Telephone with Temperature

Eli Rabett continues to try to puzzle out the weird statements about temperature in Taken by Storm:

Reading the several versions of Essex and McKitrick anyone familiar with thermodynamics (heat engines, blackbodies, chemical reactions, etc.) will start to scratch their heads. One peculiar statement after another appears dealing with temperature and other basic stuff. It turns out that Essex is using a rather special definition of temperature for a non-equilibrium radiation field. If you want to read about it look up "How hot is radiation", C. Essex, D.C. Kennedy and R.S. Berry, Am. J. Phys. 71 (2003) 969 .

Read his post for the details of Essex's definition. Rabett concludes:

So, pretty clearly Essex is talking about non-equilibrium thermodynamics, and probably playing telephone with McKitrick

Another round of telephone gives you Louis Hissink, who citing Essex and McKitrick as an authority, last year wrote:

If we now examine the ranking of sportsmen and have the class best sportsman, we could place Ian Thorpe as a swimmer, Mark Waugh as cricketer, and Dick Johnson as race-car driver, and we could then associate as best = Ian Thorpe=Mark Waugh= Dick Johnson. This is an entirely permissable equivalence and has nothing to do with quantities. It is a subjective ranking and equivalence. Temperature is the same type of category. Heat content is not. (I am using Australian sportsmen as examples). So mathematically A) above is a nonesense if 1 Deg C is regarded as a quantity - but not if it is regarded as a category of subjective value, say similar to the sports category of "Best". This nonesense comes about from the logical fallacy that if my cat has four legs, and my dog has four legs, then my cat is a dog. Therefore temperature is not a measure of heat content. Temperature is therefore not a quantity, it is a class category, conveniently described as a number. It is a means by which we rank hotness. It cannot be mathematically processed. However heat units, or in the modern jargon, energy units, can be mathematically processed. Unfortunately we have specified temperature as a numerical ranking, and this has unfortunately resulted in those in the social sciences assuming that as it is a number, we can do maths on it. (It goes without saying that temperatures can be manipulated mathematically but it is a meaningless procedure). There might an argument that air is air, and that it's specific heat is so and so, and we can count temperatures of air and make a meaningful estimate of it's temperature as an average. No, because it's specific heat is dependent on its composition, since casual inspection of both Hydrogen and Carbon Dioxide, two components of air, shows that these two gases have extremely different specific heats. If you wish to compute the temperature average of air at two localities, you must first of all demonstrate that both samples of air are compositionally identical, but it is irrelevant because temperature is not a quantity - it is a category of subjective hotness.

Update: Hissink responds:.

I suspect the confusion in Tim's audience also arises by the use of numbers to rank objects in terms of hotness. You could use the Roman system of numbers, eg, IVXIII, to rank objects in terms of temperature, only to discover this is not a terribly useful way of doing things. However assigning numbers to a ranking system does not necessarily mean that manipulating those numbers has any intrinsic meaning.

Umm, what number is IVXIII?


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Hissink (as Vizzini:)

"You've heard of Clausius, Joule, Kelvin, Boltzmann?"


I've tried to start this comment about five times. Hissink's paragraph there left me, quite literally, without words. That's the weirdest collection of bizarre statements I've ever read.

``However heat units, or in the modern jargon, energy units, can be mathematically processed.''

.... beh? Um,.... but.... ?????

Since the kinetic energy of each molecule =3/2kT and the average kinetic energy of the population =3/2kTaverage, we can therefore deduce that kinetic energy is a fictious concept.

fictitious. Whatever.

Ha! Hissink even used my comment on his site.

Louis: please do properly attribute. And here are some more quick clues:

  1. Temperature is not a ranking (although one could certainly rank things by temperature, as one could by energy content or density)
  2. Temperature is not subjective (you really think the measured temperature of something depends on the observers mood or something?)
  3. Temperature is especially not a `subjective ranking of hotness' (would you like to have a go at defining hotness in a way that doesn't depend on temperature? And no, energy content isn't right, because otherwise a cold object in fast bulk motion is `hot'. And yes, defining `hot' in terms of `heat energy' is circular. When you get to the point of talking about a disorded component of energy content, congratulations, you're just about at `Temperature'.)
  4. Yes, you can't just add temperatures; you also can't just add densities, or speeds, or averages. Unfortuately, that doesn't mean densities, speeds, or averages are `subjective rankings'. That's just nonsense. If you'd like, I'd be more than happy to help you with the more advanced mathematics involved in properly adding any of those quantities meaningfully, temperature included.

Anyway, do feel free to find some physicists or physical chemists at your local university, and share with them your Exciting! New! understandings of thermodynamics. If they seem unsure, try comparing yourself to Newton and Galileo. That'll impress 'em.

"Comment 7 is hilarious"

Simply an example of subjective hotness.

A man walks down to the beach on a chilly day, sees another man sitting on the sand, asks him "How's the water?"

The second man shrugs, says "Lukewarm".

"Great" says the first man and plunges in, only to emerge a second later spluttering and yelling "It's freezing! Why did you tell me it was lukewarm?"

Second man shrugs again, says (in thick generic middle European accent) "Eet luke warm to me."

"Umm, what number is IVXIII?"

That's the boiling point of unobtanium; subjective, of course.

This just in:

IPCC disbands, citing new evidence that temperature is merely a subjective measure of hotness. "D'oh!" says IPCC chairman.

leaves causing confusion

By Louis Hissink (not verified) on 16 Nov 2005 #permalink


Temperature is not a measurement of subjective hotness?

So you have a superior alternative?

By Louis Hissink (not verified) on 16 Nov 2005 #permalink

Temperature is not a measurement of subjective hotness?

So you have a superior alternative?

((2/3)/k)*(Mean kinetic energy of the molecules) always got me through the exams.


do you have something else for Louis to grab on to, in order to assist mendacicization?



Well, cheating a little by consulting my ancient scraps of notes, and winging it in between:

Says here, change in total (internal) energy U is defined in terms of temperature T, pressure P, volume V and entropy S as


or T=(dU+PdV)/dS

let's sanity check: i.e., if you do work on a system, temperature and/or entropy increase. Sounds correct. If you increase the pressure at constant volume, temp and/or entropy increase (note that N, number of molecules, has dropped out of this equation, which is how you increase the pressure at constant volume and temp, by increasing N, thereby increasing entropy). OK If you increase the volume at constant pressure, temp and/or entropy increase. (see last parenthetic comment)

At constant volume and N, that gives us

T= dU/dS

Abandoning rigor and relying on my notes:
Given the Sackur-Tetrode equation for entropy S of an ideal monoatomic gas, which I'm too lazy to copy here and am going to take as an axiom here anyway rather than derive it, it says here we can solve for the above derivative by doing some things with derivatives of products some of which I can no longer reproduce but which once meant something to me, to get

1/T=dS/dU = Nk(d(lnU^(3/2))/dU)

which by the good old derivatives of logarithms gives us


which leads to T=(2/3)U/(Nk)

U/N is total energy over number of molecules which is mean energy per molecule, so we're back to the identical fcalculation/formula/quantitative definition

T=((2/3)/k)*(Mean kinetic energy of the molecules)

once again (see comment 15), even though this time we calculated **entropic temperature**, starting with total energy and entropy, instead of the usual derivation of of **kinetic temperature** using the Boltzmann distribution of kinetic energy (e^(-E/(kT))) and ignoring entropy.

Wow, that was fun, sort of.

PS that was for an ideal monoatomic gas, as I said; it says further down here that given instead a solid, using the Einstein model where each molecule is free to vibrate but not to travel, the same derivation starting with entropy gives us instead


This plus the previous give us the general equation,

U/N=(kT/2)*(degrees of freedom)

i.e., a general relation between temperature, average internal energy of the molecules, and degrees of freedom of the molecules, which is sufficient to take care of the contribution of entropy to the energy balance without any other consideration of entropic factors; note that this degrees of freedom is constant for a substance unless it changes state, i.e. melts or boils, so otherwise is just a constant factor in the temp vs energy relation.

z, that "general relation" isn't going to work as a general definition of temperature. What you've written is (sort of) the Equipartition Theorem of classical statistical mechanics. It's not exact (because classical mechanics isn't). It works very well for molecular translations and rotations (except at very low temperatures) but it fails badly for vibrations. As a result, it's very good for gases and liquids, provided that temperatures are not too low and that you arbitrarily exclude vibrations from the count of degrees of freedom but it's generally terrible for solids.

If you want a general definition of temperature, one of the equations you gave in (17) works just fine: T = (dU/dS) at constant V. This implies that you regard entropy as a more fundamental quantity than temperature, but that is indeed the point of view taken in the more rigorous formulations of Thermodynamics and Statistical Mechanics.

For the purposes of atmospheric science, it's perfectly reasonable to define the temperature of a gas or liquid in terms of the average _translational_ kinetic energy, i.e. E = 3/2 N kT.

By Robert P. (not verified) on 16 Nov 2005 #permalink

This is starting to remind me of the story by Alfred Bester, "The Men who murdered Mohammed", where he talks about Boltzmann and other geniuses in science............

The second film starts off with Boltzmann giving a course in Advanced Ideal Gases, he peppers his lectures with involved calculus, which he quickly and casually works out in his head. The students, all confused and lost trying to understand the math by ear, beg Boltzmann to work out his equations on the blackboard. Boltzmann apologizes and promises to be more helpful. At his next lecture he begins with "Gentlemen, combining Boyle's Law with the Law of Charles, we arrive at the equation pv=povo(I + ar). Now obviously, if aSb = f(x)dxX(a), then pv = RT and vS f(x,y,z)dv = 0. It's as simple as two plus two equals four." At this point Boltzmann remembers his promise and turns to blackboard and writes "2+2 = 4 ". And goes back to his lecture breezing on, casually doing calculus in his head.

By The Dark Avenger (not verified) on 17 Nov 2005 #permalink

"It works very well for molecular translations and rotations (except at very low temperatures) but it fails badly for vibrations. As a result, it's very good for gases and liquids, provided that temperatures are not too low and that you arbitrarily exclude vibrations from the count of degrees of freedom but it's generally terrible for solids. "

OK, well I'm out of steam at this point. As I said, our theoretical exposure to solids was the afterthought regarding dU/dS with one less degree of freedom being consistent with U/N=(kT/2)*(degrees of freedom), and of course our practical exposure was nil. Of course, none of this supports the hypothesis that temperature is just a subjective ranking.