Maxwell y Su Demonio

7/28/2019 Maxwell y Su Demonio

1/15


2/15

Martin J. Klein Maxwell, His Demon,and the Second Law ofThermodynamicsMaxwell saw thesecond law as statistical,illustrated thiswith his demon, but neverdeveloped its theory

By the mid-sixties of the last century the science ofthermodynamics had reached a certain level of maturity. One could already describe it, in the wordsJames Clerk Maxwell would use a few years later,as "a science with secure foundations, clear definitions, and distinct boundaries" (/). As one sign ofthematurity of the subject, Rudolf Clausius, one ofits creators, reissued his principal papers on thermodynamics as a book in 1864 (2). He also set aside hisprotracted efforts to find the simplest and mostgeneral form of the second law of thermodynamics inorder to meet the need for convenient working formsof the thermodynamic equations, forms suitable fordealing with the variety of experimental situationstowhich the theory was being applied (3).Another indication of thematurity of the subject wasthe appearance in 1868 of Peter Guthrie Tait5 s book,Sketch of Thermodynamics (4). This consisted of a revision of two articles Tait had already published onthe history of the recent developments in the theoryof heat, supplemented by a brief treatment of theprinciples of thermodynamics. Tait did not claim tohave written a comprehensive treatise, but his bookdid make the basic concepts and methods availableto students.One of his reasons for writing the book was,in fact, his feeling of "the want of a short and ele

Martin J. Klein, Professor of the History of Physics at Yale,teaches both physics and the history of science at the University.A graduate of Columbia, he holds a Ph.D. fromM.I.T. (7948).He has worked on various problems in thermodynamics and statisticalmechanics, and most recently has been studying the developmentof physics in the nineteenth and twentieth centuries. His paperson Planck, Einstein, Gibbs, and others have appeared in a number ofjournals. His book, Paul Ehrenfest, Volume 7, The Making ofa Theoretical Physicist (North-Holland Publishing Co., Amsterdam), will appear this winter. Address: Department of theHistoryof Science and Medicine, Yale University, 56 Hillhouse Avenue, NewHaven, Conn. 06520.

mentary textbook" for use in his own classes (4, p.iii). Another reason was Tait's desire to set thehistorical record straight, which for him meant urging the claims of his compatriots, James PrescottJoule and William Thomson (later Lord Kelvin),against those of the Germans who had contributedalong similar lines-?Julius Robert Mayer, Hermannvon Helmholtz, and Clausius. Since Tait admittedin his preface that he might have taken "a somewhattoo British point of view" (4, p. v), it isnot surprisingthat his book became the center of a stormy controversy, but that controversy is not our concern here(5).Before sending his manuscript off to the publisher,Tait wrote to Maxwell, asking him to apply hiscritical powers to it. Tait was already expectingtrouble over his assignment of priorities and credit,since both Clausius and Helmholtz had been sentparts of the manuscript and had reacted negatively(5a, pp. 216-17; 6). Maxwell was an old friend;the two men had been together at school, at the

University of Edinburgh and at Cambridge. Theyshared a variety of scientific interests and carried on aparticularly lively and vigorous correspondence(7) . Itwas not at all unusual forMaxwell to read the

manuscripts or proofs of his friends' books and to"enrich them by notes, always valuable and oftenof the quaintest character," as Tait himself wrote(8) . his timeMaxwell provided his enrichment evenbefore he saw Tait's book.

Maxwell wrote Tait that he would be glad to see hismanuscript, although he did not "know in a controversial manner the history of thermodynamics"and so was not prepared to join his friend inwagingthe priority wars. "Any contributions I could make tothat study," he went on, "are in the way of alteringthe point of view here and there for clearness orvariety, and picking holes here and there to ensurestrength and stability" (9). Maxwell proceeded to

84 American Scientist, Volume 58


3/15

pick such a hole?in the second law of thermodynamics itself.Since its original appearance in Sadi Carnot'smemoir of 1824, the principle that would eventuallybecome the second law was always formulated as acompletely general statement, as free of exceptionsas Newton's laws of motion or his law of universalgravitation. What Maxwell challenged was just thisuniversal, invariable validity of the second law.His challenge took the strange form ofwhat we nowcall Maxwell's demon, an argument of the "quaintestcharacter" indeed. This was Maxwell's way of expressing his insight into the peculiar nature of thesecond law of thermodynamics: it was not a lawthat could be reduced ultimately to dynamics, butit expressed instead the statistical regularity ofsystems composed of unimaginably large numbers of

molecules.

Maxwell's views on the nature of the second law,expressed in brief passages and passing remarks,were never developed into a systematic statisticalmechanics, but they show how clearly he saw to theheart of thematter. He was insisting on the statisticalcharacter of the second law at a time when RudolfClausius and Ludwig Boltzmann were trying to showthat itwas a strictly mechanical theorem. His writings on this subject show, in their fragmentarycharacter as well as in their penetration, that quality

which Tait summed up in a sentence: "It isthoroughly characteristic of the man that his mindcould never bear to pass by any phenomenon without satisfying itself of at least its general nature andcauses" (S, pp. 319-20).The demon and molecular statisticsCarnot formulated his general result in these words :"The motive power of heat is independent of theagents employed to realize it; its quantity is fixedsolely by the temperatures of the bodies betweenwhich is effected, finally, the transfer of the caloric"(70). As the last word indicates, Carnot was usingthe caloric theory of heat, so that for him heat was aconserved fluid: as much heat was rejected at thelow temperature as had been absorbed at the hightemperature, when work was performed by a cyclicprocess. Carnot's proof made use of the impossibilityof perpetual motion, the impossibility, that is, of"an unlimited creation ofmotive power without consumption either of caloric or of any other agent whatever" (70, p. 12).

When the possibility of transforming work into heat,or heat into work, in a fixed proportion was con

clusively demonstrated in the 1840s, the basis forCarnot's principle seemed to be lost (//). Caloric wasnot conserved and Carnot's proof no longer held.It was Clausius who saw that the equivalence ofworkand heat could be made compatible with Carnot'sprinciple, if the latter were modified only slightly(12). Whereas Carnot had said that heat, Q, mustbe transferred from a hot body to a cold one whenwork, W, is done in a cyclic process, one could nowsay instead that when heat Q is absorbed from thehot body, only the difference, Q ? is rejected asheat to the cold body. This revised form of Carnot'sassumption allowed for the equivalence of heat andwork, and, according to Clausius, it could still serveas the basis for a proof of Carnot's theorem. Butsomething more than the usual impossibility ofperpetual motion had to be invoked as a postulateto carry out the proof.Clausius repeated Carnot's indirect reasoning, proving his result by showing that assuming the converseled one to an evidently intolerable conclusion. ForCarnot this had been the appearance of perpetualmotion; for Clausius it was something different."By repeating these two processes alternately itwould be possible, without any expenditure of forceor any other change, to transfer as much heat as weplease from a cold to a hot body, and this is not inaccord with the other relations of heat, since it always shows a tendency to equalize temperature differences and therefore to pass from hotter to colderbodies" (13). This was the new assumption Clausiusneeded for the creation of a thermodynamics basedon both the equivalence of heat and work (the firstlaw) and Carnot's principle. He phrased it morecompactly a few years later: "Heat can never passfrom a colder to a warmer body without some otherchange, connected therewith, occurring at the sametime" (14). Modern textbook formulations of thissecond law of thermodynamics are careful to specifythat cyclic processes are being considered and that the"other change"

inquestion is the performance of external work on the system, but these specificationswere implicit in Clausius' statement. The point to bestressed here is the universality of the statement, the

presence of the word "never," for example, in thesecond quotation from Clausius.It was here that Maxwell chose to "pick a hole"when he wrote to Tait in December 1867. He suggested a conceivable way inwhich, "if two things arein contact, the hotter" could "take heat from thecolder without external agency." Maxwell considereda gas in a vessel divided into two sections, A and B,by a fixed diaphragm. The gas inA was assumed to

January-February 1970 85


4/15

be hotter than the gas in B, and Maxwell looked atthe implications of this assumption from the molecular point of view. A higher temperature meant ahigher average value of the kinetic energy of the gasmolecules inA compared to those inB. But, asMaxwell had shown some years earlier, each sample ofgas would necessarily contain molecules havingvelocities of all possible magnitudes. "Now," Maxwell wrote, "conceive a finite being who knows thepaths and velocities of all the molecules by simpleinspection but who can do no work except open andclose a hole in the diaphragm by means of a slidewithout mass." This being would be assigned toopen the hole for an approaching molecule in Aonly when thatmolecule had a velocity less than theroot mean square velocity of the molecules in B.He would allow a molecule from B to pass throughthe hole into A only when its velocity exceeded theroot mean square velocity of the molecules in A.These two procedures were to be carried out alternately, so that the numbers of molecules in Aand B would not change. As a result of this process,however, "the energy in A is increased and that inB diminished; that is, the hot system has got hotterand the cold colder and yet no work has been done,only the intelligence of a very observant and neatfingered being has been employed." If one couldonly deal with the molecules directly and individually in themanner of this supposed being, one couldviolate the second law. "Only we can't," added Maxwell, "not being clever enough" (9).This is the first time that Maxwell's talented littlebeing appeared on paper. Thomson immediatelygave him the name "demon," by which he has beenknown ever since (5a, p. 214; 75). Thomson usedthis name only in its original meaning, a supernatural being, and did not want to suggest anyevil intentions on the part of this being who couldreverse the common tendency of nature. In hisletter to Tait, Maxwell probably did not make sufficiently clear his reason for introducing this fancifulconstruction. He described "the chief end" of hisdemon soon afterwards in these words: "to show thatthe 2nd law of thermodynamics has only a statistical certainty" (5a, p. 215). He meant that whileitwould require the action of the demon to producean observable flow of heat from a cold body to ahotter one, this process is occurring spontaneouslyall the time, on a submicroscopic scale. The possibility of the demon's existence is less significantthan the actuality of the statistical distribution ofmolecular velocities in a gas at equilibrium. Thisstatistical character of a system composed of anenormous number of molecules, which would form

the basis for the demon's actions, necessarily leadsto spontaneous fluctuations, including fluctuationsthat take heat from a cold body to a hotter one.Maxwell came a little closer to saying these thingsexplicitly when he repeated his argument a fewyears later in a letter to John William Strutt (laterLord Rayleigh). This time he referred to the possibility of a complete reversal of the motion of allparticles in theworld, thereby reversing the sequenceinwhich events normally occur. This possibility wasquite consistent with the assumption that "thisworld is a purely dynamical system." In this timereversed state the trend would always be away fromequilibrium; such behavior would be in flagrantviolation of the second law. Maxwell knew, of course,that "the possibility of executing this experiment isdoubtful," but he did not "think it requires such afeat to upset the 2nd law of thermodynamics." Itcould be done more easily with the help of the demon,now described more graphically as "a doorkeepervery intelligent and exceedingly quick, with microscopic eyes," who would be "a mere guiding agent,like a pointsman on a railway with perfectly actingswitches who should send the express along oneline and the goods along another." The demon argument was introduced, however, by this sentence:"For if there is any truth in the dynamical theory ofgases, the different molecules in a gas of uniformtemperature are moving with very different velocities." That was the essential thing; the demon onlyserved tomake its implications transparently clear.Maxwell even drew an explicit "moral" from hisdiscussion: "The 2nd law of thermodynamics hasthe same degree of truth as the statement that ifyouthrow a tumblerful of water into the sea, you cannotget the same tumblerful ofwater out again" (76).It is, after all, not surprising that Maxwell shouldhave been ready to take the consequences of thevelocity distribution so seriously: he was the onewho had introduced this concept into physics. Maxwell became interested in the molecular theory ofgases in 1859 when he read Clausius' papers on thesubject in the Philosophical Magazine (77). Clausiushad made use of the idea of the average distancetraveled by a molecule between its collisions withthe other molecules of the gas. Itwas Maxwell, however, who showed how the theory could be subjectedto experimental test, as he derived the relationshipsbetween Clausius' mean free path and the measurable coefficients of viscosity, thermal conductivity,and diffusion. Again, although Clausius had re

marked several times that "actually the greatest possible variety exists among the velocities of the several86 American Scientist, Volume 58


5/15


6/15

was a measure of the average kinetic energy of amolecule. He also proved a very interesting mechanical theorem, a generalization of the principleof least action, on the strength of which he claimedto have given a mechanical explanation of the secondlaw. This theorem will be discussed later; it isenough for the present to point out that Boltzmanncould prove it only under a very restrictive assumption. He had to limit himself to periodic systems.For a system whose entire molecular configurationrepeats itself after a time, r, he found a mechanicalcounterpart to the entropy, S. Boltzmann's equationfor the entropy of such a system had the form,

where the sum is over all molecules. The absolutetemperature, T, is the kinetic energy of one moleculeaveraged over the period,

Since the period, r, appears explicitly in the entropyequation one is inclined to guess that the periodicityof the system is an essential aspect of the theorem.Boltzmann tried to extend his proof to nonperiodicsystems, where the particle orbits are not closed,but his argument was not cogent. It concluded ratherlamely with the remark that "if the orbits are notclosed in a finite time, one may still regard them asclosed in an infinite time" (23). (It may be worthnoting, however, that one can evaluate the entropy,with thehelp of (3), fora very simplemodel of agas?a collection of particles bouncing back andforth between the walls of a container of volume V,all particles moving with the same speed, v.The result does depend linearly on the quantity In (VT^2),as it should for an ideal gas of point particles.)Boltzmann was not the only physicist who tried toreduce the second law to a theorem in mechanics.Rudolf Clausius had been thinking about the secondlaw since 1850; "the second law of thermodynamicsismuch harder for themind to grasp than the first,"he wrote once (3, p. 353). This is not the place tofollow the evolution of his ideas, but itmust be pointedout that Clausius arrived at a very particular wayof looking at the second law (24). He introduced aconcept that he named the disgregation, intendedas a measure of "the degree inwhich the moleculesof a body are dispersed." It was to be a thermodynamic state function, denoted by Z, related to thetotal work, internal as well as external, done by asystem in a reversible process. This relationship wasfixed by the equation,

S = 2 ln(7?2 + constant, (3)

(4)

dL = TdZ (5)

where dL represents the total work, an inexact differential. (Clausius considered the internal energy,U, of a system to be the sum of two terms, both statefunctions?the heat in the body, H> and the internalwork, /. The total work dL was the sum of dl andthe usual external work, dW, or PdV.) It was (5)that Clausius saw as the ultimate thermodynamicformulation of the second law: "the effective forceof heat is proportional to the absolute temperature"(25). And itwas (5) forwhich Clausius tried to finda mechanical interpretation.Clausius5 first attempt, in 1870, did not succeed, butit could hardly be called a failure since it led him tothe virial theorem (25). The following year he wasconvinced that he had solved the problem, as he entitled his paper, "On the Reduction of the SecondLaw of Thermodynamics to General MechanicalPrinciples" (26). This title sounds very much likethat of Boltzmann's paper of 1866, and with goodreason. Clausius had independently discovered thetheorem published by Boltzmann five years earlier.

Although the results were the same, there were somedifferences in approach. Boltzmann had been looking for a mechanical interpretation of entropy andits properties, while Clausius gave disgregation thecentral position in the theory. The two functions aresimply related, however, and the entropy Clausius derived from his mechanical expression for disgregationwas identical with the one Boltzmann had founddirectly (see (3) above).Boltzmann wasted no time in pointing out his considerable priority in having established this mechanical analogue of the second law (27). He showedthat all of Clausius' basic equations were identicalwith his own, apart from notation, reinforcing thepoint by reproducing verbatim the relevant pages ofhis earlier article. "I think I have established mypriority," Boltzmann concluded, adding, "I can onlyexpress my pleasure that an authority with Mr. Clausius' reputation

is helping to spread the knowledge ofmy work on thermodynamics" (27, p. 236).Clausius had, of course, overlooked Boltzmann'soriginal memoir. He had moved from Z?rich to

W?rzburg in 1867 and again to Bonn in 1869, andthe resulting "extraordinary demands" on his timeand energy had prevented him from keeping up withthe literature properly. He obviously granted Boltzmann's claim to priority for all the results commonto both papers, but Clausius was not convinced thatBoltzmann5s arguments were as general or as soundas his own, and he proceeded to discuss some of thesematters in detail (28).



7/15

Limitations of the second lawMaxwell observed this and later disputes over themechanical interpretation of the second law withdetachment?and no little amusement. "It is raresport to see those learned Germans contending forthe priority of the discovery that the 2nd law of0Acs [thermodynamics] is theHamiltonsche Princip,"he wrote toTait, "when all the time they assume thatthe temperature of a body isbut another name for thevis viva of one of itsmolecules, a thing which was suggested by the labours ofGay Lussac, Dulong, etc., butfirst deduced from dynamical statistical considerationsby dp/dt [i.e.Maxwell: see Appendix]. TheHamiltonsche Princip, the while, soars along in aregion unvexed by statistical considerations, whilethe German Icari flap their waxen wings in nephelococcygia amid those cloudy forms which the ignorance and finitude of human science have investedwith the incommunicable attributes of the invisibleQueen of Heaven" (29).The prize for which "those learned Germans" werecontending was an illusion : the second law was not adynamical theorem at all, but an essentially statisticalresult.

Maxwell expressed some of his own ideas on themeaning of the second law in his Theory ofHeat,published in 1871 (30). This book appeared as one ofa series, described by the publisher as "text-booksof science adapted for the use of artisans and ofstudents in public and science schools." They weremeant to be "within the comprehension of workingmen, and suited to their wants," with "every theory.. . reduced to the stage of direct and useful application" (31). Maxwell's book did not quite fit thisdescription. Tait thought that some of itwas probably "more difficult to follow than any other of hiswritings" (!) and that as a whole it was "not anelementary book." His explanation of this fact wasinteresting, and probably accurate. "One of thefew knowable things which Clerk-Maxwell did notknow," he wrote, "was the distinction which mostmen readily perceive between what is easy and whatis hard. What he called hard, others would be inclined to call altogether unintelligible." As a consequence Maxwell's book contained "matter enoughto fill two or three large volumes without unduedilution (perhaps we should rather say, with thenecessary dilution) of its varied contents" (8, p. 320).Maxwell did not hesitate to include discussions ofthe latest work in thermodynamics in the successiveeditions of his book ; one wonders what his intendedaudience of "artisans and students" made of something like Willard Gibbs's thermodynamic surface,

which Maxwell treated at some length, less thantwo years after the publication of Gibbs's paper(32).In discussing the second law, Maxwell emphasizedthat Carnot's principle does not follow from thefirst law, but must instead be deduced from an independent assumption, hence a second law. Hequoted Thomson's and Clausius' versions of this law,both ofwhich asserted, in effect, the impossibility ofa cyclic process converting the heat of a body intowork without allowing heat to pass from that bodyto a colder one. He advised the student to comparethe various statements of the law so as "to make himselfmaster of the fact which they embody, an acquisitionwhich will be ofmuch greater importance to himthan any form of words on which a demonstration

may be more or less compactly constructed." Andthen in his next two paragraphs Maxwell went tothe crux of the question.Suppose that a body contains energy in the formof heat, what are the conditions under which thisenergy or any part of itmay be removed from thebody? If heat in a body consists in a motion of itsparts, and ifwe were able to distinguish theseparts, and to guide and control their motions byany kind of mechanism, then by arranging ourapparatus so as to lay hold of every moving partof the body, we could, by a suitable train of

mechanism, transfer the energy of the movingparts of the heated body to any other body in theform of ordinary motion. The heated body wouldthus be rendered perfectly cold, and all its thermalenergy would be converted into the visible motion of some other body.

Now this supposition involves a direct contradiction to the second law of thermodynamics, but isconsistent with the first law. The second law istherefore equivalent to a denial of our power toperform the operation just described, either by atrain of mechanism, or by any other method yetdiscovered. Hence, if the heat consists in themotion of its parts, the separate parts which movemust be so small or so impalpable that we cannotin any way lay hold of them to stop them [30,pp. 153-54].

This argument, so deceptively simple in appearance,brought out the point that had escaped Boltzmannand Clausius, among others. Those processes thatare declared to be impossible by the second law areperfectly consistent with the laws of mechanics.The second law must, therefore, express some es

January-February 1970 89


8/15


9/15

some of these points, and thiswas the reason he didnot grant Boltzmann's absolute priority for themechanical derivation of the second law. His ownway of treating the work involved making the potential energy function depend on a parameter.This parameter, in turn, which varied from oneorbit to another, was assumed to change uniformlywith time as the particle went through a completeorbit. It must be remembered that Clausius, likeBoltzmann, could make even reasonably precisearguments only when the particles moved in closedorbits, that is, for a periodic system. Boltzmann wasnot happy about Clausius' way of "allowing the lawsof nature to vary with time," and never adopted thisprocedure in his later discussions of the problem

Perhaps the best way of seeing the difficulty ofseparating work and heat in a mechanical theory isto look at the particularly clear exposition of theBoltzmann-Clausius theorem given by Paul Ehrenfest (34). One considers a system whose Lagrangiandepends on a set of generalized coordinates, q, thecorresponding generalized velocities, q, and a parameter, a, such as the volume in the case of a gas.The system is assumed to be periodic, and to remainperiodic (but with a changed period) in a variationfrom the original orbit to a neighboring orbit. Thisvariation is of the kind considered in the principleof least action, i.e. nonsimultaneous, but the twoorbits are also assumed to differ because the parameter has the value a + Aa rather than a on the neworbit. By the usual variational procedures Ehrenfestderived the equation,

The A represents the change in the generalized variation just described. T is the kinetic energy, E is thetotal energy, and r is the period of the system. Thequantity A isdefined by the equations,

so that (? ^4) is the generalized force that must beexerted on the system to hold the parameter,


10/15

second law in purely mechanical terms, he was apparently unfamiliar with what Maxwell had writtenon the theory of gases. When he quoted the relationship between the pressure of a gas and the velocitiesof itsmolecules, he referred toKr?nig, Rankine, andClausius, but did not mention Maxwell or his lawfor the distribution ofmolecular velocities (36). Weknow that Boltzmann was learning to read Englishat this time-?in order to read Maxwell's papers onelectromagnetism (37). He returned to the theory ofgases in 1868, however, with fresh ideas promptedby his study ofMaxwell's new analysis of the kinetictheory (38). Boltzmann had embarked on a seriesof lengthy memoirs in which the statistical description of the gas was absolutely central to his treat

ment.

By the time Clausius was criticizing the fine pointsof his mechanical interpretation of the second law,Boltzmann was already committed to the statisticalapproach. In that same year, 1871, he offered a newproof of the law, but this time it was a statisticalmechanical, rather than a mechanical, proof (39).This new proof dealt only with the equilibrium aspect of the second law?that is, with the existenceof the entropy as a thermodynamic state function related to heat and temperature in the proper way,through equation (1). Work and heat were nowdistinguished with the help of the distribution function: roughly speaking, a change in the total energyproduced by a change in the molecular potentialenergy with a fixed distribution was work, whereasheat was identified with a change in the energy dueonly to a change in the distribution. The exponentialenergy distribution at equilibrium played an important part in the analysis. The essential featuresof Boltzmann's argument have survived the transition from classical to quantum physics, and it isstill to be found in textbooks on statistical mechanics(40).

A year later Boltzmann was able to provide a molecular basis for the other aspect of the second law,the increase of the entropy of an isolated systemwhenever an irreversible process occurs (47). Thiscame as a by-product of an investigation into theuniqueness of the Maxwell-Boltzmann equilibriumdistribution. Boltzmann's result, the famous //-theorem, was based on his analysis of how the distribution evolved in time as a result of binary molecularcollisions. Although much more limited in its scopethan his discussion of equilibrium, the //-theoremoffered the first insight into the nature of irreversibility.It must be emphasized, however, that while Boltz

mann made constant use of the statistical distribution of molecular velocities and energies, the resulthe asserted was supposed to be a certainty and notjust a probability. The //-theorem of 1872 said thatentropy would always increase (47, p. 345). Boltzmann did not revise this statement until 1877, whenJosef Loschmidt pointed out that it was untenablein its original form (42). Since the equations of

motion of the molecules do not distinguish between thetwo senses in which time might flow (that is, theyare invariant to the replacement of / by ?thetime reversal of any actual motion is an equallylegitimate solution of the equations. As a consequence, for any motion of the molecules inwhichthe entropy of the gas increased with time, one couldconstruct another motion in which the entropy decreased with time, in apparent contradiction to thesecond law. It was only in his reply to Loschmidt'scriticism that Boltzmann recognized "how inti

mately the second law is connected to the theory ofprobability," and that the increase in entropy canonly be described as very highly probable, but not ascertain. He elaborated this view in a major articlelater that same year, in which he formulated therelationship between the entropy of a thermodynamic state and the number of molecular configurations compatible with that state (43). Entropybecame simply a measure of this "thermodynamicprobability."Boltzmann's work can be viewed legitimately as adevelopment of the insight first expressed by Maxwell?an extended, detailed, and quantitative development of a brief qualitative insight, to be sure,but a natural development, all the same. NeverthelessMaxwell seems to have taken little or no interestin these papers by Boltzmann. He did follow someparticular aspects of Boltzmann's work in statisticalmechanics; Maxwell's last scientific work was anew analysis of the equipartition theorem, takingBoltzmann's 1868 memoir as its starting point andpresenting an alternate way of handling some of thedifficult assumptions (44). Maxwell was certainlyaware of much of Boltzmann's other work. HenryWilliam Watson's little book on the kinetic theory,which appeared in 1876 (45), followed Boltzmann'smethods and included a modified version of Boltzmann's first statistical derivation of the existence of anentropy function. Watson acknowledged "much kindassistance" fromMaxwell in his Preface, and Maxwell also reviewed the book forNature (46). But nowhere did Maxwell discuss Boltzmann's statistical

mechanical theory of the second law of thermodynamics. It is not even mentioned in his review ofTait, where it would have been completely appropriate.



11/15


12/15


13/15


14/15

AcknowledgmentsThis work was supported in part by a grant fromthe National Science Foundation. I thank Dr.Elizabeth Garber for many informative discussionson Maxwell, and my colleague Professor Derek J.de Solla Price for the use of his copy of the CambridgeUniversity collection ofMaxwell correspondence.

Motes1. J. C. Maxwell, "Tait's Thermodynamics" ature 17 (1878),257.Reprinted inThe Scientificapers ofJames ClerkMaxwell,ed. W, D. Niven (Cambridge, 1890), Vol. 2, 660-71.

Quotation from p. 662.2. R. Clausius, Abhandlungen ?ber die mechanische W?rmetheorie(Braunschweig,1864).3. R. Clausius, "?ber verschiedene f?r die Anwendung

bequeme Formen der Hauptgleichungen der mechanischenW?rmetheorie," Pogg.Ann. 125 (1865), 353.4. P. G. Tait, SketchofThermodynamicsEdinburgh, 1868).5. For further discussion of this controversy see: (a) C. G.Knott, Life andScientificork of eterGuthrie ait (Cambridge,1911), 208-26. Referred to below asKnott, Tait, (b)M. J.Klein, "Gibbs on Clausius," Historical Studies in thePhysicalSciences1 (1969), 127-49.6. R. Clausius, Die Mechanische Warmetheorie, 2d ed. Vol. 2(Braunschweig, 1879), 324-30.7. Knott, Tait, contains extensive excerpts from this corre

spondence as well as a description of the relationship of Taitand Maxwell. Also see L. Campbell and W. Garnett, TheLife of amesClerk axwell (London, 1882).8. P. G. Tait, "Clerk-Maxwell's Scientific Work," Nature 21(1880), 321.9. J. C. Maxwell to P. G. Tait, 11 December 1867. Reprinted inKnott, Tait, 213-14.

10. S. Carnot, Reflections on theMotive Power ofFire, trans. R. H.Thurston, ed. E. Mendoza (New York, 1960), 20. Thisvolume also contains papers by E. Clapeyron and R. Clausius. It is referred to below asMendoza reprint.11. See, e.g., E. Mach, Die Principien der W?rmelehre, 3d ed.(Leipzig, 1919), 269-71. Also seeM. J.Klein, n. 5, forfurtherreferences.12. R. Clausius, "?ber die bewegende Kraft der W?rme, unddie Gesetze, welche sich daraus f?r die W?rmelehre selbstableiten lassen," Pogg. Ann. 79 (1850), 368,500. Trans, by

W. F. Magie inMendoza reprint. Also see J.W. Gibbs,"Rudolf Julius Emanuel Clausius," Proc. Amer. Acad. 16(1889), 458. Reprinted in The Scientificapers ofJ. WillardGibbs (NewYork, 1906),Vol. 2, 261,13. R. Clausius inMendoza reprint, 134.14. R. Clausius, "On a Modified Form of the Second Fundamental Theorem in the Mechanical Theory of Heat,"Phil.Mag. 12 (1856), 86.15. Also see P. G. Tait, Lectures on Some Recent Advancesin Physical Science, 2d ed. (London, 1876), 119, and SirWilliam Thomson, Baron Kelvin, Mathematical and PhysicalPapers,Vol. 5 (Cambridge, 1911), 12,19.16. J. C. Maxwell to J.W. Strutt, 6 December 1870. ReprintedinR. J. Strutt,Life ofJohnWilliam Strutt, hirdBaronRay

leigh Madison, 1968), 47.17. R. Clausius, "The Nature of theMotion Which We CallHeat," Phil.Mag. 14 (1857), 108; "On theMean Lengthsof thePathsDescribed by theSeparateMolecules ofGaseousBodies," Phil. Mag. 17 (1859), 81. Both are reprinted inS.G. Brush,KineticTheory, ol. 1 (Oxford, 1965).18. J.C. Maxwell toG. G. Stokes, 30May 1859. Quoted byBrush (n. 17), 26-27.19. J. C. Maxwell, "Illustrations of the Dynamical Theory ofGases," Phil.Mag. 19 (1860), 19; 20 (1860), 21. ScientificPapers, Vol. 1, 377-409. Quotation from p. 380.20. J. C. Maxwell, "On the Dynamical Theory of Gases," Phil.Mag. 32 (1866), 390; 35 (1868) 129, 185. Scientific apers,Vol. 2, 26-78.21. L. Boltzmann, "?ber die mechanische Bedeutung deszweiten Hauptsatzes der W?rmetheorie," Wiener Berichte 53(1866), 195. Reprinted in L. Boltzmann, Wissenschaftliche



15/15

Documents

Maxwell y Su Demonio