a unitary way. So, what happens if we do a free expansion experiment but now erything is really 100% isolated. My take on this is similar to what my Prof. wrote in his lecture notes (he didn't like Reif because of his lack of rigor). To define entropy in general, you need to distinguish between the fine grained entropy, which you get from the von Neumann formula applied to the exact pure state of the isolated system and a coarse grained entropy, that you get when you thow away information about microscopic details of the system.

Let's assume that you do know the exact initial state of the system before the free expansion. Then under unitary time evolution, after the free expansion, the system is still in some well defined pure state. Every initial state the system could have been in, maps one to one to the set of final states the system can end up in, so it should be clear also to non-experts following this discussion, that there is a problem with saying thatthe entropy has increased. We want to say that the number of possible states the system can be in, is much larger after the expansion, than it was before, but this isn't really true. Most of the states you can put the system in when it has expanded cannot be reached from the intial state, these states will not evolve back to the smaller volume after time reversal, and are thus not the states the system can end up in.

Now, the solution can be obtained by performing a coarse graining. Obviously, we didn't really know the initial pure state of the system, so we still would describe it using a density matrix, which reflects our ignorance about the initial state. Any random intitial state will have similar macroscopic characteristics, and given some of these macroscopic characteristics, the probability that the system is in some pure state, should be a uniform distribution. The density matricx then yields the correct entropy via the von Neumann formula.

After the expansion, you use the same trick. The states the system creally can be in are uniformly distributed among the states you can put the system in, and then given some macroscopic characteristics, the set of states the system could be in consistent with those characteristics is much larger, this will yield the correct entropy increase.

It actually all boils down to recognizing that entropy is nothing more than the amount of information we don't have about the exact state of a system when given only a macroscopic specification (like volume, energy etc. etc.) Count Iblis (talk) 23:30, 22 April 2012 (UTC)

Thanks for the response. I agree with you in general that decoherence/coarse graining should suffice to guarantee that the entropy change is non-negative. But I'm still not clear on why the pis changing corresponds to entropy change, while the |i>s changing does not, at least for isolated systems.

Let's take your example of a system coupled to an environment. I agree the states of the system will decohere rapidly, which means the density matrix will become diagonal. But then changing the pis will increase the entropy only if it increases the Shannon entropy. Now, I suppose it's the case that for a decent sized system away from equilibrium "nearly all" (in some appropriate technical sense) changes will increase the Shannon entropy, for the usual statistical reasons. So that is probably fine.

But the case of coarse graining an isolated system is a lot less clear to me. How exactly is this coarse graining defined? If we want to include all states that have macroscopic characteristics (expectation value of H, perhaps?) that are within some range of the microstate, it seems that changing the |i>s while leaving the pis alone will in general change the entropy, because it will bring more states in or out of that range. Is there some other method of coarse graining that avoids this? Waleswatcher (talk) 13:42, 23 April 2012 (UTC)

The coarse graining in the agrument by my old Prof. was just defined in a rather trivial handwaving way. All he did was justify the standard argument that entropy should increase in case of e.g. free expansion. So, what you do is you assume that the initial system is in some pure state. That pure state contains the information about the macroscopic properties, like the volume of the gas. Then you switch from the pure state to the density matrix of the microcanonical ensemble corresponding to these macroscopic properties. If pure state |X> evolves to pure state

|Y>, then after perform this procedure on both |X> and |Y>, you should find the standard entropy increase. Count Iblis (talk) 22:37, 24 April 2012 (UTC)

One of you thanking the other in advance, both of you telling each other what experts you are, you two are stroking each other's egos with blithe discussion of such remote and abstract questions as whether a thermodynamically isolated system can be represented by a quantum mechanically isolated system, or as to what entropy means. I get the impression that you have to do this ego-stroking as a distraction, because you can't engage with the relevant bulk matter physics here, which is asking whether you can show that you can in general define amount of work transferred for a process for which temperature cannot be defined.

For equilibrium thermodynamics, whenever one can uniquely define amount of work transferred, one can define temperature and thus heat transfer independently of work transfer. But it's not so obvious for non-equilibrium thermodynamics. This is what other editors are concerned about. This is where you are spoiling the clarity of the article. You seem to be insisting that you can make such a general definition, but you are not coming up with the goods to support your apparent insistence. So far, you haven't engaged with this physics.Chjoaygame (talk) 04:01, 23 April 2012 (UTC)

Counterexample. Consider a system consisting of two thermally insulated subsystems, each at a different temperature. Defining work and heat is trivial for this system, yet the system can be very far form thermal equilibrium, no temperature can be defined for the system. Count Iblis (talk) 23:13, 24 April 2012 (UTC)

response A2

I would like some assistance with you comment, Count Iblis; just a few points to clarify:-

1/ "you are given a PV diagriam, and all you know is that the system has visited some points on that diagram," I need to know what kind of diagram this is; is it a graph or just P & V axes? I ask because the well known PV = Const. curve is, I think, a constant temp. curve. Thus are you considering changes at a constant temperature?

2/ You write further "...the work done by the system, the latter contribution is then what is left when this is taken into account, which can be defned as heat." Does this "work done" result in a temperature change? And also, during the "quasistatic changes", does your sytsem undergo a thermal interaction with the surroundings, i.e. an exchange of energy. --Damorbel (talk) 17:54, 21 April 2012 (UTC)

1. Yes, the familar diagram with P & V axes. It can indeed be a curve with constant temperature if it is an ideal gas and PV = const., but it doesn't necessarily have to be that.

You write "... it doesn't necessarily have to be that..." But what it is is at the heart of the matter; a generalised P-V diagram without system restrictions does not, of itself, convey any meaning; after all there is always some P x V = C curve will pass through a given point on a PV diagram; that is what I was seeking by way of clarification. Are you able to go further? --Damorbel (talk) 10:16, 23 April 2012 (UTC)

Yes, so the system has to be specified for the P-V diagram to give sufficient information. In case of an ideal gas, you would have to specify the total number of molecules, and then everything is fixed. Count Iblis (talk) 00:06, 25 April 2012 (UTC)

2. Yes, if temperature is defined, it can change, it can have thermal interaction with the environment. Count Iblis (talk) 00:35, 23 April 2012 (UTC)

You write further "...if temperature is defined, it can change...." My problem here is that, if a thermal system is undergoing an interaction with its environment e.g. energy exchange of one sort or another it is not in equlibrium so ita temperature is undefined; which I see as a contradiction. Of course I have probably misunderstood the point you are making so it is with just a little humility that I must seek additional clarification! --Damorbel (talk) 10:16, 23 April 2012 (UTC)

Indeed, so what one does is assume that the system was in (internal) thermal equilibrium first, then it is in thermal contact with some external source, and then you wait (perhaps after dcoupling it from the source) until the system is again in internal thermal equilibrium. The temperature is then defined in both the final and the initial state. Count Iblis (talk) 00:23, 25 April 2012 (UTC)

response A1

Count Iblis writes: "I agree with Chjoaygame, but I would drop the requirement of being able to define temperature, ..."

We are now talking turkey. As I read this comment of Count Iblis, I would have written his sentiment thus: 'I disagree with Chjoaygame because I would drop the requirement of being able to define temperature.'

I have to say that I don't think Reif is likely to provide the conceptual apparatus for this discussion.Chjoaygame (talk) 17:36, 21 April 2012 (UTC)

It's not a sentiment, it's just about how I understand the topic from deeper principles. That is what I can't drop, at least not without an alternative framework. And then I would have to see how you define temperature from first principles. Count Iblis (talk) 18:00, 21 April 2012 (UTC)

• Count Iblis knows that we who study thermodynamics in its own right are just ignorant shallow players, hand-wavers, with only obsolete and outdated ideas in our cotton-wool-filled heads, hovering vaguely above the realities. He knows that the deeper principles, the real things, belong to quantum statistical mechanics. This is not just his sentiment. It is the reality.

We half-witted, shallow players, in our ignorance, regard statistical mechanics as providing explanations of essentially macroscopic phenomena: explanations that are splendid, valuable, valid, flawless, rigorous, admirable, deep, insightful, enlightening, excellent, admirable, respectable, fundamental, up-to-date, contemporary, modern, and meritorious and praiseworthy in every way; but still explanations, not definitive of the essence of the phenomena of which we speak, say we ignoramuses. The very choices of statistics and side conditions that are calculated in the statistical mechanical explanations of our phenomena are in essence choices of macroscopic entities, say we. Without them, the statistical mechanics would have no definite phenomenon to explain. We think that a thing is what it is, not something else. In particular, we, in our ignorance, regard a thing as what it is, not merely as a manifestation of its deeper explanatory principles. So we do not regard heat as the microscopic adventures of microscopic particles. We regard heat as explained by the microscopic adventures of microscopic particles. Clearly this marks us out as shallow and naive.

(What of this word 'essence' that I write? I mean it as a logical term. I mean by it that the essence of something is just precisely what is specified in its definition. Its essence does not extend to its properties that are not specified in its definition, and does not extend to its explanations in terms of other things, and does not extend to its analogues, and does not extend to other entities that are like it. That's all.)

We do not deny that Count Iblis might flawlessly explain all our phenomena, but still we get to say what phenomena are to be explained.

Temperature, as Count Iblis rightly points out, is basically defined rigorously for bodies in thermodynamic equilibrium. This definition is well explained by statistical mechanics, and Count Iblis can tell us about it in an admirable way. But the macroscopic way is to start with various empirical observations, getting to empirical temperature and a host of other experimental observations, and eventually arrive at thermodynamic temperature by a process of reasoning that makes no reference to microscopic motions or particles.

Count Iblis will then tell us that there is no rigorously valid reasonable way of extending our definition of temperature to bodies or processes not in thermodynamic equilibrium. He means that he does not intend to offer a microscopic explanation of the temperatures of bodies or processes not in thermodynamic equilibrium, because no such explanation can exist. We would say then that he can offer explanations of classes of processes that start and end in states of thermodynamic equilibrium, for which temperature is defined; the heat transfer, that he will admit as well defined, took the states of the bodies from initial to final thermodynamic equilibrium state, for each of which temperature is defined.

I do not see why he thinks he can talk about any other kind of heat transfer in any rigorous way if he sticks to his principles of microscopic explanation being the only real thing.

We ignoramuses will reply that the notion of thermal equilibrium will rescue him and us. Thermal equilibrium is not the same thing as thermodynamic equilibrium. Thermal equilibrium is a process word, not a one-body word. On the other hand, it makes sense to say that one isolated body is in thermodynamic equilibrium. When the process of heat exchange between two bodies is showing a zero rate for a fair duration of time, they are in thermal equilibrium. (A body can be in thermal equilibrium with another body, but it hardly makes physical sense to say that it is thermal equilibrium with itself. This of course will drive experts on the zeroth law of thermodynamics to apoplexy, and perhaps to order that I be shot at dawn every morning for a year. Nevertheless, dare I say it, the mathematical relation of thermal equilibrium between bodies is to be regarded as mathematically symmetric, and though it makes little physical sense, the mathematical relation of thermal equilibrium is also to be regarded as mathematically reflexive.)

A reference body (to be called a thermometer) that is isolated apart from its physical connection with another body (to be called the body of interest) by way of a thermal conductor or by way of a radiative pathway, is in thermal equilibrium with the body of interest when its thermometric property is stationary in time, or changes slowly enough to provide important information about the adventures of the body of interest. Then, subject to a further important condition, the thermometer is recording the temperature of the part of the body of interest with which it has thermal connection. The further important condition is that specified local properties of the relevant part of the body of interest obey certain mathematically and physically and chemically specified conditions to a specified degree of approximation. If this important further condition is not satisfied, we will not claim that we have defined a temperature. The body of interest is permitted to be in a state of continuously changing flux of matter and energy with other here unspecified bodies, and not in thermal equilibrium with any body other than the thermometer, and not in thermodynamic equilibrium in itself. (To be very careful, we will check the spectrum of the radiation that pervades the radiative pathway to see that it is Planckian; we will have made arrangements to ensure that only Planckian radiation pervades the pathway. We will check out the thermal conductor to see that it is suitable for its task. The thermometer will have suitable properties, for example it will not be made of water at 4°C.)

We will then turn to Count Iblis and ask him to provide an explanation of this in terms of the microscopic adventures of microscopic particles, with the aid of deeper principles, his first principles, and we will duly appreciate and admire his skill in this.Chjoaygame (talk) 21:13, 21 April 2012 (UTC)

• My comment just above is rather rambling. Please let me try again.

•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.

•I am trying to say that whenever Count Iblis can calculate a definite amount of work for a process he uses conditions in which temperature is defined and which would enable also a direct calculation of heat for that process. In this situation, his plan to define heat indirectly, following the Carathéodory-Born prescription, as a residual from internal energy (which is subject to a conservation law) by subtraction of work, is only a mathematical manoeuvre that relies on the conservation law. It is not an advance in physics.

•I am also trying to say that there will be conditions for which Count Iblis and I will agree that temperature cannot be defined. In those conditions, I deny that in general Count Iblis will be able to calculate the work, and so his method of defining heat as a residual from work will not in general work, and he will not in general have defined heat in the absence of a definable temperature.

•Count Iblis is dutifully following the symbolic formula for the Carathéodory-Born prescription, and, unless I misunderstand him, seems to think it will work even beyond the axiomatic context in which it is defined. But that doesn't enable him to actually define work for conditions when there is no temperature. To make his case he needs to show that he can define work in a general way when temperature cannot also be defined.

•The crocodile that Waleswatcher shot was the insistence that it makes sense to define heat when temperature is not defined, the insistence being based on a merely formal following of the Carathéodory-Born prescription, beyond the axiomatic context in which it is defined. Fortunately, Waleswatcher knows that heat and temperature are essentially coherent concepts, and fortunately he appears to give no truck to the Carathéodory-Born prescription taken beyond its axiomatic context.

•That crocodile was the reason for the problem that SBHarris said above was "stinking up the lede".

•To bring the crocodile back to life, someone would have to show that he could define work in a general way when temperature could not be also defined. I am waiting.Chjoaygame (talk) 20:10, 22 April 2012 (UTC)

• Looking again at Waleswatcher's new lead, I see that I was mistaken to say that he shot the crocodile. He defines heat in the first sentence of the lead through the phrase "thermal interaction".

This use of the term thermal interaction in the lead does not mention temperature. Waleswatcher's references for the first sentence are Reif and Kittel & Kroemer. Talk of "thermal interaction" in Reif carefully and very deliberately avoids mention of temperature. This makes Reif a rigid Carathéodory-Born man. In Reif, thermal interaction is defined to mean energetic interaction other than through 'external variables', that means energy transfer other than as work. But Waleswatcher's new lead doesn't reveal this to the reader. Kittel & Kroemer do on the cited page 227 explicitly mention temperature as related to heat transfer, so one may say that they are not such rigid Carathéodory–Born men as is Reif. Kittel & Kroemer assume that the reader knows what entropy is as a presupposition for their definition of heat. So does Waleswatcher's new lead.

Thus Waleswatcher new lead has just hidden the physical meaning that was clearly visible, and objected to by several editors, in the previous lead ("a quantity of heat is an amount of energy produced or transferred from one body, region of space, set of components, or thermodynamic system to another in any way other than as work"). Not only avoiding the notion of temperature as coherent with the notion of heat, but also hiding that the definition of heat that he uses depends essentially on work not temperature, Waleswatcher has succeeded in making the first sentence of the lead thoroughly uninformative.

On this basis, it looks as if Waleswatcher is helping the crocodile lurk invisible. My mistake. Justifying the presence of the crocodile would call for someone to show that he could define work in a general way when temperature could not be also defined. I am waiting.Chjoaygame (talk) 23:28, 22 April 2012 (UTC)

Comment B

Work is easily defined as force X distance in closed systems. It only gets complicated in thermo if you open the system to mass transfer with the mass bringing chemical potentials, etc, etc. Temperature is dE/dS, and you can see the statistical definition which amounts to looking at S in terms of first principles in fundamental thermodynamic relation. The WP article on temperature also mentions this. For reversible processes that leaves you with dQ = TdS. Work doesn't add entropy to systems until it is converted to thermal energy within them (but after that, you have an irreversible process and the entropy of the universe increases). This is merely a way of saying that once work has passed into heat, you can't get all the work back. Open the system to mass and now heat flow gets complicated since heat is coming in in other than the traditional slow reversible way. See the interesting paper here. This paper also notes, BTW, that modern thermo does not bother with inexact/imperfect differentials for heat and work, δW and δQ, but has passed to being able to talk about these in terms of perfect differentials dW and dQ. See reference 4. SBHarris 05:34, 23 April 2012 (UTC)

The question that the crocodile raises is whether one can define quantity of heat transferred in situations when one cannot define temperature. If one can define quantity of heat transferred in situations when temperature cannot be defined, then it seems that we should define quantity of heat transferred as a residual, that is to say, as 'energy transferred in any way other than as work'. If one cannot define quantity of heat transferred in situations when temperature cannot be defined, then it would be reasonable to say that heat transfer is always associated with temperature variation, and even reasonable to include that in one of the admissible alternative definitions, according to an alternative point of view.

The paper to which you refer does not stop using the imperfect differentials because it cannot be bothered to use them. I stops because it has a sound physical reason for stopping. The sound physical reason is that it refers throughout to situations in which temperature can be defined.

The paper to which you refer also refers to texts in which it is pointed out that under some situations, temperature cannot be defined. Such situations are far from thermodynamic equilibrium. For example, on page 87, Kondepudi & Prigogine 1998 write: "This is the assumption of local [thermodynamic] equilibrium. There are systems in which this assumption is not a good approximation, but they are exceptional." This means that these authors consider it exceptional to deal with a system in which temperature cannot be defined. The ordinary situation for these authors is one in which temperature and entropy can be defined, and then it is feasible to define work also. The present question, raised by the lurking of the crocodile, refers to the exceptional situations in which temperature cannot be defined, and asks for those situations, can one define work? It is those exceptional situations that govern whether in general quantity of heat transferred can be defined when temperature cannot be defined. It is about including or excluding mention of temperature in a definition of quantity of heat transferred.Chjoaygame (talk) 11:00, 23 April 2012 (UTC)

I think it's fair to say that "heat" cannot be defined in any way if temperature cannot, since the idea behind both Q and T is that they are both measures that apply only to situations of maximal entropy change for the energy you are transferring (or, in the termperature case, to the maximum entropy that you can have for the "thermally distributable" energy contained in your local ensemble of particles-- this is local equilibrium). Although you can always calculate dS from first principles (or at least be sure that it exists) you cannot then calculate dQ = TdS if you have no good number for T for the system that lost or gained the Q energy. You also cannot calculate a dE/dS to give your T, because this equation also assumes that E is the definable function of S for a canonical particle ensemble, which by definition is in equilibrium with a well-defined T, a maximal S per E, and again a nice dS for every dE.

The nice thing about defining heat as only "thermal energy transfer" is that you get away from all the quantitative problems so long as the target system has a temperature. In that cause, heat transferred is just E where E is energy transferred, provided that E is also TΔS for the target system temperature. For strictly thermal energy transfers (ie those driven by a T gradient and nothing else) the transferred E is always TΔS (or some integral of that) so you can leave that part of the definition out, and simply say that heat is always ANY and ALL energy transfered ONLY by a thermal gradient (no matter if by conduction, convection, radiation, or some combo). If the energy transfer is only partly due to a temperature gradient, now you have to calculate some TΔS-like term for your target system (it's nice if heat capacity is so large, that T is constant) and then say that TΔS was the heat part, and that any remaining part of the energy transfered was "thermodyamic work". That makes "thermo work" easy to define as dW = dE-TdS. I merely objected to turning this around and trying to define heat as dQ = dE-dW, inasmuch as the thermo work is far more than easily-defined mechanical work, and really is a garbage bag of any process that transfers energy without the full entropy cost of Q/T_target that you see for heat Q. We thus need to keep away from defining thermodynamic work until we're clear on heat and temp and entropy already. Then it can be easily defined above as dW(thermo) = (dE-dQ) = (E-TdS). If you don't do that, you're in danger of the circular definitions we have had.

In systems that have not yet come to equilibrium, the key question to ask is whether they are going to come to (internal) equilibrium thermally, or by some other process in which other types of energy are slowly to be transformed into heat. If thermally only (and no heat generated), it doesn't matter how complex they are (it could be cold jello shot full of hot beads or BBs, each of which has an internal temp gradient within it) and you can still calculate what the final temp will be, and thus what the heat transferred by the hot BBs was. But if the BB's are made of radium and generate heat continuously out of some other type of potential entropy-free energy, now all bets are off since there is no equilibrium in an adiabatic system that has heat being generated inside it out of something else, and the answers are all time-dependent. That is why I think the term "thermal energy" as an integral from absolute zero to T, of C(T)dT where C(T) is the heat capacity, makes sense for systems in which all energy is thermal (defined as able to be transfered by a temp gradient and heat conduction/convection/radiation without other processes). If such systems have not come to internal thermal equilibration yet, but will eventually, by simple intermal heat transfer, you can always wait till they do, and get the same number for thermal energy or heat content, and all other variables. In this sense, heat does act like caloric and I have no problem with thinking of it that way. It's not mixed up with work and it can be defined as a part of internal energy that is definable. It's only when heat is being generated (converted from thermo work, as in the radium example) that it is not conserved, and all the assumptions of treating it like caloric break down. SBHarris 19:38, 23 April 2012 (UTC)

• SBHarris writes just above here: "I think it's fair to say that "heat" cannot be defined in any way if temperature cannot, ..."

This thread began with a quote from SBHarris: "Heat is that energy that flows spontaneously from one place to another as a result of a difference in temperature between one place and another."

At the risk of being accused of entertaining the bizarre idea that some kind of consistency or agreement is possible, I would say that it seems to me that these two statements of SBHarris are consistent with one another. Going to an even wilder extreme, I would suggest that this consistent thought of SBHarris represents a reasonable point of view, held by a number of editors.Chjoaygame (talk) 22:09, 23 April 2012 (UTC)

• Even more bizarre, I think there is support for that point of view in the literature, as follows.

In Equilibrium Thermodynamics, second edition, McGraw-Hill, London, 1968, C.J. Adkins writes about his own presentation of the Carathéodory 1909 story: "The exposition we give here derives from that proposed by Buchdahl.[with three references to Buchdahl]"

In Generalized Thermodynamics. The Thermodynamics of Irreversible Processes and Generalized Hydrodynamics, Kluwer, Dordrecht, ISBN 1–4020–0788–4, 2002, B.C. Eu writes of his formulations of the second law: "The following statements of the Clausius and Kelvin principles are the modern forms phrased by more recent workers [including here a reference to Buchdahl 1966] in thermodynamics, ..."

I think this makes Buchdahl a fair seraph of the Carathéodory 1909 story, and perhaps even a reliable secondary source for some purposes.

On page 10 of The Concepts of Classical Thermodynamics, Cambridge University Press, London, 1966, H.A. Buchdahl writes: "... no finite set of numbers, intended to represent the 'pressure', can be assigned to a gas moving turbulently within an enclosure."

Carathéodory 1909 requires the walls of his enclosures to be deformable, so as to require control of external pressure to keep the shape of his system constant. I ask, how can this be done if the gas is as Buchdahl describes? I answer my own question, it can't. The pressure is needed to calculate the work. So I infer that the work cannot be calculated for a process of this kind. I say this establishes the existence of processes for which the work cannot be calculated. It is no a priori certainty that the work can be calculated for an arbitary process. For a process in which temperature cannot be defined, that was also of the kind here mentioned, we would not in general be able to calculate the heat transferred through the deformable wall, supposing it now to be diabatic, by the method of residual from a work calculation through the law of conservation of energy or the first law of thermodynamics. This looks to me like support for the viewpoint advocated by SBHarris.

Other support for this point of view of SBHarris is to be found in Glansdorff, P., Prigogine, I., Thermodynamic Theory of Structure, Stability, and Fluctuations, Wiley–Interscience, London, ISBN 0–471–30280–5, 1971, on page 15: "... the assumption of local [thermodynamic] equilibrium will certainly fail in highly rarefied gases when collisions become too infrequent, or for interacting fermions at very low temperature where dissipative processes will become ineffective. A continuum hydrodynamic description is then impossible."Chjoaygame (talk) 22:09, 23 April 2012 (UTC)

Try this (2):-

Overview

The heat of a substance or body is the property that gives the sensation of hotness or warmth. Heat is measured by temperature, indicated by a thermometer. A number of different scales have been devised so that thermometers can indicate temperature in a convenient way, usually by the inventors of thermometers. Currently the most used scales are Celsius and Fahrenheit but many have been used down the ages; for some scientific work the Kelvin or Rankine scales is used; these scales have as zero the lowest possible temperature, known as absolute zero; the Kelvin scale has the same size of divisions as the Celsius scale but they are called Kelvins (K); the Rankine scale has the same size of divisions as the Fahrenheit scale the divisions are called 'degrees Rankine' (°Ra).

Heat is an effect arising from the microscopic motions (or vibrations) of atoms, molecules and all particles above 0K. These particle motions are described by kinetic theory. In kinetic theory the particles exchange kinetic energy by various means, the simplest is for gases where the particles exchange kinetic energy by [[elastic collision]. Energy exchange in solids and liquids is less simple but basically it is through the electronic bonds that define the solids and liquids. Even electrons can have heat if they are free to move in a random manner. For a time the electronic/atomic theory of matter could not explain why the specific heat of matter was not much higher than the observerd value; in classical mechanics the number of electrons should have given a much higher value. The answer was that most of the electrons are locked in quantum states that require much more than thermal energy to excite them, so they are unable to participate in thermal interactions. Metals are an example where free (conduction) electrons contribute to heat processes, the relatively high thermal conductivity of metals is due to the (electrical) conduction electrons.

The measure of the vigour of the particle vibrations is their temperature, absolute zero temperature is the condition where there are no more (measurable) vibrations (but see zero point energy). That is to say: temperature is the measure of the amount of (thermal) energy possessed by a particle. This thermal energy is a closely related concept, it is the sum of the vibrational energies of all the particles under consideration, e.g. the thermal energy of a block of ice is the sum of the (vibrational) energies of all the particles in the ice block, thus the energy depends on the size (mass) of ice block but the temperature is proportional to the average energy of the particles.

--Damorbel ([[User talk:|talk]]) 07:02, 20 April 2012 (UTC)

Comment α

I don't know whether he quite understands it, but at least CHJ knows of my view of what he calls terseness; however, in this case I must grant that Damorbel's "Heat is an effect arising from the microscopic motions (or vibrations) of atoms..." is absolutely no improvement. It neither adds nor information nor clarity to the original; It even is debatable whether it is meaningful. Not that I am happy with the original either: "motions (or vibrations)"? what does "motions or" add to the meaning or clarity? "Fresh fish sold here daily" say I. Anyway, what is all this about "above 0 Kelvin?" And when do electrons not "have heat"? Sorry to be negative, but what I see there seems to me to have a long way to go. What is more, the reason it has far to go, is that the approach to the article is wrong. I am not a fan of thoughtless application of top-down design, but round here I don't know what else would work, other than getting a literate writer versed in the necessary physics, non-technical, and engineering concepts, to go away, write alone, check, and install the product when done. The teamwork here is poisonous. Any bets on how or when it will improve? JonRichfield (talk) 12:32, 20 April 2012 (UTC)

There are links to Kinetic theory and elastic collisions for further explanation of the relevant dynamics of the atoms and molecules. The suggested text also makes it clear that electrons do not take part in thermal processes when their quantum state require energy far above thermal energy to activate them.

You appear not to be familiar with the nature of 'heat', you write: "getting a literate writer versed in the necessary physics, non-technical, and engineering concepts, to go away, write alone...." For centuries good people have be looking for ways to describe the phenomenon of heat, perhaps the invention of temperature scales 270 years ago was the first big step of modern times. Since then the steps have been slow and painful, frequently in the wrong direction; the reversal of these mistakes taking up to a century to take place.

You do not seem to be familiar with the history of the subject, this gives you two severe disadvantages when making your (vey welcome) contributions; first you are unable to distinguish the useful contributions and those that aren't; and secondly you are not distinguishing between the residues of failed theories like caloric and the more consistent theories such as kinetic theory.

'Heat' is quite a complicated matter, the modern science is not at all intuitive. Kinetic theory was considered by Daniel Bernoulli in 1738 but it took another 140 years before a relatively complete explanation was assembled by Clausius, Maxwell, Kelvin, Boltzmann, Rumford and many others. Famous scientists such as Humphrey Davy strongly opposed kinetic theory (the theory of particles) and were well enough placed in the scientific institutions to block the developement of this new science.

Science is not like the script of a play, you cannot learn it in a few sittings, there are too many false trails, you must understand exactly why these false trails became intellectual dead ends so that you do not repeat the misunderstanding that started the false trail in the first place. For example, you really should understand why the concept of heat 'flowing' is of little or no use outside the nursery, quite simply it is not supported by observations. And please do not ask 'what observations' until you have made a thorough study of the subject yourself; without the study you will not understand the answer. --Damorbel (talk) 13:49, 20 April 2012 (UTC)

Such charity and condescension chasten the spirit and wring the withers. Once we have paid deference to the philology and logic, who could cavil? Mmmm... Who indeed? Possibly some few readers so small of spirit as to insist on meaningful discourse? Let us see.

For a start, permit me to assist you out of the main original point of confusion in which you stumbled over the distinction between "science" and language usage. In the interests of everyone's patience, I shall pass over your difficulties in comprehension of the concept of science in itself (Script of a play indeed! And you wish to dictate the words in the script hmmm...?) Instead forgive my pointing out, in my admittedly attenuating faith in your capacity to absorb such concepts, the distinction between the material of science and the language in which assertions about such material are couched. <siiigh...> For example, expound you never so learnedly upon the empirical and analytical study of thermodynamics or haemodynamics, you cannot, in defiance of common usage, mitigate the inappropriateness of your assumption of personal authority for passing strictures on the language in which anyone may refer to their attributes, actions and interactions. Doubly so when you imperfectly understand the terminology. For example it is a pity that you failed to understand the explanation of the reasons for accepting particular terms in particular contexts, such as the "flow of heat", "bottom" "quark" and so on. I suppose that you would similarly fail to accept the innocuity of "path of heat" on the grounds that heat does not walk? Well well, when the person who read the passage to you has some spare moments, no doubt you could ask for an explanation of such intricacies. Meanwhile you might as well spare yourself the trouble (and the rest of us the tedium) of yet again explaining why any student who has encountered any expression such as "heat flow" falls an instant victim to the blandishments of caloric theory and its temptations to the application of fluid flow equations. Strange that no one else complains of similar difficulties among his students. You say: "For centuries good people have be looking for ways to describe the phenomenon of heat..." and apparently on that vast insight you elect to justify disqualification of "flow" from the mode of speech of persons referring to heat? Because of a private conviction that only fluids can be associated with flow? When I quoted the expression "Du wisst ein Quark davon" before, I had not meant you personally; sorry about that. I had no intention of over-burdening your technical vocabulary. Meanwhile, forgive the possibly too-pointed implication, but we still lack a decent heat article, and if there is one thing we do not desperately need in overcoming that lack, it is unfounded obsessional semantic nit-picking. Please try to pick some more helpful nits for a change. JonRichfield (talk) 19:09, 20 April 2012 (UTC)

Whoops, sorry, I forgot. In future when you see a question such as: 'Anyway, what is all this about "above 0 Kelvin?" And when do electrons not "have heat"?' do please try reading and understanding the question before answering it. It is difficult to respond to your unthinking response without embarrassing reflections out of place in this forum. JonRichfield (talk) 19:16, 20 April 2012 (UTC)

The purpose of the talk pages is to improve the article, it would help if you could identify moreclearly the improvements you want. Also I am not sure if you have any objections to the technical side of my conribution - care to clarify?

You write "I shall pass over your difficulties in comprehension of the concept of science in itself"; please don't 'pass them over', it reducse your contribtion too much, your help on these matters will be most welcome. --Damorbel (talk) 06:09, 21 April 2012 (UTC)

You're trolling, aren't you? I'm busy even if you are not. In case you're having difficulties, get someone to read you my earlier comments on what the article needs. In case you can't understand them, ask him to explain them very loudly and slowly. As for your technical bits, Oh Lordy... How about looking up some of the relationships between heat and temperature? And science? Oh well, I suppose it could be worse; you could have been girning again about philology and flow instead. Look Db, you explain carefully how far you have progressed beyond a comprehension of scientific proof, naive Popperian assaults on induction, and elementary falsificationism, and I'll consider how much time to ration you. Meanwhile explain to Chj all about your views on temperature and heat. I am sure he'll be much nicer to you than I have been. Ciao for niao. JonRichfield (talk) 19:34, 23 April 2012 (UTC)

Comment β

No.Chjoaygame (talk) 15:12, 22 April 2012 (UTC)

No....what? --Damorbel (talk) 17:11, 22 April 2012 (UTC)

No overview like that.Chjoaygame (talk) 19:30, 22 April 2012 (UTC)

Not really helpful - care to say what is wrong with it?

I suggest my proposal explains a number of important points, most importantly it draws a distinction between heat and energy not found in the current overview; a serious article should contain such a basic explanation. --Damorbel (talk) 05:57, 23 April 2012 (UTC)

No, I don't care to say.Chjoaygame (talk) 10:12, 23 April 2012 (UTC)

In this case am I to understand your contributions are to be seen as merely one-sided? --Damorbel (talk) 10:20, 23 April 2012 (UTC)

No.Chjoaygame (talk) 10:22, 23 April 2012 (UTC)

I am not satisfied with your response because you are using the facilities of Wikipedia for your own agenda, your recent reponses to my contributions such as 'no'' and 'No overview like that', are not positive. My suggestion for the opening statement for the article contains a publicly accepted position of at least one University science department on the matter, it can be found here. Please give an educated response or none at all --Damorbel (talk) 12:10, 23 April 2012 (UTC)

A quote from your internet source: "The flow of heat is from a high temperature region toward a lower temperature region." This is the only occurrence of the word heat in your internet source. You have been lecturing us that we should not speak of flow of heat.

Our article is about heat. Your internet source is about temperature, not heat.Chjoaygame (talk) 15:32, 23 April 2012 (UTC)

You write "....about temperature, not heat..." And your position is that temperature is not a measure of heat...yes?. This is an interesting point. In that case, just what the unit of heat is, let us agree, for the 2nd law of thermodynamics? --Damorbel (talk) 16:04, 23 April 2012 (UTC)

The unit of heat is the joule. With the understanding that only those joules that cause the maximum possible amount of entropy change per joule, which is E/T where E is the number of joules and T the temperature of the place the joule winds up, count as heat joules. Okay? The rest are work joules. SBHarris 18:06, 23 April 2012 (UTC)

Sbharris, you write "The unit of heat is the joule". Er - I don't think so; the Joule (the link has:- 'This article is about the unit of energy. For other uses, see Joule (disambiguation)'is quite definitely the measure of energy; including thermal energy.

It is perfectly possible for two objects to have equal (thermal) energies but very different temperatures; likewise two objects with the same temperature may have very different (thermal) energies

There can be no doubt about it; this kind of innocent error detracts very greatly from the merit of your contributions. --Damorbel (talk) 19:47, 23 April 2012 (UTC)

Damorbel, the SI unit of heat is of course the joule. Heat and temperature are not at all the same thing, and have different units. That is quite literally thermodynamics 101.

I don't mean to be cruel, but your comments on this and other thermodynamics wiki pages make it obvious that you aren't even slightly familiar with this topic. Why then say things like "...this kind of innocent error..." that simply irritate and distract others? Wiki talk pages aren't for giving or receiving lessons in the absolute basics, they're for discussing the material in the article and how to improve it. You clearly cannot participate in that process for pages on thermodynamics, at least not for now. If you are so interested, might I suggest a course or textbook to get you started? Waleswatcher (talk) 20:11, 23 April 2012 (UTC)

In a slightly different take, I would say that Damorbel is considerably familiar with this topic, as to many details of it. But his overall perspective, his ways of thinking, the organization of his conceptual apparatus, his frame of understanding, or his intellectual approach, are not those of conventional science, and indeed are fairly described by some such epithet as 'rather idiosyncratic'. For the purposes of Wikipedia, rather idiosyncratic approaches are usually not appropriate. To remedy this situation, I have in the past suggested to Damorbel that he undertake a study of logic, but I don't think he accepted my suggestion.Chjoaygame (talk) 21:16, 23 April 2012 (UTC)

Waleswatcher, you write "the SI unit of heat is of course the joule". So your position is that the measure of heat or hotness is not the degree Fahrenheit, Celsius, the Kelvin etc. but the Joule; so when the doctor ask what your temperature is you answer "it's 10 Joules this morning" do you?

Waleswatcher; Chjoaygame; neither of your two most recent comments has anything to do with the matter in hand which is the distinction between measurement units for heat and thermal energy. Instead you have made personal remarks about me; please don't, I am not the subject of any article in Wikipedia therefore your comments are, at the very least, off topic. For this article please stick to thermal matters or just keep quiet. --Damorbel (talk) 06:15, 24 April 2012 (UTC)

Comment: Guys, I think that Damor is trolling us. I suggest that we comply with the Wikipedia:Deny recognition exhortation. His previous contributions might have been abject mental confusion, but IMO he has overstepped any plausible mark with "...your position is that the measure of heat or hotness is not the degree Fahrenheit, Celsius, the Kelvin..." etc. DNFTT say I. JonRichfield (talk) 07:14, 24 April 2012 (UTC)

Jon, I'm not sure s/he's trolling us, but I do think you're right that we simply shouldn't respond. Waleswatcher (talk) 16:18, 24 April 2012 (UTC)

JonRichfield, do you have a position on the measurment of 'heat'? Do you measure heat in Joules i.e. energy as does Sbharris (the SI unit of heat is of course the joule). Or do you go for temperature i.e. 'the degree Fahrenheit, Celsius, the Kelvin etc.'? --Damorbel (talk) 10:12, 24 April 2012 (UTC)

Dear Damorbel, you moved in the direction of personal comment with "I am not satisfied with your response because you are using the facilities of Wikipedia for your own agenda." Are all black bodies black? Is the kettle blacker than the pot?

In your edit here [1] you wrote "No, I don't care to say" which is a refusal to engage in discussion. The Wiki talk pages are for improving the article, not explaining your position is therefore not an option. Below you write "When I wrote "No." above, I was hoping to save you...", thank you but the only thing I need saving from is your failure to respond! --Damorbel (talk) 12:31, 24 April 2012 (UTC)

You write above: "the distinction between measurement units for heat and thermal energy." From the context I judge that you think that measurements of heat are measurements of temperature. That is not the accepted usage of physics, chemistry, engineering, or thermodynamics. If my judgment is right and if you persist in that thought, you will be wasting our time here. You have no prospect of changing us on that point.

Again "you think ... measurements of temperature. That is not the accepted usage of physics, chemistry, engineering, or thermodynamics." Dou you have a link for this? I know of none. I have given a link to kinetic theory more than once, I have asked how your position over heat, temperature and energy is compatible with the other aspects of kinetic theory such as pressure and the speed of sound your argument must satisfy these requirements also, do they? --Damorbel (talk) 12:31, 24 April 2012 (UTC)

From what you write, I judge that you seem to think that "thermal energy" is a well defined term of art for a well defined physical quantity. That imputed thought is mistaken, at least for physics, chemistry, and thermodynamics. For engineers I would not like to say. For me, talk here of "thermal energy", as if it referred to well defined term of art for a well defined physical quantity, is a waste of time. You have no prospect of changing me on that point; there are just too many reliable texts that explain why.

The Wiki article on thermal energy is little if any better than this one, but it gives a link to the Encyclopaedia Britanica to support the deffinition of thermal energy

"internal energy present in a system in a state of thermodynamic equilibrium by virtue of its temperature. Thermal energy cannot be converted to useful work as easily as the energy of systems that are not in states of thermodynamic equilibrium. A flowing fluid or a moving solid, for example, possesses energy that can be converted to work in some mechanical device, such as a windmill or a waterwheel, but the same fluid or solid in a thermodynamic equilibrium state having the same energy (as thermal energy) can do no work unless it is combined with another substance at a different temperature, as in a heat engine."'

Note it says ony that: "it requires a state of thermal equilibrium by virtue of its temperature" - nothing at all about the energy being measured by the temperature! --Damorbel (talk) 12:31, 24 April 2012 (UTC)

When I wrote "No." above, I was hoping to save you from a time-consuming futile exercise but my intention was probably unrealistic. I made a mistake in responding to you at all. It is probably better that I continue my usual policy, which agrees with your advice, and just keep quiet about what you write.Chjoaygame (talk) 11:04, 24 April 2012 (UTC)

definitions of heat flow

According to M. Bailyn on page 308 of A Survey of Thermodynamics, American Institute of Physics Press, New York, 1994, ISBN 0–88318–797–3: "A particularly interesting feature of multicomponent fluids is that heat-flow is no longer a unique concept." He goes on to list three conceptually different definitions of heat current density. He comments: "The definitions coincide only in the absence of diffusion." Perhaps I may add that the entropy appears explicitly in the first of his definitions, and from it he immediately derives an expression involving the temperature explicitly. The temperature appears explicitly in the other two. There is literature about this.

From this I infer that there is a reasonable point of view that makes the existence of temperature an essentially coherent supposition for the definition of heat flow, a point of view that the crocodile opposes.Chjoaygame (talk) 11:24, 24 April 2012 (UTC)

It depends on the level of intellectual rigour you need; if you wish to be precise and work with mathematical precision you will soon conclude that 'heat' and 'fluid' have no characteristics in common: the mathematics of heat transfer is quite different from fluid flow. For a start fluid has a readily determined mass and viscosity, heat has neither; fluids have readily determined density (mass/vol.), what does heat have, not even mass equivlent (E = mc²)?

The term 'heat flow' is a metaphor and it will eventually lead you to false conclusions. Metaphors are great for grandiose statements but only lead to screwed up science. --Damorbel (talk) 13:59, 24 April 2012 (UTC)

The term "heat flow" is not a metaphor. Most texts and papers use "heat" and "heat flow" interchangably. Heat MEANS "heat flow." I believe there is concensus on this (at least) among editors here, and you've been left out. I can't say I'm sorry. We've tried to teach you, and you've been resistant. SBHarris 19:22, 24 April 2012 (UTC)

Perhaps it is too fussy of me to say so, but I would say that 'heat flow' is verging on the metaphorical. This particular metaphor is usually not too harmful, but one should be careful not to rely too much on that.

Physics lives on usages that are, or verge on, metaphor, more or less disguised or unrecognized. It is too often true, I think, that it does happen in a seriously harmful way, that physicists are not good at knowing when they are using metaphor and when their language is categorical. Physicists are far from the only offenders in this, of course. In ordinary language, metaphor is also a commonly occurring way in which the language grows. There is no chance of escaping it.Chjoaygame (talk) 20:50, 24 April 2012 (UTC)

Indeed, consider "wave" and "particle." Their meanings refer to macro-objects like water waves and sand particles. If we use them for the mathematical behavior of light or electrons, we're being metaphorical. Which is why the terms don't work sometimes very well at quantum level. It's not that quantum objects are both waves and particles, it's that they are really neither, for wave and particle are metaphors stolen from the big non-quantum world. And as Joseph Campbell reminds us, all metaphors, taken literally, are lies. Bill is not a actually a rat-- or a tiger. The boss is not literally an asshole. ;). And so on. SBHarris 21:15, 24 April 2012 (UTC)

Chjoaygame, you write "Physics lives on usages that are, or verge on, metaphor, more or less disguised or unrecognized." If this is the basis of your understanding may I suggest you add mathematics to the list. I wrote before that physicists sometimes uses words that may appear obscure to others, I suggested that the peoperties of quarks this link will show that there is nothing metaphorical about the properties of quarks, quite the reverse. It is precisely becaus the concept of 'heat flowing' is completely misleading, even though it was the basis of the caloric theory, now totally discredited.

I am surprised you are defending such poor usage; yes there are plenty of teachers still using this outdated concept, this is the unfortunate consequence that teachers tend to use oldfashioned text books and such teachers even write their own books, often without doing the research necessary to endorse their ideas, they are often have little familiarity with the most relevant physics.

User:Sbharris, your idea that the use of 'wave' and 'particle' in physics somehow are metaphors is quite odd. The whole point of scientific enquiry is to compare observations with a (usually) mathematically tractable representation that enables (theoretical) predictions to be made and tested. Have you read Francis Bacon on this? His ideas lie at the heart of modern scientific investigation and progress, they are thee complete opposite to the essential imprecission of metaphor. --Damorbel (talk) 06:24, 25 April 2012 (UTC)

heat transfer and heat production

It is useful in non-equilibrium thermodynamics to deal with entropy production, as well as entropy transfer. Entropy production can be by friction, viscosity, and chemical reaction at speeds faster than quasi-static. These are dissipations of kinetic energy of bulk motion or of chemical potential energy into heat. When the local density of entropy production is well defined, the second law can be stated as the universal non-negativity of local density of entropy production.

When local density of entropy is well defined, for processes that can nearly enough be analyzed by classical non-equilibrium thermodynamics, it makes sense simply to distinguish entropy production and entropy transfer.

The heat so produced simply goes into the pool of internal energy, but under suitable circumstances, such as constant volume, it will be manifest directly as temperature increase, and that is why it is often, perhaps naughtily, called heat production, closely parallel with entropy production. It can be very reasonably argued that this is a violation of the policy of insisting that heat be considered only as heat transferred by conduction or radiation. In the respectable literature there are plenty of respectable violators of this kind, and it is probably not too wicked for Wikipedia to admit their existence, with suitable warnings of the dangers. Such violation is not, in the hands of competent thermodynamicists, taken to lead to ideas of conservation of "thermal energy". They know it goes straight into the internal energy pool, but the fact that it is simply produced by dissipation and is directly linked to entropy production makes the usage 'heat production' seem not too evil. Whether we like it or not, it is found in respectable chemistry and physics texts, often with appropriate warnings about the dangers. What is being pointed to here is increase of temperature also being called heating.

There is another kind of increase of temperature that meteorologists call heating, namely adiabatic heating. This happens when air is simply compressed without time for heat to leave it. For a descending body of air, work is being done on the body of air by the surrounding air, and the body of air is losing gravitational potential energy. From the viewpoint of strict insistence on the transfer definition of heat, this is a wicked abuse of language, but again it makes heating simply refer to a process that causes temperature increase. It is distinctly more wicked than the heat production usage mentioned just above.Chjoaygame (talk) 20:36, 24 April 2012 (UTC)

Well, yes. Compress a gas adiabatically and its temperature goes up. Have you added heat? No. You did work on the system and it didn't become heat until the temperature went up. Did temperature have to go up in the whole gas volume to equilibrium? No. Entropy is maximal by then, but before that, all kinds of hydrodynamic things happen where entropy is at some intermediate value. Ram the piston in fast and you get a shock wave that travels down the cylinder in one direction. In that shock the gas is compressed and very hot. Outside it, the gas isn't heated at all. The shock wave (so long as it's a nice well-behaved adiabatic shock) still contains in each bit of it enough gas to have a temperature and a pressure-- you could calculate it and hydrodynamicists do it all the time. That temperature is far higher than it will be later when the shock has bounced around and thermalized further. But you can take your shock energy E and divide by shock temperature T, and calculate an E/T and that's how much entropy has been produced from your work so far. It's how irreversible the system is, at this point. This E/T does have a value, although since T is so high, it's not as bad as it's going to be. That's the entropy production so far. More comes later as T falls until finally the shock and sound die away completely. T is now minimized for the work you added, and now ALL the work has been turned into heat. At this point you can't get any of work you put in back out, unless you allow production of entropy in some other way, such as letting the gas expand and do work (just letting the gas occupy more volume increases its entropy, even if it doesn't change temperature). But at the point that you have a shock wave bouncing up and down, you could have extracted far more of your initial work from this system than you could later.

Anyway, yes, you can have entropy produced in all kinds of ways that don't involve heat (volume increases, concentration decreases, mixing, chemical reactions that put atoms in places where you don't know where they are, etc). The naked entropy-density changes at all these points require one other piece of information (the temperature at those points) to tell you about how much of the internal energy is now unavailable to be made into work. That's why the various types of free energies are not simple internal energies or enthalpy changes. The part of work degraded by the entropy needs to be accounted for (this ends up being the defacto heat, just as if it appeared by thermal transfer methods), and you can't do that without knowing the temperature at which the entropy change took place.

So I agree with you. The TdS term is surely heat by the old-fashioned accounting, if the TdS is a dE that was transfered by a T gradient. However, there might not be a T gradient and yet there is still a TdS term that looks like heating, smells like heating, and acts like heating from the viewpoint of free energy, energy degradation, in irreversibility. But it's not. So that is why the "thermal gradient" method of the transfer of energy is needed in the narrow definition of heat, but why many other TdS-looking things seem to be defined also as heat by liberal thermodynamicists, since they end up degrading energy into irreversibility in the same way as "thermal heat". Heh, now I'm having to talk about "thermal heat." SBHarris 01:39, 25 April 2012 (UTC)

Thermodynamics according to Reif and other sources

I made the mistake in the discussions so far of replying based on my own understanding of the topic, which is based by what is written in Rif, but also from what I've learned from other sources. However, I think it is better to spend a little time to stick to one source, e.g. Reif, re-read precisely how he sets up things and then write up the essential points. Also, if we stray into non-equilibrium phenomena, it's better to give the POV from the same source, in case of Reif that would be Chapter 15 on irrevesible processes and fluctuations.

Other editors will have their own favorite sources, they can then take one of their sources and explain here how the author sets up the entire topic from start to beginning. This has the advantage of having different POVs with each of these POV being internally consistent and well developped. And it is then also more suitable for inclusion in this Wiki article, as it is taken from reliable sources.

What we should not do is to immediately start arguments along the lines of "source X is wrong, because source Y says something different". One can at a later stage, when how each source treats the topic has been made clear in all its details, have some arguments about how to present the topic in the article based on the different approaches in the literature.

I'll give the perspective from Reif on all the relevant issues raised here in a few hours from now. Count Iblis (talk) 16:18, 25 April 2012 (UTC)

This sounds good to me.

Reif as I understand you is the introductory student textbook published in 1965. The Preface on page viii states: "I have therefore abandoned the historical approach in favor of one that emphasizes the essential unity of the subject matter and seeks to develop physical insight by stressing the microscopic content of the theory." As I read you, Reif presents a point of view, a POV, to use a Wikipdia acronym?

Sad to say I cannot subscribe to any one "favorite source". I find I need to read many sources to get a fair picture of the subject.

I agree with you, as I read you, I think, that there are different valid approaches in the literature. Moreover as I see it, Wikipedia allows the presentation of several points of view provided they are properly sourced?Chjoaygame (talk) 16:52, 25 April 2012 (UTC)

point of view of Khanna, Malbouisson, Malbouisson, Santana 2009.

I refer to Khanna, F., Malbouisson, A.P.C., Malbouisson, J.M.C., Santana, A.E. (2009). Thermal Quantum Field Theory. Algebraic Aspects and Applications, World Scientific, New Jersey, ISBN 978–981–281–887–4.

They write on page 3:

"Tisza [1] and Callen [2], in a rigorous presentation, used the entropy function and the notion of an extremum principle as an ontological starting point to build the thermodynamic theory. ... We present an outline of the main elements of equilibrium thermodynamics along the lines introduced by Tisza and Callen.

[1] L. Tisza, Ann. Phys.(N.Y.) 13, 1 (1961). See also, L. Tisza, Generalized Thermodynamics (MIT Press, Cambridge, 1966).

[2] H. B. Callen, Thermodynamics and an Introduction to Thermostatistics (J. Wiley and Sons, New York, 1985)." [Callen 1985 is a second edition of Callen's text of 1960.]

According to my observation, both Tisza and Callen are widely cited.Chjoaygame (talk) 17:15, 25 April 2012 (UTC)

point of view of Glansdorff & Prigogine 1971

I refer to Glansdorff, P., Prigogine, I. (1971). Thermodynamic Theory of Structure, Stability and Fluctuations, Wiley–Interscience, London, ISBN 0–471–30280–5.

On page 126 they write: "For this reason such problems cannot be treated by the variational calculus in its classical form." This means that they are about to consider problems of non-equilibrium thermodynamics that are not accessible by the methods indicated by Khanna, Malbouisson, Malbouisson, Santana (2009) as derived from Tisza and from Callen.

On page 15 they write: "... the assumption of local [thermodynamic] equilibrium will certainly fail in highly rarefied gases when collisions become too infrequent, or for interacting fermions at very low temperature where dissipative processes will become ineffective. A continuum hydrodynamic description is then impossible."

From this I infer that there are physical processes for which it is not 'a priori' known that work can be calculated.Chjoaygame (talk) 17:29, 25 April 2012 (UTC)

point of view of Grandy 2008

I refer to Grandy, T.W. Jr. (2008), Entropy and the Time Evolution of Macroscopic Systems, Oxford University Press, Oxford UK, ISBN 978–0–19–954617–6.

In Chapter 5, on page 59, Grandy writes: "In classical thermodynamics, it is axiomatic that the entropy is additive for a combination of two independent subsystems, S = S₁ + S₂, and thus it is natural to presume that S is extensive. But additivity is not guaranteed in general as exemplified by any system in which the particles interact under long-range forces (e.g., ionic crystals or spin systems in which the Heisenberg Hamiltonian is not restricted to nearest neighbours): Owing to long-range correlations, S < S₁ + S₂, as in (4.12), ..."

From this I infer that simple considerations based on classical thermodynamics do not necessarily extend to cover all physical problems. It is no longer a priori knowable that work can be calculated for all physical processes.Chjoaygame (talk) 17:46, 25 April 2012 (UTC)

point of view of Callen 1985

I refer to Callen, H.B. (1985), second edition, as cited above by Khanna et al. 2009, and whose 1960 edition is recommended by Reif 1965 on page 83.

On page 6, Callen writes: "By definition, suggested by the nature of macroscopic observations, thermodynamics describes only static states of macroscopic systems."

I observe that static states of macroscopic systems in general allow the definition of temperature. Callen is not focusing his attention on processes for which temperature cannot be defined.

On page 307, Callen writes: "Irreversible thermodynamics is based on the postulates of equilibrium thermostatics plus the additional postulate of time reversal symmetry of dynamical laws."

Callen here is not extending his considerations to apply to processes for which temperature cannot be defined.Chjoaygame (talk) 18:07, 25 April 2012 (UTC)Chjoaygame (talk) 23:42, 27 April 2012 (UTC)

point of view of Zemansky 1957/1968

I refer to Zemansky, M.W. (1968), Heat and Thermodynamics. An Intermediate Textbook, fifth edition, McGraw–Hill Book Company, New York. The fourth edition (1957) is recommended by Reif 1965 on page 83.

Talking about non-equilibrium states, on page 28 Zemanksy writes: "The pressure would not be a thermodynamic coordinate because it would not only depend on the velocity and the acceleration of the piston but would also perhaps vary from point to point."

From this I infer that at this stage of his exposition, Zemansky does not envisage the calculation of work for a passage between non-equilibrium states. Such a passage would be a process for which the work cannot be calculated. This text does not make a general examination of non-equilibrium processes.

Nevertheless, on page 91 Zemansky writes: "When two parts of a material substance are maintained at different temperatures and the temperature of each small volume element of the intervening substance is measured, experiment shows a continuous distribution of temperature."

From this I infer that Zemansky is not in this text intending to describe the progress of passages between states for which temperature cannot be defined.Chjoaygame (talk) 03:23, 26 April 2012 (UTC)Chjoaygame (talk) 23:44, 27 April 2012 (UTC)

point of view of Kittel & Kroemer 1980

I refer to Kittel, C., Kroemer, H. (1980), Thermal Physics, second edition, W.H. Freeman and Company, San Francisco, ISBN 0–7167–1088–9.

On page 227, these authors introduce their idea of heat. They ask the reader to "Consider the energy transfer dU from a reservoir to a system with which the reservoir is in thermal contact at temperature τ; ..."

From this I infer that Kittel & Kroemer regard heat as a concept that is essentially coherent with the existence of temperature.Chjoaygame (talk) 17:56, 25 April 2012 (UTC)

Kittel & Kroemer just happend to be lying on my desk. Have you read how they define work (on p227)? Work is the transfer of energy to a system by a change in the external parameters that describe the system. The parameters may include volume, magnetic field, electric field or gravitational potential. I think this is not a satisfactory definition because work should be 'force x distance' shouldn't it? Thus work should include frictional forces, these are not included in the list; and further, neither does friction change the external parameters.

They certainly rattle on, these two. A few lines further (p 227, top para. 3) they write about 'entropy transfer' as if entropy was a conserved quantity. Um, I don't think so! --Damorbel (talk) 18:30, 25 April 2012 (UTC)

material from Kittel & Kroemer 1980

On page 227 Kittel & Kroemer 1980 define heat transfer as "the transfer of energy to a system by thermal contact with a reservoir."

On pages 1–2 they talk about two systems, each isolated (in our terminology; they use the word 'closed'), each in its own thermodynamic equilibrium. They then let the two systems transfer energy solely by thermal contact. They do not explicitly say that their systems do not do work on each other, but this is implicit in their statement that the energy transfer is by thermal contact and the fact that their systems are otherwise isolated. They then say: "One system will gain energy at the expense of the other, and meanwhile the total entropy of the two systems will increase." Relying on the existence of entropy and internal energy for each system, for this encounter they offer reasoning that necessarily generates a definition of their "fundamental temperature", τ. They then write: "The use of 1/τ assures that energy will flow from high τ to low τ; no more is needed."

Looking at this, one sees that Kittel & Kroemer 1980, without mention of work, have required the definability of temperature as necessary to account for the energy transfer by thermal contact, and have stated that the values of the temperatures are sufficient to determine whether such transfer will occur.

On page 33 they consider the same situation. They write: "What determines whether there will be a net flow of energy from one system to another? The answer leads to the concept of temperature." They go on to explicitly define their temperature by their equations (22) on page 40 and (23) on page 41, in the usual way. Again, there is no mention of work here. (One can add the comment that no work is done in this process of net flow of energy.)

Looking at this, one sees that Kittel & Kroemer 1980 consider the definability of temperature as determining whether there will be heat flow.

On page 227, Kittel & Kroemer 1980 define heat transfer: "Heat is the transfer of energy to a system by thermal contact with a reservoir." They comment on that same page that the reservoir has temperature τ.

Looking at this, one sees that for Kittel & Kroemer 1980, the definition of heat transfer entails the definability of temperature.Chjoaygame (talk) 15:41, 26 April 2012 (UTC)

On page xv, Kittel & Kroemer 1980 say that Callen 1960 gives an excellent development.

On page 28, they quote a sentence from Planck about probability, along with sentences from Boltzmann and from Gibbs.

On page 88, they quote a paragraph from Planck.

I did not find any reference by them to Carathéodory.Chjoaygame (talk) 20:17, 26 April 2012 (UTC)

point of view of Wilson 1957

I refer to Wilson, A.H., (1957), Thermodynamics and Statistical Mechanics, Cambridge University Press, Cambridge UK. Wilson is cited by H.A. Buchdahl 1966 in his bibliography, the rest of which lists just Callen 1960, Guggenheim 1950, Landau & Lifshitz 1938, Landsberg 1961, Pippard 1957, Prigogine & Defay 1954, Tolman 1934, Wilks 1961, and Zemansky 1957.

On page 3, Wilson writes: "The subject of thermodynamics deals with the extension of ordinary mechanics to those processes in nature in which the concept of temperature cannot be ignored; and to carry out this extension we have to introduce the two fundamental notions of temperature and quantity of heat."

On page 8, Wilson writes: "Having defined quantity of heat in a way which only involves the mechanical variables P, V and not the temperature, we can now give the following criterion for determining which of two bodies is the hotter without being involved in circular argument. We define the temperature θ_A of a body A to be greater than the temperature θ_B of a body B if, when the bodies are put in contact through a diathermal wall and neither performs any mechanical work, heat flows from A to B, i.e. U_A decreases and U_B increases."

From the definition of heat flow in terms of work, and the fact that heat flow is observed to occur in nature, Wilson has deduced the necessary definability of temperature.Chjoaygame (talk) 16:14, 26 April 2012 (UTC)

point of view of Kirkwood & Oppenheim 1961

I refer to Kirkwood, J.G, Oppenheim, I. (1961), Chemical Thermodynamics, McGraw–Hill Book Company, Inc., New York. This is one of the texts recommended in Reif's bibliography, on page 632. Subsidiary to this, I refer to Eu, B.C. (2002), Generalized Thermodynamics. The Thermodynamics of Irreversible Processes and Generalized Hydrodynamics, Kluwer Academic Publishers, Dordrecht, ISBN 1–4020–0788–4. On page 11, Eu cites Kirkwood & Oppenheim 1961 for his statement of the zeroth law of thermodynamics.

Kirkwood & Oppenheim 1961 in their Chapter 4 distinguish what they call "physical" from what they call "mathematical" statements of the second law. They explicitly write two "physical" statements of the law, those of Clausius and of Kelvin, which they consider to be "equivalent". They also write what they call "Carathéodory's principle". They present careful arguments that derive Carathéodory's principle from the two "physical" statements, and from Carathéodory's principle they derive their "mathematical" statement of the second law in terms of entropy. Then they show that the mathematical statement is "equivalent" to the "physical" ones. On page 31, they comment that "All natural processes are irreversible." (A natural process is one that can in fact occur in nature.)

On page 18 Kirkwood & Oppenheim 1961 write: "From the macroscopic point of view, heat is energy exchanged between systems in thermal contact by virtue of a temperature difference."Chjoaygame (talk) 17:14, 26 April 2012 (UTC)Chjoaygame (talk) 20:00, 27 April 2012 (UTC)

point of view of Buchdahl 1966

I refer to Buchdahl, H.A. (1966), The Concepts of Classical Thermodynamics, Cambridge University Press, London.

In his preface on page ix, Buchdahl writes: "I adhere strictly to the phenomenological point of view, not least in order to counter the widely held opinion that one can gain an understanding of the concept of entropy, for instance, only on a statistical basis. ... Be that as it may, it involves an obvious logical difficulty: a statement of the kind 'the results of statistical mechanics must not lead to contradictions with the laws of thermodynamics' becomes meaningless if the latter can be 'understood' only on the basis of the former: to grant that it is meaningful is to grant that the conceptual frameworks of both theories are separately well defined."

Buchdahl is a thorough supporter of the Carathéodory story.

He is writing about classical thermodynamics, allowing quasi-static processes, for every state of which temperature is defined.Chjoaygame (talk) 01:44, 27 April 2012 (UTC)

Does this mean that he is unable to apply the First Law to the free expansion experiment and conclude that the internal energy does not change? If not, then exactly how does he arrive at this conclusion? And I have the same question for all the other books you have mentioned above. Count Iblis (talk) 02:25, 27 April 2012 (UTC)

You ridicule the books that I refer to. They are the books that Reif recommends one should read. I haven't put up the point of view of Tolman 1938 because it is rather hard to summarize it briefly for the present purpose.Chjoaygame (talk) 03:46, 27 April 2012 (UTC)