Müller I. A history of thermodynamics. The doctrine of energy and entropy (Müller I. A history of thermodynamics. The doctrine of energy and entropy.pdf), страница 69

8. Let us concentrate on equilibriuminstead:Seeing that the collision term vanishes for the Maxwell-Jüttnerdistribution, we must ask whether the Boltzmann-Chernikov equation issatisfied by that distribution, or what conditions on the fields a(xB), T(xB),and UA (xB) are required by the equation. Insertion of the distribution leads tothe requirementswawx A§U ·§U ·0 and ¨ B ¸ ¨ A ¸© kT ¹ ; A © kT ¹ ;B0,where the semi-colon denotes covariant derivatives.20The possibility of such a term was ignored in Chap. 4, because I wished to be brief.

Theterm is only present in a non-inertial frame.21 See: I. Müller, T. Ruggeri: “Rational Extended Thermodynamics.” loc. cit.Ott-Planck Imbroglio303Since a is a function of n and T, it follows that a temperature gradientmust exist in equilibrium, if there is a density gradient. That conclusion maybe made more concrete by exploiting the second condition for the specialcase of a gas at rest on a carousel. We obtainT~ homogeneous or, see above :g00T (r )Ȧ2 r 21 2c~ homogeneous.This result is eminently plausible, because it reflects the inertia of thethermal energy in the field of the centrifugal potential Ȧ2r2. Indeed, ifenergy has mass – and weight – it should be subject to sedimentation, as itwere, by centrifugation.Einstein has postulated – in his general theory of relativity – that inertialforces and gravitational forces are equivalent.

Accordingly non-homogeneous temperature fields are also created by gravitational fields – notonly by centrifugal fields – because they lead to stratification of massdensity. I have already commented on that aspect in the context of Eckart’srelativistic paper.In view of the following argument, I should like to stress that the lastrelation does not imply a transformation formula for the temperature.

Itrepresents a property of the scalar temperature field as a solution of theenergy balance equation in a centrifugal force field.Ott-Planck ImbroglioIn 1907 the theory of relativity was new. A fundamental change hadoccurred in mechanics, and physics in the immediate aftermath was in astate of flux.

The extension of the new concepts to thermodynamics wasclearly desirable. Everything seemed possible and so Planck22 came up withthe idea to modify the Gibbs equation. Einstein23 elaborated on that idea andintroduced a working term –qdG into the heating of a body moving with the22M. Planck: “Zur Dynamik bewegter Systeme.” [On the dynamics of moving systems]Sitzungsberichte der königlichen preußischen Akademie der Wissenschaften (1907).Printed version: Annalen der Physik 26 (1908) p.

1.23A.. Einstein: “Über das Relativitätsprinzip und die aus demselben gezogenenFolgerungen.” [On the principle of relativity and the conclusions drawn from it] Jahrbuchder Radioaktivität und Elektronik 4 (1907) pp. 411–462. Reprinted in: “Albert Einstein,die grundlegenden Arbeiten.” [Albert Einstein, the basic works] K.v. Meyenn (ed) ViewegVerlag (1990).In the reprinting the modified Gibbs equation is misprinted: It says dQ instead of dG.30410 Relativistic Thermodynamicsspeed q. G is the momentum; it includes a relativistically small term,because the mass is mc cU2 . The modified Gibbs relation thus readsTdSdQd U p dV q d G .The transformation of dU, p,dV, and dG between the moving body andthe body at rest were known and thus Einstein produced the relationdQq21 2 dQ0cbetween the heating of the moving body and the heating of the body at rest.Now Planck had already argued that the entropy of the body should beunaffected by motion, and therefore the second law written as dq = TdSseemed to requireT1q2T0 .c2That relation was later rephrased by epigones of the argument in thewords: A moving body is cold.On the surface the argument appears plausible.

It does ignore, however, the factthat the Gibbs relation is a relation for a body at rest: The heating consists of thenon-convective part of the energy flux and the internal energy is the non-convectivepart of the energy. The power, or working of the force dG has no place in the Gibbsequation therefore, or it should not have.Also, the heating of a body in the Gibbs equation is the integral of the heat fluxover the surface. And relativistically the heat flux forms three components of theenergy-momentum tensor. It is that fact which determines the transformation of theheating, not its position in the Gibbs equation.None of the serious physicists in the following years and decadesfollowed Planck and Einstein in this precarious thermodynamic argument,neither Eckart, nor Synge, nor Chernikov.

Consequently one might havethought that the argument was discarded as a valiant, perhaps, thougherroneous early attempt on relativistic thermodynamics.Not so, however! In 1962, H. Ott24 revisited the argument on a slightlydifferent basis involving Joule heating, and he came to the conclusion that24H.

Ott: “Lorentz-Transformation der Wärme und der Temperatur.” [Lorentz transformation of heat and temperature] Zeitschrift für Physik 175 (1963) 70–104.Ott-Planck ImbrogliodQdQ 012qc2holds, henceTT01q2c2305,such that: A moving body is hot.Serious people in the field ignore the subject, which was appropriatelytermed the Ott-Planck imbroglio by Israel and Stewart.25 However, the farcecontinues and Peter Thomas Landsberg26 – himself an enthusiasticcontributor to the imbroglio – cites papers on the subject of temperaturetransformation in special relativity as recent as the late 1990’s.2725W. Israel, J.M.

Stewart: “On transient relativistic thermodynamics and kinetic theory II.”Proceeding of the Royal Society London Ser. A 365 (1979).26 www.maths.soton.ac.uk/staff/Landsberg27 I have a personal memory of all this: Ott’s paper was in the process of publication when hedied. So the proof sheets – already adorned with the multi-coloured marks of the copyeditor of the pre-computer era – where sent to Josef Meixner for his evaluation. Meixnerwas my advisor at the time and he gave the paper to me, his most junior assistant.Naturally, perhaps, I thought that my opinion was being requested. And so – havingalready studied Jüttner’s papers and Synge’s booklet – I put my precocious and very juniorthumb down on the paper. But Ott had been an important member of the German PhysicalSociety, and he was not to be embarrassed, not even posthumously, and certainly not bythe Zeitschrift für Physik.

So the paper was published, and the imbroglio took anotherturn.11 MetabolismIf the truth were known, thermodynamics would be seen as explaining littleabout the details of life functions in animals and plants, at least compared towhat there is to be explained. This is no different than with engines:Thermodynamics cannot provide a recipe for their construction, or giveinformation about where and how to arrange seals and boreholes forlubrication, and how to operate the valves and where to install them.

Whatthermodynamics can do about engines is to give an account of the balanceof in- and effluxes of mass, momentum, energy and entropy, and that isessentially what it can also do about life. For the engine that task has beendone satisfactorily; for animals and plants maybe there remains somethingto be done.Having said this, I hasten to stress that, what thermodynamics is able toprovide, is good enough to refute esoteric theories, and to convince peoplewith an open mind that nothing unnatural occurs in the living body: Novitalistic force of old, nor Niels Bohr’s complimentarity of life and physics,akin to the wave-particle dualism of quantum mechanics.1I have previously – cf.

Chap. 4 – warned against an over-interpretation ofentropy as a measure of disorder and I stress that caution again. To be sure,an animal definitely seems more ordered than the sum of its atoms, looselydistributed, and it does probably have a lower entropy. But then, what is theentropy of an animal? Or let us ask the easier question: What is the entropyof a molecule like hemoglobin, one of the simpler proteins with only about500 amino acids? Maybe molecular biologists can come up with an answer;if so, I do not know about it. But I do know that surely it must be a case ofsimplism when Schrödinger says2 that animals maintain their highly orderedstate, because they eat highly ordered food. Indeed, before the animal bodymakes use of the food in any way, – and sets about to create order – itbreaks the food down to much less ordered fragments than those which itingests.12In his later years Bohr expressed doubts that life functions can be reduced to physics andchemistry.

See: N. Bohr: ‘‘Atomphysik und menschliche Erkenntnis.” [Atomic physicsand human knowledge] Vieweg Verlag, Braunschweig (1985).E. Schrödinger: ‘‘What is life? The physical aspect of the living cell” Cambridge: At theUniversity Press, New York: The Macmillan Company (1945) p. 75.30811 MetabolismIn writing this chapter on metabolism I disregard Schrödinger’s warningthat a scientist is usually expected not to write on any topic of which he isnot a master.3 But then, Schrödinger did not heed that warning himself. Andthe subject is interesting, and it seems to be replete with unsolved problemsof a quantitative nature. Therefore it is easy to yield to the temptation towrite about it, albeit in a layman’s manner.Carbon CycleOne of the truly mind-expanding discoveries of all times, concerning lifeand life functions, was the observation that carbon, hydrogen and oxygencycle through living organisms, driven by solar radiation: Plants use waterfrom the soil and carbon dioxide from the air to produce their tissue andthey release oxygen.

Animals on the other hand breathe oxygen and use it tobreak down plant tissue. In the process they release carbon dioxide andwater. The plants perform their task only in the light.Jan Baptista van Helmont (1577–1644) was an alchemist on the verge ofbecoming a chemist or, perhaps, a biochemist. On the one hand he claimedto have seen and used the philosopher’s stone – the hypothetical ultimatetool of alchemy – but on the other hand he was keen enough as anexperimenter to see that water was essential for plant growth, while soil wasnot, or not to the same degree. Helmont did not recognize the importance ofcarbon dioxide for plants, even though he actually discovered that gas,which he called gas sylvestre, i.e. wood gas, because he had found that itwas released by burning wood.

It took another hundred years before thesignificance of that observation was recognized by Stephen Hales (1677–1761). Carbon dioxide has originally entered the wood from the airsurrounding the leaves of a plant, thus furnishing the second component –after water – that is essential for plant growth.Another generation later Joseph Priestley (1733–1804), one of the discoverers of oxygen, noticed that oxygen was used up in the air by breathingand that, plants can restore the freshness of used-up air, obviously bygiving off oxygen. These observation were all couched in the languageof the phlogiston theory, – even then obsolete4 –, but Jan Ingenhousz(1730–1799) was able to penetrate the verbiage and to see a broad schemeof balance in nature: Plants consume the carbon dioxide of the air and34Ibidem.

p. vi.The phlogiston theory is the forerunner of Lavoisier’s caloric theory, see Chap. 2. In the18th century a weightless fluid called phlogiston was supposed to flow from a body whenthat body burns, or rusts, or is just cooling. As far as burning and rusting was concerned,Lavoisier refuted the concept, because he showed that both phenomena are due to thecombination of a body with oxygen.