Talk:Thermodynamic temperature

How do you link to a category page without putting linking page into category?

I don't think this article belongs in so many categories, but I wanted to link to the pages. Is there a way?

User:Pifvyubjwm 11:49, 30 December 2005 (UTC)

Heat Energy and Temperature and Proportionality

The article says: "Regardless of the substance though, a change in its heat energy produces a proportional change in its temperature on the thermodynamic (absolute) temperature scale" This statement is in general incorrect. The relationship between change in heat and change in temperature is given by the heat capacity. The heat capacity itself is, in general, a function of temperature. That is to say the amount of heat required for a given temperature change depends on the temperature. In general, there is no proportionality between change in heat and change in temperature, although they are related by the heat capacity. In some substances, over a limited range, there is a reasonable proportionality, eg water between 1C and 99C has an approximately linear relationship between change in heat and change in temperature. This breaks down significantly at phase changes, where heating a substance might not change its temperature at all. I don't want another edit war, so I won't correct the article on this issue, but hopefully someone else will. LeBofSportif 08:50, 8 June 2006 (UTC)

I generally agree with what you say above. I wanted to convey the concept without burdening the paragraphs with caveats like phase changes and volume changes. I was thinking about that sentence and came back to add the caveats anyway. What do you think of it as currently revised? Greg L 17:31, 8 June 2006 (UTC)

I still don't like proportional being in there. It misses the point that the heat capacity can vary significantly with temperature, even when one wouldn't expect it to. Explanation of anomalous heat capacities at low temperatures is one of the triumphs of the quantum theory of solids - the Dulong-Petit law doesn't hold at low T, and nobody knew why. The point, I suppose, is that Temperature and Energy are two very different things, which because of certain coincidental linearities often follow each other closely, eg water at nice temperatures. The article, especially since it is concerning "thermodyanic temperature" should strive to make the point that temperature and energy are different and in general ("in general", rather than "often") temperature and energy do not follow each other in a nice way at all. The only thing we can say heat capacity is never negative - you can never add heat and reduce the temperature, while keeping sensible things constant like volume - except for a few quirky experiments with only a few atoms. LeBofSportif 08:59, 9 June 2006 (UTC)

I appreciate your thoughts. Text mustn't be simplified to the point of making it incorrect. OK, revised again. It mentions that temperature is the “speed” of movement, and it expands on “specific heat.” What do you think?
Greg L 13:17, 9 June 2006 (UTC)

absolute zero and classical physics

I have rephrased the following sentence:

The thermodynamic temperature scale’s null point, absolute zero, is where all kinetic motion in the particles comprising matter ceases and they are at complete rest in the “classic” (non-quantum mechanical) sense.

There is no "classic" sense in which all motion ceases at absolute zero. Rather, classical physics predicts (incorrectly) that all motion ceases. --Trovatore 05:36, 11 July 2006 (UTC)

another try

My previous wording was a bit awkward; the parenthetical "incorrectly" kind of interrupted the flow. But the current version's still not good; it suggests that the difference between the classical and quantum accounts is one of interpretation, which it's not. How about this?

... absolute zero has traditionally been defined as the point at which all kinetic motion in the particles comprising matter ceases, and they are at complete rest. In fact, it is now known that, owing to quantum effects, some motion would remain even at absolute zero.

Of course, it's true that this version doesn't really say what absolute zero is, but that can come later; the lead section doesn't have to give all the details of a precise definition. --Trovatore 04:29, 12 July 2006 (UTC)

Classic Physics and absolute zero

• Trovatore. You recently made a contribution to an article on Thermodynamic temperature. You stated that absolute zero is "where classical physics (as opposed to quantum mechanics) predicts (incorrectly) that all kinetic motion in the particles comprising matter ceases." Please explain your reasoning. If one reduces the motion of particles to the point where all that remains are the fluxuations of random quantum uncertainty, then this is the point where it is no longer theoretically possible to remove any more kinetic energy from a substance. Isn't that right? This is the point in thermodynamic equations where absolute zero is defined to be precisely -273.15. Everything in the universe has random quantum uncertainty as to their position and this sets the baseline for "zero"; nothing can be more stationary that quantum uncertainty. Any motion beyond quantum uncertainty is kinetic motion. Is this not correct?

Expanding with a thought experiment: If there are two particles in a closed container and they have kinetic energy (move with respect to each other and/or the container), they must eventually collide; they have kinetic energy. At the classic definition of absolute zero, there is no particle motion as measured from particle-to-particle or particle-to-container. All that remains is quantum uncertainty as to their precise location at any one moment. All that remians is probabilities. According to quantum mechanics, there is an very remote chance a particle can briefly appear outside of the container. But on average, the particle's position remains at its original position and will never collide and recoil away from each other. Even if they momentarily appear at the same position due to quantum uncertainty, they will still reappear elsewhere (most probably near their "most probable" position again). If this is all true, then what is incorrect with the statement that "absolute zero is the point where all kinetic motion in particles (in the classic, non-quantum mechanical sense) ceases"?
Greg L 17:27, 11 July 2006 (UTC)

• Actually, the article has been reviewed by four Ph.D.s. One works for Argonne National Labs, one is a chemist, another works for the NIST (he was on the team that set a record cold temperature of 700 nK), and the fourth teaches second-year thermodyamics at a university. I've got two patents on new ways to calculate the equation of state of gases. A friend of mine who is an afficionado of quantum physics is currently reviewing the article (which is why I wanted to leave it as is until his review is done). The paragraph you have issue with is used througout Wikipedia in other articles like Kelvin and Absolute zero. It has withstood months of being read by others without being modified.

Perhaps there is another way to re-word this without leaving it like you had it "(incorrectly)". That's entirely unsatisfactory. If you want to use such a broad paint brush, you need to cite sources. I think it would also help if you could get the backing of some Ph.D.s to peer review what you are proposing.
Greg L 23:29, 11 July 2006 (UTC)

• Trovatore:
  

Here are some definitions I've found:
Meriam-Websters: a theoretical temperature characterized by complete absence of heat and motion and equivalent to exactly -273.15°C or -459.67°F

ChemiCool Dictionary: The zero point on the absolute temperature scale; -273.15°C or 0 K; theoretically, the temperature at which molecular motion ceases.
Greg L 00:03, 12 July 2006 (UTC)

Please point me to these Ph.D.'s. I freely admit I'm not a physicist (my PhD is in math) but the wording as it stands looks like nonsense to me. It would be like saying "classically, tunnel diodes don't work". If classical physics were correct, they wouldn't work. But the fact is that they do work, and the fact is that the particles do move at absolute zero (more precisely, the particles' state is a superposition of states with nonzero momentum). --Trovatore 00:44, 12 July 2006 (UTC)

• Trovatore:
  

You make an interesting point about tunneling diodes. The guy who really knows his quantum mechanics is the founder of the fuel cell company I worked at called Relion. He once went to a convention in Hawaii. While there in his spare time, he went to the beach, sat in a lawn chair, and read up on his favorite subject. I will forward your comment to him and will get back to you probably no later than Thursday. I shouldn't conjecture about the difference, but it could be that the huge de Broglie wavelength of electrons, coupled with the fact that they are under a huge voltage field (small voltage but really small joint) amounts to a different picture. Regards
Greg L 01:43, 12 July 2006 (UTC)

• All you can even hope to get from that is a quantitative difference, which is to say that the zero-point motion is small. Sure, it's small, but it has observable macroscopic effects (for example, it's what prevents helium from ever becoming a solid at atmospheric pressure, even at absolute zero). --Trovatore 02:37, 12 July 2006 (UTC)

Trovato: I see what you are saying. I Googled on your statement and see from an article (click here) about these effects. I think the existing statement needs revision. But it should be sweet and simple without a parenthetical caveat that leaves people dangling. Now the question becomes this: Is absolute zero the point where there would be zero atomic drift velocity if you release them? By this definition, if all the heat that "could" be removed were removed (a practical impossibility) and only the residual, unremovable effects of zero-point energy remains, then is that absolute zero? For helium (MW = 4.002602), a temperature of 1 pk equals an atom drift speed (not vector-isolated velocity) of 79.94 µm/s. Helium's vector-isolated velocity would be 45.58 µm/s @ 1 pk. Or is absolute zero where zero-point energy would also be absent? This isn't even a practical impossibility, it's a theoretical impossibility. My guess is that absolute zero is "yes" to the former question; that two particles with, for instance, 1 mm of separation and which theoretically have zero drift velocity with respect to each other would never collide because only zero-point motion remains. This answer is satisfying in one way because it follows the PV=nRT slope; that is, that classic velocity gives gases their pressure. It is unsatisfying because it doesn't account for the observable effects on helium. Still, it could be that zero-point's effect upon helium simply means that helium is another tool that opens a window into the quantum world and is distinct from thermodynamic issues. If the answer to the former conjecture is "yes", perhaps wording like this is in order: Absolute zero is the temperature where no more kinetic motion can theoretically be removed and all that remains is quantum mechanical zero-point energy. Upon reflection, that's not all that technically different from what's already in place. If the answer is "yes" to the second conjecture, then other wording is required. I think I need to contact the researcher in the here-cited article: P. G. Klemens at the University of Connecticut.Greg L 05:36, 12 July 2006 (UTC)

Done. I've e-mailed Dr. Klemens. Greg L 05:54, 12 July 2006 (UTC)

Are you guys arguing about what the proper definition of absolute temperature is? You don't have to email researchers in the field for the answer; it can be found in standard textbooks. In classical statistical mechanics, the parameter β is defined as a particular derivative of the number of states with respect to internal energy. Absolute zero occurs when this derivative goes to zero. It is true that for an ideal gas, classical statistical mechanics predicts that the absolute temperature goes to zero when the internal energy is removed. The appellation "incorrectly" doesn't seem to apply; this prediction is vacuously satisfied even by quantum systems. There is also a phenomenological definition of absolute temperature, which is nothing but an extrapolation of some curves. -lethe ^{talk +} 06:07, 12 July 2006 (UTC)

dU = T*dS - P*dV - other terms, where U is the internal energy, T is temperature, S is entropy, P is pressure, V is volume. Entropy, S = k*ln(#microstates consistent with the macrostate), where k is Boltzmann's constant. At absolute zero, you must consider the quantum mechanical effects. So with quantized levels (and holding volume, etc. constant), we get U1 - U0 = T0*(S1 - S0). Notice that temperature is not associated with a particular energy level, but with a transition between two neighboring levels. In reality, T0 can never be zero, because then the energy levels would be equal which they are not. JRSpriggs 06:28, 12 July 2006 (UTC)

Lethe, I think you're quibbling a bit on the "vacuous satisfaction" thing. First of all I'm not convinced it's vacuous; it seems to me that it is possible for a system to attain a temperature of absolute zero, if just by chance it radiates out its last quantum of heat and no more come in. Also ISTR that superfluid helium II is considered a mixture of two phases, and the actual superfluid part of it is at absolute zero (though the average temperature of the whole liquid, of course, is not). That may not be up-to-date.

But even if it were true that no system can attain absolute zero, it's still the case that quantum mechanics predicts a minimum kinetic energy per particle (in a given bound system) and classical mechanics does not. Classical mechanics is observed to be incorrect on this point. --Trovatore 08:16, 12 July 2006 (UTC)

(Edit conflict) I don't know anything about superfluid helium, so I can't comment on that. But for your final statement, let me make two comments. First, standard classical mechanics does indeed predict that a bound system can have no internal energy, which does violate the principles of quantum mechanics. However, the third law of thermodynamics states that absolute zero is unattainable, and I think this follows from the law of large numbers and the principles of energy transfer, and so applies even to classical systems. Thus classical statistical mechanics (the context in which temperature is defined) also seems to disallow absolute zero, so saying that classical mechanics makes incorrect predictions may not be accurate (at least in the thermodynamic limit). Secondly, the edit states that absolute zero is where all energy is lost. If the edit said that classical mechanics predicts this state is attainable, well we could argue about whether classical mechanics were correct or not. But the edit in question doesn't say that. It says there is no internal energy in a system at absolute zero. If classical mechanics also decrees that this state is not physically attainable (and there's no mention one way or the other than I can see), then the statement is not actually wrong. I do concede that this superfluid helium may be a counterexample though. If that is a system at absolute zero, then classical stat mech probably makes incorrect statements about it. -lethe ^{talk +} 08:47, 12 July 2006 (UTC)

I'm having a look at Kerson Huang's Stat Mech book. He shows that the first and second laws of thermodynamics can be derived from statistical methods, but is ominously silent about the third law. And in his treatment of the third law, he says it is the thermodynamic manifestation of quantum phenomena. So it may be the case that classical statistical mechanics alone does allow for violations of absolute zero. I might then modify my position to say that classical thermodynamics (including the third law as a postulate) does not allow systems to attain absolute zero, and this is not in disagreement with observation. -lethe ^{talk +} 08:59, 12 July 2006 (UTC)

Thanks to you all for weighing in on this subject. But the two answers seem somewhat contradictory to me. The only question at hand is whether this statement is true: Absolute zero, is where all kinetic motion in the particles comprising matter ceases and they are at complete rest in the “classic” (non-quantum mechanical) sense. This definition is located early in the article where it should be simple indeed. Whatever statement goes there for defining absolute zero, it shouldn't be burdened with formulas, constants, and caveats. It should be extremely concise, understandable to a 10th-grader (at this point in the article anyway), should avoid the standard weasely Wikipedia equivocations that occasionally result from “committee-itis”, and must be 100% scientifically true. The above definition doesn't say that absolute zero is achievable or not, it just says what it is. I believe the question boils down to whether absolute zero would theoretically be achieved if there was zero classic kinetic drift in the atoms and only zero-point energy remained. Is that absolute zero? Or is absolute zero where zero-point energy must also be absent? To this extent, I've e-mailed a Ph.D. researcher who's been studying zero-point effects on matter. I've already run this wording by a Ph.D. instructor who teaches 2nd-year college thermodynamics and he had no problem with it. If there is anyone who knows there stuff at this level, how say you? Greg L 08:44, 12 July 2006 (UTC)

I have edited the disputed sentence to something I think is closer to a good description, what do y'all think of my edits? -lethe ^{talk +} 09:09, 12 July 2006 (UTC)

Lethe: No, I don't think that does it. Quantum mechanics, per se, does not say absolute zero is not achievable (see my remarks above on that); rather, it says that even at absolute zero, some motion remains. Greg, Lethe's edit summary about there being "no such thing as 'at rest in the classic sense'" is right on target. The kinetic energy of the atoms at absolute zero is the actual state of affairs, not simply the prediction of quantum mechanics. What you're calling the "classic kinetic drift" is not separable from the quantum-mechanical motion; it's just the prediction of a different theory, classical mechanics; a prediction that happens to be wrong. --Trovatore 15:42, 12 July 2006 (UTC)

My understanding from some tengential remarks by Huang is that this is exactly what quantum mechanics says, though he wasn't entirely explicit about it. I can't go looking more carefully at the moment, but I guess what I want to find is some reference that says that absolute zero is attainable. My current understanding is that absolute zero is not attainable, precisely because of the residual motion of the ground state, and that this is codified in the third law. -lethe ^{talk +} 17:05, 12 July 2006 (UTC)

No, I don't think that's right. As I recall from Kittel and Kroemer, the precise definition of temperature is the reciprocal of the partial derivative of entropy with respect to internal energy, where entropy is defined as the logarithm of the degeneracy. This fudges over some points about discreteness; I've never been sure just how those are resolved. But it should work out that a system large enough for statistics to be applicable is at absolute zero when it's in the lowest-energy eigenstate of its overall Hamiltonian. --Trovatore 17:55, 12 July 2006 (UTC)

Yeah, that's the right definition of temperature. Does that number go to zero for quantum systems approaching their ground state? -lethe ^{talk +} 18:20, 12 July 2006 (UTC)

I believe so. Of course there's this quibble about what "derivative" means in the discrete case; technically you probably have to let the number of particles go to infinity as well, to make rigorous sense of it (and I'm not exactly sure what "degeneracy" means either, if energies can be close but not exactly the same; I think this is probably also a smoothing of a discrete picture). --Trovatore 18:24, 12 July 2006 (UTC)

In the thermodynamic limit (infinite number of particles), energy states form a continuum, and one speaks of density of states instead, and may use the methods of calculus with impunity. The thermodynamic limit is of course only an approximation of our discrete universe, but then so is everything in physics. -lethe ^{talk +} 18:32, 12 July 2006 (UTC)

• My ex-boss at a fuel cell company agrees with you guys. He's extremely technical and into the deep depths of quantum mechanics. He thinks absolute zero would include all motions, including zero-point energy. I think now that Trovatore was right all along: any definition must be consistent with the reality of zero-point energy because zero-point energy is actually able to make phonon waves in crystal latices. What Lethe has written—while a tad wordy—appears technically correct given what we believe at this point. I'm still expecting an answer from the Ph.D. who researched zero-point-induced phonon waves in helium to get his input too but I don't think we have to wait to revise what we have. I may also contact the Ph.D. instructor of college thermodynamics and see why he didn't flag this sentence. On a separate note: I think a detailed definition of absolute zero is probably best dealt with in the Wiki article: Absolute zero. When we're dealing with the introductory second paragraph in an article that doesn't deal directly with absolute zero, we should be able to make it simpler yet. I would propose something along the lines of:

The thermodynamic temperature scale’s null point, absolute zero, is a theoretical temperature characterized by complete absence of motion ^[1]

This definition has the twin virtues of being 1) suscinct, and 2) in harmony with Meriam-Webster's definition. The  [1] would be a reference stating that no motion includes quantum mechanical zero-point energy and that, while scientists can get close, absolute zero unachievable. The provided link to absolute zero would give the reader an opportunity to learn more. What do you think?
Greg L 19:37, 12 July 2006 (UTC)

The problem is that it's false; absolute zero is not characterized by the complete absence of motion. I agree with a point you made earlier in the talk page, that material should not be simplified at the expense of accuracy. That's what your proposed text above does. --Trovatore 19:43, 12 July 2006 (UTC)

latest version doesn't work

Greg, no, the latest version does not solve the problem. Absolute zero is not characterized by the complete absence of motion, and (this point refers to the footnote) the zero-point motion is not a barrier to attaining absolute zero, but rather is motion that would persist even at absolute zero. --Trovatore 20:36, 12 July 2006 (UTC)

Just to put my 2 cents in: Yeah, what Trovatore said. Thermodynamic temperature is defined as the partial derivative of the average interval energy with respect to entropy, and absolute zero is the point where that derivative is zero. In a classical universe all motion would stop, and in a quantum universe the system would be in the ground state, but that isn't how absolute zero is defined. The Meriam-Webster's definition is simple wrong. (Pilled Higher and Deeper) Nonsuch 20:55, 12 July 2006 (UTC)

So you are saying Meriam-Webster's definition is wrong. I still don't get it. Your logic seems circular. You stated that zero-point energy means that motion persists even at absolute zero. That suggests that absolute zero is where there is zero classic motion and all that remains is zero-point motion. But this is what you had a problem with. Your point is that helium can not crystalize at one standard atmoshpere because zero-point energy causes motions that prevent it. That objection is founded on the notions that 1) zero-point energy is motion, and 2) true absolute zero can not be obtained due to its effect. This reasoning is inescapably founded on the notion that absolute zero is a theortically unachievable point of zero motion where, even if one removes all classic kinetic motion, zero-point-induced motion still causes a background of motion. If this is true, then statement that "absolute zero is a theoretical temperature characterized by the complete absence of motion" is true. It also avoids having to declare that dictionaries and encyclopedias are wrong. Greg L 21:01, 12 July 2006 (UTC)

(1) is true, (2) is false. Even if you get helium to a temperature of absolute zero, at atmospheric pressure, it will still be a liquid. --Trovatore 21:07, 12 July 2006 (UTC)

A definition of absolute zero needs to cite an authoritative reference. Isn't it as simple as this: Either absolute zero is an unachievable state where all classic kinetic motion has ceased and all that remains is zero-point energy, or absolute zero is an unachievable state where threre is no motion whatsoever, not kinetic, and no zero-point energy. Use plain-speak. Absolute zero is where there is no what? Greg L 21:09, 12 July 2006 (UTC)

I think what Trovatore seemed to have been first saying makes the most sense. If helium can not freeze at room-temperature due to the kinetic effects of zero-point energy, then this is motion. I don't think the Meriam-Webster definition was poorly thought out and is incorrect; I belive it is spot-on precise. Absolute zero is where there is no atomic motion whatsover. It doesn't matter what causes that vibrational motion, if something makes it move (zero-point energy, “classic” kinetic translational motions) then it is motion and one has not achieved absolute zero. Greg L 21:26, 12 July 2006 (UTC)

There is no such thing as "classic kinetic motion". There's motion, period. Absolute zero is where classical physics predicts there would be no motion. Classical physics is wrong. I wonder if you've come to terms with that fact? --Trovatore 21:27, 12 July 2006 (UTC)

You don't have to be glib and patronizing. I've "come to terms" with the fact that classic physics breaks down when one presses sufficiently far into the realm of quantum mechanics. I also know that if one wants to be precise in the definition of absolute zero, then the definition must be consistent with quantum effects since these come into play when one tries to define someting with a "zero" in it. And I agree, when we are talking about "zero," that motion is motion. That's why absolute zero is correctly described as as state where there is none of it. It seems utterly ludicrous to suggest that absolute zero is where "there is no motion but there is still a little bit of motion due to zero-point energy which causes compresson waves in cystal lattices and prevents helium from freezing". Greg L 21:38, 12 July 2006 (UTC)

No one is claiming that there both is and isn't motion. Absolute zero is not correctly described as where there is no motion. I'm not being glib, just terse. --Trovatore 21:45, 12 July 2006 (UTC)

Ok. You don't think absolute zero is correctly described as where there is no motion. So you must believe absolue zero is where there is some motion. Is that right? Greg L 21:55, 12 July 2006 (UTC)

There is some motion at absolute zero, right. --Trovatore 22:07, 12 July 2006 (UTC)

Then doesn't that take us back to the beginning? Are you suggesting that absolute zero should be defined as a state where there is no motion except for quantum mechanical motion? Greg L 22:16, 12 July 2006 (UTC)

No, there is no distinction between "classical motion" and "quantum mechanical motion"; it's all just motion. Absolute zero is not defined in terms of motion. It's defined in terms of the derivative of entropy with respect to internal energy. (It is true, I think, that it's where there's the minimum possible motion, but I'm not 100% sure of that—as I said, I'm a mathematician, not a physiscist.) --Trovatore 22:20, 12 July 2006 (UTC)

Greg, are you perhaps taking the simplified definition near the top of the article to literarily? At its simplest, “temperature” is the measure of the kinetic energy resulting from the motions of matter’s particle constituents (molecules, atoms, and subatomic particles). The full variety of these motions comprises the total heat energy in a substance, which is a form of kinetic energy. The relationship of kinetic energy, mass, and velocity is given by the formula Ek = 1/2m • v 2. That is a reasonable, and relatively intuitive, approximation to the truth that needs to be modified, in particular, in the quantum realm. The true, but technical definition of thermodynamic temperature is the last equation in the article. Nonsuch 22:22, 12 July 2006 (UTC)

I don't pretend to have the expertise to decided for myself what the definition of absolute zero ought to be. I don't own a copy of Encyclopedia Britannica (its way too expensive). However, Encyclopedia Britannica Online directly addressed absolute zero and how it relates to zero-point energy in its truncated (but informative) explanation of zero-point energy. It defines zero-point energy as the “vibrational energy that molecules retain even at the absolute zero of temperature.” I trust this better than Merriam-Webster which was succinct but unfortunately didn't direct address the nuance of zero-point energy. Still, for confirmation, I e-mailed Dr. Beamish at the University of Alberta. They've performed recent work on Bose-Einstein condensates in helium and how zero-point energy affects things. Greg L 00:14, 13 July 2006 (UTC)

P.S. Don't beat up on me too hard. A lot of effort went into adding that table and all those notes. Most of all, I want everything there to be true. I also think really expansive discussions on the nature of absolute zero belong in Absolute zero. But this is a great forum for fleshing out its true definition because "they can read it here first." Greg L 01:02, 13 July 2006 (UTC)

No one wants to beat up on you. But the latest version still isn't true; there is no "non-quantum mechanical sense" in which the "particles are at complete rest" at absolute zero. --Trovatore 01:11, 13 July 2006 (UTC)

Oops. That wasn't what I intended to do. I think I've been staring at this for too long. Will fix. Greg L 01:40, 13 July 2006 (UTC)

I suggest "Absolute zero is the condition when the heat energy is at a minimum, that is, no more heat can be removed from the system.". This avoids all the theoretical stuff about zero-point motion and hypotheticals about what would be true if only classical physics were true. JRSpriggs 04:49, 13 July 2006 (UTC)

Redundant With Temperature?

This article seems to have great overlap with the article on temperature. Indeed, since temperature is a thermodynamic concept, the title Thermodynamic temperature sounds a little like the Department of Redundancy Department. I guess I don't clearly see what the distinction between the two articles is meant to be? Perhaps this article is meant to contain the technical thermodynamic discussion, and the other one is meant to be the broad, intuitive introduction? In which case there is a lot of material that should switch places. For example, the section on Theoretical foundation of temperature should come over here, and some of the introductory material and the nice table of temperatures should migrate over there? And, perhaps this article should be renamed to make the distinction clearer? For example "Theory of temperature?" or "Foundations of temperature"? Nonsuch 22:43, 12 July 2006 (UTC)

No kidding. It's no fun trying to edit there.  Greg L 00:16, 13 July 2006 (UTC)