The Caloric Theory of Adiabatic Compression Thomas S. Kuhn Isis, Vol. 49, No. 2. (Jun., 1958), pp. 132-140. Stable URL: http://links.jstor.org/sici?sici=0021-1753%28195806%2949%3A2%3C132%3ATCTOAC%3E2.0.CO%3B2-7 Isis is currently published by The University of Chicago Press.
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The Caloric Theory of
Adiabatic Compression
A
B y Thomas S. Kuhn * HIS paper t deals with the eighteenth- and early nineteenth-century investigations of the temperature variation in an enclosed gas when it is rapidly compressed or expanded. Today these compressions or decompressions are called adiabatic, and their defining characteristic is that they occur so rapidly, or in a vessel so well insulated that there is no transfer of heat between the gas and its environment. I n gases, adiabatic volume change is invariably accompanied by a large-scale change of temperature, and most contemporary science texts introduce this constant concomitance of phenomena as evidence for the conservation of energy. The work done on the gas during compression, say these books, appears as the heat which raises temperature. Furthermore, the quantity of heat evolved is always precisely proportional to the quantity of work done. Because this conceptual connection is direct and because many adiabatic phenomena are readily demonstrated, energy conservation and adiabatic change are often treated together in modern science courses. T o many students they seem two sides of a single coin. The same intimate connection between theory and phenomena appears very clearly in the early history of thermodynamics. All seven of the men who between 1824 and 1845 independently enunciated the law of the conservation of energy made immediate use of adiabatic phenomena to document, elaborate, or quantify their new hypothesis. Sadi Carnot and Robert Mayer both found presumptive evidence for energy conservation in an adiabatic expansion experiment performed by Gay-Lussac in 1807, and both computed early values of Joule's constant from other well-known experiments on adiabatic change.l Karl Holtzmann's value of the conversion constant has a similar source, as does the third of the values determined by James J o ~ l e . The ~ other three
T
*University of California at Berkeley. t This paper is a slightly modified \&on of one read at the History of Science Society meeting in New York on 2 December 1956. l Sadi Carnot's reluctant elucidation of the conservation of energy is recorded in manuscript notes, mostly written between the publication of his Rdflections sur & puissance motrice du feu in 1824 and his death in 1832. In the convenient version of the notes published with the recent facsimile edition of the Rdflections (Paris: A. Blanchard, 1g53), the references to Gay-Lussac's experiment occur on pp. 129 and 140, and the value for Joule's constant on p. 135. Carnot does not record the method employed in computing the conversion coefficient, bct it was almost certainly the same as the one used by Mayer and Holtzmann (see below and note 2 ) . A figure almost identical with that given by Carnot is obtained by applving Mayer's method to the data on adiabatic compression, etc., given in Carnot's memoir. Besides, given the sorts of data available to Carnot, there seems to be no other method he could have used.
Mayer's value of the coefficient is given in his first published paper, "Bemerkungen iiber die Krafte der unbelebten Natur" (Annalen der Chemie und Pharmacie, 1842, 42: 233-240), and the method of computation is explained in his Die organische Bewegung in ihrem Zusamnzenhange mit dem Stoffwechsel (Heilbronn, 1845). Both are reprinted and discussed in J. J. Weyrauch's Die Mechanik der Warme in gesammelten Schriften von Robert Mayer (Stuttgart, 1893) where the relevant passages occur on pp. 29, 32, and 55-56. The last of these passages is immediately preceded (p. 53) by Mayer's first published reference to GayLussac's experiment. Earlier and more signscant references to Gay-Lussac's experiment and to other experiments on adiabatic compression are found from 1841 on in Mayer's letters to Baur. These are reprinted in J. J. Weyrauch's Kleinere Schriften und Briefe von Robert Mayer (Stuttgart, 1893). See particularly pp. 130-132, 145-146, and 152-154. 'Karl Holtzmann, Ueber die Warme und Elasticitat der Gase und Dampfe (Mannheim, 1845). I here follow the account of the computation given by Georg Helm, Die Energetik
T H E CALORIC THEORY O F ADIABATIC COMPRESSION
I33
known pioneers - Seguin, Mohr, and Colding -made no quantitative use of adiabatic phenomena, but all gave to heating and cooling by compression and expansion the leading place in their catalogue of qualitative evidence Historically, as well as logically, the for the new view.3 This list is unanimou~.~ conservation of energy is intimately related to adiabatic volume change. Yet, how can the relationship be this close? Joule is the only one of the thermodynamic pioneers who performed his own experiments on gases, and he was simply repeating, with refinements, experiments which had been performed twenty-five and more years before. The other pioneers were able to make use of adiabatic phenomena only because, by the middle I ~ Z O ' S , a vast literature dealt with them. And that literature, both experimental and theoretical, was developed by men who uniformly espoused the caloric theory. A few had doubts about the finality of the theory, but these doubts were quite unrelated to their work on adiabatic compression. On the contrary, adiabatic phenomena provided some of their strongest qualitative and quantitative evidence for the existence of caloric. Until the middle 1840's the changes in gas temperature generated by compression or expansion were as intimately tied to the caloric theory -a theory which conserved heat -as they have since become to the dynamical theory -a theory which conserves energy. How, without felt strain, could those logically and historically fundamental examples of heat's destructibility play a constructive role in the evolution of the caloric theory? How, for that matter, did the phenomena of adiabatic change enter the literature at all?
The principal adiabatic phenomena in gases emerged as recognized scientific problems between 1755 and 1802. Historically, their origin remains somewhat obscure, but they seem to provide a typical example of the quasiinevitable accidental discovery caused by the increasingly routine deployment of a novel laboratory instrument, in this case the thermometer. The Scottish physician, William Cullen, usually cited then and now as the discoverer of adiabatic temperature change, was actually investigating cooling by evaporation when he stumbled upon the adiabatic effects5 Hoping to learn whether or not the reduced temperature of a wet-bulb thermometer could be due to the absorption of air by the liquid on the bulb, he placed his thermometer in nach ihrer gesckicktlicken Entwickelung (Leipzig, 1898), pp. 62-64. James Joule, On the Changes of Temperature produced by the Rarefaction of Air, Philosophical Magazine, 1845, 26: 369-383. 'Marc Seguin, De l'injluence des chemins de jer et de l'art de les tracer et de k s construire (Paris, 1839), pp. 383-396. Carl Friedrich Mohr, Ueber die Natur der Warme, Zeitschrift fur physik, 1837, 5: 419-432, 433-445, and Ansichten iiber die Natur der WBrme, Annalen der Pharmacie, 1837, 24: 141-147. Ludwig Augustus Colding, On the History of the Principle of the Conservation of Energy, Philosophical Magazine, 1864, 27: 56-64. Colding's first discussion of conservation was read to the Royal Society of Denmark in 1843, but was not publishfd until 1851. Some readers will wonder at the omission of Rumford, Davy, Young, and the other early nineteenth-century proponents of the dynamical theory of heat. But these men emphasized
.
only the convertibility of mechanical motion to heat. They thus helped their successors to reach the concept of conservation without catching a glimmer of it themselves. In the early nineteenth century, as throughout the seventeenth, the notion that heat was motion did not imply any concept of conservation. For that matter several of the early exponents of conservation, most notably Mayer, were insistent and lifelong opponents of the dynamical theory of heat. Cullen's paper, "Of the Cold produced by evaporating Fluids, and of some other means of producing Cold," was read on I May 1755, to the Philosophical Society of Edinburgh and was published in the Society's Essays and Observations, Physical and Literary, vol. 2 (Edinburgh, 1756). I have used the second edition of this volume (Edinburgh, 177o), pp. 159-171. Cullen's paper was also reprinted twice more (Edinburgh, 1777 and 1782) together with Black's Experiments on Magnesia Alba.
I34 THOMAS S. KUHN the receiver of an air pump and noted in passing that the thermometer always rose or fell a few degrees as air entered or left the receiver. Cullen seems to have viewed this unexpected effect as a special case of evaporation. His report of 1755 devotes only two passing sentences to it, and he investigated what we should call adiabatic temperature change no further. Yet within a few years, perhaps only one, of its first publication Cullen's passing remark provided the research problem which Johann Christian Arnold discussed in his inaugural dissertation as professor of physics at the University of Erlangen.6 Arnold concentrated his entire attention upon the cooling and heating effects which accompany the evacuation and refilling of the receivers of air pumps, and his investigation is therefore far more complete than Cullen's. But he persisted in explaining adiabatic cooling as a consequence of the evaporation of water vapor, and he explained the converse heating effect as the result of friction between the thermometer and the air current rushing into the receiver. After Arnold's paper there are no further published reports of adiabatic heating and cooling for more than twenty years. But beginning in 1779, the effects were discussed repeatedly and with steadily increasing frequency. In that year J. H. Lambert discussed both Cullen's and Arnold's experiments in his Pyrometrie, and he explained their results in terms of the changing density of fire particles in the receiver^.^ Four years later, in his very influential Hygromdtrie, H. B. de Saussure reinvestigated the phenomena with a credit to Cullen and also to Lambert, whose explanation he a d ~ p t e d . Then ~ the pattern of development changes. The next two published reports seem to record independent rediscoveries, the first by Erasmus Darwin and the second ~ Darwin nor Pictet quite claims an original disby M. A. P i ~ t e t .Neither covery. But they point for their precedent to the formation of frost in Hero's compressed air fountains and in the jets from high-pressure mining pumps, and they show no evidence of an acquaintance with the earlier work on thermometers in evacuated receivers.1° That work, however, was not lost from view. In 1799 it was discussed once more by the essayist, L. A. von A full abstract of Arnold's inaugural address on 3 November 1759 is given in the Erlangische Gelehrte Anmerkungen und Nachrichten, X L I X Stiidr ( ~ f s g ) ,pp. 436-440. I am grateful to Professor Charles C. Gdhspie of Princeton for discovering this abstract and making it available t o me. Both the abstract and Poggendorf (vol. I, p. 63) refer to an earlier printed discussion of the problem by Arnold, De Thermometri sub campana antliue pneumaticae suspensi variutionibus, and Poggendorf describes it as Erlangen, 1757. I have not yet seen this Latin version. [A microfilm received since the preceding was written confirms both Poggendorf's date and the accuracy of the 1759 absfract.] Pyrometrie oder vom Maase des Feuers und der Warme (Berlin, 1779)~pp. 266-271. Lambert seems to be the only figure in this series of investigations who knew Arnold's work. Essais sur lJhygromttrie (Neuchltel, 1783), pp. 193 n., 271-272 and n., 329-333. OErasmus Darwin, Frigorific Experiments on the mechanical expansion of Air, Philosophical Darwin states Transactions, 1788, 78: 43-52: that some of his experiments (mcluding a direct repetition of Cullen's and Arnold's) were performed as early as 1773 or 1775, and he mentions in a letter of 1784 to Josiah Wedgwood that he "can prove from some experiments, that
air when it is mechanically expanded always attracts heat from the bodies in its vicinity." I am indebted to Professor Robert E. Schofield of the University of Kansas for calling this letter to my attention. See Ernst Krause, Erasmus Darwin, with a preliminary note by Charles Darwin (New York, 1880), p. 101. Marc Auguste Pictet, Note sur un froid considerable produit par la sortie prompte de I'air atmospherique, fortement comprime, Journal de physique, 1798, 47: 186. This is really just a brief account by the editor, Jean-Claude Delametherie of some observations made by Pictet on a high-pressure mining pump. Except for a brief comparison with the cooling produced by evaporating ether (a comparison which may be Delamktherie's), there is no attempt at explanation. Yet Dalton (note 11) says that his explanation of adiabatic phenomena is the same as that borrowed by Pictet and by Saussure from Lambert, a remark which does not square with the content of Pictet's note. There may therefore be another Pictet piece, but, if so, it has evaded considerable systematic search. loDarwin could easily have known Cullen's work, and Pictet ought to have known Saussure's, but neither writes as though aware of any concrete precedents for his report. In the case of Pictet's note, of course, the ignorance may be only Delamktherie's.
T H E CALORIC THEORY O F ADIABATIC COMPRESSION
I35
Amim, in Gilbert's Annalen, and in 1802 Dalton referred to it in an article reporting a careful experimental reexamination of the entire problem.ll Dalton was particularly proud of this piece of work and repeatedly referred to its originality, but today it is hard to find concrete justification for any such claim. The difficulty is typical and significant. There is almost a continuum from Cullen, who did not recognize the phenomena he had "discovered," through Lambert, who recognized them but did not investigate them, to Dalton, who did both. Given a developmental pattern so complex, it seems less appropriate to speak of the "discovery" of adiabatic compression than of its gradual "emergence" as a recognized scientific problem.12
Dalton's definitive paper was widely reprinted in England and on the Continent during 1802 and 1803.l' After this time heating and cooling by compression and expansion were common knowledge, and study of the problem entered a new phase. Scientists began, both by experiment and by the elaboration of theories, to relate adiabatic phenomena to other recognized problems in physics and chemistry, particularly to the theoretical problem of the speed of sound and to the experimental problem posed by the specific heats of gases. Significantly, though the early investigators had all been English, Swiss, or German, this second stage of development occurred almost exclusively in France. Leslie in 1804, Delarive and Marcet in 1823, and Ivory in 182 7 were the only investigators outside France who attempted original investigations of adiabatic change between 1802 and 1840.'~ Their work is uniformly inferior to the best done by the French. Once the new phenomena had been established, a process in which the French did not participate at all, the locus of investigation shifted to France where more powerful experimental and theoretical techniques were brought to bear upon it. Perhaps we have here one more illustration of the contrasting strengths and weaknesses of nations with and without highly institutionalized scientific traditions. The use of adiabatic phenomena in investigating the otherwse experimentally intractable specific heats of gases was first suggested in Dalton's widely circulated paper. From the fact of adiabatic heating, Dalton concluded that the heat capacity of a given volume of gas increases steadily with decreasing gas pressure and is greatest of all for the void. On this theory, decreasing the mass of gas in a given receiver would raise the capacity of the receiver's content and thus, the quantity of caloric being fixed, lower the temperature.
...
UL. A. von Arnim, algemeiner Beweis des Mariottischen Gesetzes, und Bemerkungen iiber dieses Gestz, Annalen der Physik, 1799, 2: 238-245. This paper contains the only textual citation of Pictet's work that I have discovered. John Dalton, Experiments and Observations on the Heat and Cold produced by the Mechanical Condensation and Rarefaction of Air, Memoirs of the Literary and Philosophical Society of Manchester, 1802, 5: 515-526. * The structure of this developmental pattern and the related problem of originality will be examined in more detail in a later and fuller report on the research whose preliminary results are sketched in this paper. UNicholson's Journal, 1802, 3: 160-166; Jourrml des Mines, 1803, 13: 257-260; Annulen der Physik, 1803, 14: 101-1x1. There are also
abridged reports in Annaks de Chimie, 1802, 45: 104-107, and in Bulletin des sciences de la socUtd philomatiqw, 1803, 2: 165-166. John Leslie, An Ezperimentd Inquiry into the Nature and Propagation of Heat (London, 1804), pp. 165-169. Auguste Delanve and Franqois Marcet, Experience relative au froid produit par I'expansion des gaz, Annaks de Chimie et de Physique, 1823,23: 209-216. This is a reprint of an article printed during the same year in the Bibliothbque universe&. James Ivory, Investigations of the Heat extricated from A i i when it undergoes a given Condensation, Philosophicd Magazine, 1827, I: 89-94, 165-170; Application of the Variations of Temperature in Air that changes its Volume to account for the Velocity of Sound, ibid., 249-255.
1 3 ~
T H O M A S S.
KUHN
ClCment and Desormes were the only investigators to take Dalton's theory even approximately literally. I n I 8 I 2 they submitted an experimental memoir based upon the void's caloric capacity in competition for the prize offered by the French Academy for the best investigation of the specific heat of gases.15 Other workers, however, found it possible to follow Dalton's suggestion without accepting the whole of the theoretical analysis which underlay it. Leslie, in 1804, announced that hydrogen and oxygen must have the same specific heat since they produce the same temperature increment when rushing into a receiver initially a t one-tenth atmosphere.16 Three years later, in 1807, Gay-Lussac again applied adiabatic phenomena to the problem of heat capacity, but he first rejected Dalton's analysis and this time Leslie's as well.17 To discredit the heat capacity of a void, Gay-Lussac suspended a sensitive thermometer at the top of a long mercury barometer and observed that it remained stationary when the volume of the void was rapidly changed.ls I n addition, he pointed out that Dalton had ignored the caloric carried out of his receiver by the escaping gas. Nevertheless, Gay-Lussac proceeded to derive a whole series of significant conclusions about the heat capacity of gases from a series of experiments all his own. These last experiments are particularly intriguing because of the recurrent references to them in the early literature of thermodynamics. I n order to examine the heat carried off by the escaping gas and also in an effort to work with well-dried gases, Gay-Lussac employed two equal reservoirs, one full and the other evacuated at the start of his experiments. After each expansion from the full into the empty reservoirs, he noted that the cooling in one was equal to the heating in the other. This is the result which later provided first Carnot and then Mayer with their first concrete and quantitative evidence that there can be no net heating or cooling if the gas does no external work.ls As Joule pointed out when he repeated the experiment, here was energy conservation demonstrated by thermometers alone.20
An even more consequential tie between adiabatic and other phenomena was provided by Laplace, who suggested, in or before 1802, that heating by compression might plausibly account for the well-known error in Newton's theoretical value for the speed of sound in air.21 This discrepancy, about twenty "Determination experimentale du zero absolu de la chaleur et du calorique sp6dfique des gaz, Journal de Physique, 1819, 89: 321-346, 428-455. The first part purports to be the 1812 prize paper, the second an extension based on later work. " OP. cjt., PP. 533-534. "Prem~er essai pour determiner les variations de tempkrature qu'kprouvent les gaz en changeant de densitk, et consideration sur leur capacitC pour le calorique, Mdmoires de physique et de chimie de la Socidtd d1Arcueil, 1807, I : 180-203. Is Ibid., and also a later, more careful repetition of the experiment in Ann. chim. phys., 1820, 13: 304-308. The latter was probably a response to the work of Clement and Desormes (see note IS). "For Carnot's and Mayer's references to the experiment see note I. Carnot seems to have known of it only through hearsay. Though Gay-Lussac's paper was twice reprinted in Ger-
man journals during 1808 (see the R o y d Society Catalogue), Mayer's knowledge of it almost certainly derived from G. Lamb, Cours de physique de l'dcole polytechnique, probably 2nd ed. (Paris, 1840), vol. I, pp. 488-490. =See note 2. =Laplace's suggestion was first made public b y Jean-Baptiste Biot, Sur la propagation du son, Bulletin des sciences de la socidtd philomatique, 1802, 3: 116-118. A much fuller report by Biot (from which the preceding was clearly abstracted) is, Sur la theorie du son, Journal de physique, 1802, 51: 173-182. Laplace's first remarks on the subject are in a note added to C. L. Berthollet's famous Chimique statique (Paris, 1803), pp. 245-247. The penultimate paragraph of this note includes the puzzling remark that Laplace has determined the extent of adiabatic heating with a calorimeter and that the resulting revision of the speed of sound checks well with the observed value. I t is hard to see how Laplace could have obtained
T H E CALORIC THEORY O F ADIABATIC COMPRESSION
I3 7
percent, had been one of the scandals of physical science for more than a century and had repeatedly though fruitlessly drawn the attention of Europe's outstanding theoretical scientists, including Euler and Lagrange.22 When Laplace's suggestion was made, direct confirmation was impossible. Until 1819 there were no published measurements of the number of degrees by which a given compression heats a gas. The heat capacity of existing thermometers was too large, and they responded too slowly to permit measurement by straightforward technique^.^^ But Biot provided qualitative evidence by an experiment which, for simplicity and ingenuity, ranks as a minor clasIn the absence of adiabatic heating, thought Biot, sound would not be transmitted through a pure saturated vapor. The vibrations of a bell, for example, would condense the vapor on the bell's surface without producing any sort of pressure wave. If sound were transmitted through vapors, and in 1807 Biot showed experimentally that it was, then adiabatic heating must intervene to keep the vapor from liquefying. Laplace's suggestion had, therefore, been at least partially confirmed. Of course, the confirmation surprised no one. Even before the experiments were published, both Biot and Poisson had assumed the validity of Laplace's theory, or at least they had used existing measurements of the speed of sound in order to compute the extent of heating by compre~sion.~~ They thus determined a new physical constant, one which could not at this time be measured directly. Poisson's value, I " Centigrade for each I / I I ~change in volume, remained a standard in the literature from 1808 until the early 1820's. In 1824, Carnot used it repeatedly in his famous analysis of the heat engine cycle.26 Desire for more direct and quantitative confirmation of Laplace's suggestion continued, however, and this desire must have partially motivated the French Academy's prize for which ClCment and Desormes competed, and which was won by the classic memoir of Delaroche and BCrard.27 Unlike ClCment and Desormes, whose results were not published until 1819, the prize winners made no direct measurements of adiabatic heating. Their results could not be directly applied to the speed of sound. But they did measure the heat capacity of air at two quite different pressures (in fact their high-pressure measurement yielded one of the two really bad experimental values in their memoir), and by applying the caloric theory, Laplace was able to derive from this inaccurate pair of measurements the first good theoretical value for the speed of sound in air.28 In retrospect, the agreement was artificial. Modern theory indicates that Laplace used the caloric theory in a region where it any such results at this date. In any case, he published nothing comparable until 1816 and then he made use of experimental data of a sort unavailable until 1812 or 1813 (see below). "For a full and penetrating account of this problem and others presented by the theory of sound see Clifford Truesdell's introduction to Leonhardi Eukri Opera omnia, series 11, vol. 13 (Zurich, 1956), pp. xix-lxxii. "The largest measured change in temperature was about 5o0C, recorded with an early trimetallic strip constructed by the brothers Breguet (Ann. chim. phys., 1817, 5: 315-316). No one, however, took this reading to represent the full temperature variation of the gas. GayLussac, for example, estimated from the tinder ignited in a fire syringe that air must be heated at least goo°C, and perhaps several thousand, when compressed to one-fifth volume (ibid.,
1818, 9 : 305-310).
" Exfinences sur la production du son dans
les vapeurs, Mdmoires d'Arcueil, 1809, 2 : 94-
103.
=Biot's computation i s given in the articles cited in note 21. The standard computation was, however, that of Simon Denis Poisson, Memoire sur la thbrie du son, Journul de Pdcole polytechnique, 1808, 7 (Cahier 14) : 319392. See particularly pp. 332-333, 360-364. "Carnot, Rdflcxions (Paris, 1g53), p. 43. This is the point at which Poisson's figure is introduced. Thereafter it is basic to almost all the numerical computations in the memoir. =Memoire sur la determination de la chaleur sp6cifique des differents gaz, Annales de C h i ~ i e ,1813, 85: 72-110, 113-182. Sur la vitesse du son dans l'air et dans I'eau, Ann. chim. phys., 1816, 3: 238-241.
138
THOMAS S. K U H N
will not work. But in this case, as in remarkably many others throughout this period, errors of theory and experiment compensated more than well enough to satisfy expectation. Small disagreements remained, however, until the period 1822 to 1825. Then Laplace reconciled theory and experiment almost completely by using a new value for the speed of sound, measured a t his suggestion by the Bureau of Longitude, and by utilizing more direct data on adiabatic compression, data provided first by ClCment and Desormes' experiments and then by experiments performed for him by Gay-Lussac and Welter.29 This line of development culminates in 1828 with Dulong's acoustic measurements of the relative speeds of sound in a number of simple gases.30 For the caloricists, Dulong's memoir summarized the best available experimental information about adiabatic heating, and added to it. Yet, from the same memoir the pioneers of energy conservation later derived even more impressive evidence than from Gay-Lussac's expansion experiments. Dulong had concluded, among other things, that the heat liberated by a given compression was the same in all simple gases, and both Mayer and Colding readily interpreted this result as evidence that the same amount of work always generates the same amount of heat.31 Mayer also found in Dulong's memoir the data with which to compute the value of Joule's constant given in his first published paper.
It is only in these later, post 1815, investigations that the full scope of the caloric theory becomes apparent in the published discussions of adiabatic phenomena. Dalton and Leslie had, of course, developed explicit versions of the theory for application to adiabatic change. But Leslie's, being badly garbled, found no followers, and Dalton's was thoroughly discredited, at least in France, by the work of Gay-Lussac. ClCment and Desormes seem to have been the only investigators to follow Dalton. Until 1815 the other main workers in this field - including Gay-Lussac himself, Biot, Berthollet, Dulong, and Poisson - relied on a largely qualitative theory hinted a t by Lambert and Saussure and further developed in a quasi-quantitative form by Laplace in 1 8 0 3 . ~ ~ I n Laplace's early formulation, this theory held first that pressure is entirely due to the mutual repulsion of the caloric aggregated around all gas molecules, and second that the quantity of caloric in a given gas volume depends only on the temperature, not at all on the pressure of the gas. I t followed that sud"The first announcement is, Note sur la vitesse du son, Ann. chim. phys., 1822, 20: 266-269 (this paper seems to have been omitted from the Oeuvres compktes). The same computation is described in the papers cited in note 33. For Clement and Desormes see note IS. The Gay-Lussac and Welter results seem to have been communicated privately to Laplace and published only by him. A brief report on some qualitative anomalies in their early experiments (Sur la dilation de I'air, Ann. chim. phys., 1821, 19: 436-437) was published by Gay-Lussac and Welter themselves, but they seem never to have published their data or a description of their equipment. =Recherches sur la chaleur specifique des fluids elastiques, Mdmoires de PAcade'mie, 1831, ro: 147-191. For the several reprints see the
R O ; ~Society Catalogue.
For Mayer see Weyrauch's Kleinere sclrrif-
ten, pp. 155, 189. Dulong's work, like Gay-
Lussac's, was known to Mayer through Lame's
textbook (note 19). For Colding see note 3.
"For Dalton and Leslie see notes 11 and 14.
For Dulong, Gay-Lussac, and Poisson see notes
17, 25, and 30. Berthollet's fullest account of
the caloric theory is in his Chimique statique (Paris, 1803), vol. I, sec. 3, and Biot's is scattered through his Traitd de physique expdrimentale et mathdmatique (4 vols., Paris, 1816)~ particularly vol. I, chap. 5. Laplaces' earliest version of the theory is cited in note 21. An immediate revision was introduced in a second note (no. 15) added to Berthollet's text. Later developments of Laplace's theory are cited in notes 28, 29 and 33.
T H E CALORIC THEORY OF ADIABATIC COMPRESSION
I39
denly removing half the gas (and caloric) from a given volume would immediately reduce the temperature of the remaining gas. As Laplace later recognized, this theory was deficient both in logic and precision, yet until 1816 there is no published evidence for a more developed version. Writers on adiabatic compression continued to indicate only that compressing a gas increases caloric density and therefore temperature. But Laplace's first theoretical computation of the speed of sound implies the existence, at least by 1816, of a more developed theory, and that theory was made explicit in a series of articles first published in 1821-1822 and reissued with minor revisions in the following year as Book X I 1 of the M t ckanique c d l e ~ t e I. n~ ~Laplace's new theory each molecule still attracted its own semi-permanent atmosphere of caloric, and the mutual repulsion of the particles of caloric fluid still accounted for pressure. But temperature was no longer a function of the amount of this bound caloric in a unit volume of the gas. Instead, it was identified with the density of radiant caloric, a highly attenuated space-filling fluid which maintained constant equilibrium with the bound caloric atmospheres of individual molecules by continuous radiation and absorption. A mathematical statement of these conceptions enabled Laplace to derive both Boyle's and Gay-Lussac's Laws as well as several of the major mathematical relations governing adiabatic phenomena. He showed, in particular, that if gamma is defined as the ratio of the heat capacity of a gas a t constant pressure to its capacity a t constant volume, then the speed of sound must have Newton's value multiplied by the square root of gamma. Among his other results was the more familiar relation that, in all adiabatic compressions and expansions, gas pressure times gas volume to the power gamma is a constant. I n the same year that Laplace first reissued his theory in collected form, Poisson published an incisive paper showing that the same results and others besides could be derived from far more restricted caloric hypo these^.^^ He began by taking from the caloric theory only the hypothesis that the heat content of a gas is a state function; that is, that heat content depends exclusively on pressure and density. From this single caloric premise, he was able to derive Laplace's value for the speed of sound, as well as the whole battery of relations governing pressure, volume, and temperature during adiabatic change. By invoking the further hypothesis that a t fixed pressure caloric content is proportional to volume, Poisson was able to derive explicit formulas for the dependence of heat capacity on pressure. At this point the caloric theory was showing itself a powerful instrument indeed! And this was not the last stage of its development. Carnot's famous Rdflexions sur la puissance motrice du feu appeared in 1824 only a year after the publications of Laplace and Poisson, and it seems the culmination of this entire line of research. From premises whose relation to the caloric theory is the same as Poisson's and with the aid of his own consequential conception of the reversible cycle, Carnot was able to extend still further the thermal gas laws derived by his predecessors. Carnot's results have been discussed too often to require comment here.35 "The Mdchanique cdkste, Book XI1 (Paris, 1823) is the most convenient source and the one from which most of Laplace's contemporaries took their information. But a succession of fragmentary drafts had been published earlier in the Ann. chim. phys. (1821) and in the Connaissance des Temps (1821 and 1822). These preliminary papers are conveniently col-
lected in Laplace's Oeuvres complttes (14 vols., Paris, 1 8 4 3 - I ~ I Z )vol. , 13, pp. 273-305, vol. 14, pp 304-311. Sur la chaleur des gaz et des vapeurs, Ann. chim. phys., 1823, 23: 337-352. "They do, however, need to be related far more explicitly to the preceding development of the mathematical theory of gases, a theory
140 THOMAS S. KUHN But the line of theoretical development which includes Carnot poses a puzzle which may need a closing remark. How could such precise and powerful theoretical methods proceed so far without encountering the experimental disproof with which we can now readily confront the caloric theory? Part of the answer is immediate. The caloric theory was a better and more fully developed theory than we usually imagine; many of its consequences coincide precisely with those of kinetic theory and modern experiment. But this is not true for all its consequences. Poisson showed, for example, that the specific heat of a gas must increase with decreasing pressure, and Carnot proved that heat capacity must vary as the logarithm of gas volume. Neither statement can today be experimentally confirmed. They provide good grounds for rejecting the caloric theory. In the first half of the nineteenth century, however, they provided no such ground, for the thermal properties of elastic fluids were too difficult to measure. The heat capacity of calorimeter and thermometer was usually far larger than that of the gas they contained. As a result, few empirical bench marks were available to those who developed the caloric theory of gases, and it was difficult to tell which of the available and by no means consistent experimental measurements was reliable. In this area of research, as in contemporary nuclear physics, theoretical and experimental techniques developed together into a region where neither was entirely secure. The selection and evaluation of empirical tests was as much a matter of taste and judgment as the selection and evaluation of theory. No caloricist was ever forced to maintain his theory in the face of clear-cut experimental counter-evidence. On the contrary, the caloricists occasionally produced experimental evidence for relationships that we are quite unable to confirm today. An examination of Laplace's first theoretical value for the speed of sound or of the consistent results gained by those who first investigated the variation of heat capacity with pressure may well tempt the puzzled historian to proclaim with Oscar Wilde that, where theory and experiment are both insecure, "nature imitates art." which Carnot knew through the Mkchanique ckleste. That problem will be undertaken in a later paper which will also provide a fuller his-
torical and analytic description of the caloric theory of gases itself.
