Impact of Gibbs’ and Duhem’s approaches to thermodynamics on the development of chemical thermodynamics. (English) Zbl 1464.01007

Dais, Photis

Arch. Hist. Exact Sci. 75, No. 2, 175-248 (2021).

The paper provides detailed analysis of the thermodynamical work of Josiah Gibbs and Pierre Duhem. Particular emphasis is placed on the elements relevant for chemical thermodynamics. Gibbs is characterized as being essentially concerned with thermal equilibrium. Duhem is characterized as more interested in dynamical processes, attempting to subsume thermodynamics and analytical mechanics under a more general theory of dynamics. The paper continues with a multi-faceted discussion of how Gibbs’s (and to some extent also Duhem’s) work was slowly adopted by chemists. While Gibbs’s work is identified as more influential in the development of chemical thermodynamics (as witnessed by the prominence of Gibbs’s chemical potentials and the relative insignificance of Duhem’s thermodynamic potential), the influence of Duhem’s more general framework in other fields, in particular continuum mechanics is emphasized.

Reviewer: Alexander Blum (Berlin)

MSC:

01A55	History of mathematics in the 19th century
80-03	History of classical thermodynamics

References:

[1]	Andrews, T., The Bakerian lecture: On the Gaseous state of matter, Philosophical Transactions of the Royal Society of London, 159, 575-590 (1869)
[2]	Andrews, T., The Bakerian lecture: On the Gaseous state of matter, Philosophical Transactions of the Royal Society of London, 166, 421-449 (1876)
[3]	Baierlein, R., The elusive chemical potential, American Journal of Physics, 69, 423-434 (2001)
[4]	Balian, R., François Massieu et les potentiels thermodynamiques, Comptes Rendus Physique, 18, 526-530 (2017)
[5]	Bancroft, W., Review: Traitė ėlementaire de mėchanique Chimique, fondėe sur la thermodynamique, Science, 10, 81-82 (1899)
[6]	Bordoni, S. 2010. Taming complexity. Duhem’s pathway to thermodynamics. Doctoral Dissertation. Universita Deglis Studi di Bergamo. 359 pp.
[7]	Bordoni, S., Unearthing a buried memory: Duhem’s third way to thermodynamics, Part 2, Centaurus, 54, 232-249 (2012)
[8]	Bordoni, S., Routes toward an abstract thermodynamics in the late nineteenth century, The European Physical Journal H, 38, 617-660 (2013)
[9]	Boynton, WP, Gibbs’ thermodynamical model. Physical Review, 10, 228-233 (1900)
[10]	Boynton, WP, Gibbs’ thermodynamical model for a substance following van der Waals’ equation, Physical Review, 11, 291-303 (1900)
[11]	Boynton, WP, Thermodynamical potentials. Physical Review, 20, 259-267 (1905)
[12]	Bumstead, HA; Van Name, RG, The scientific papers of Gibbs, 1-353 (1906), New York: Longman, Green and Co, New York
[13]	Clark, AL; Katz, L., Thermodynamic surfaces of H_20, Transactions of the Royal Society of Canada, 3rd series Sec. III, 33, 59-71 (1939)
[14]	Clausius, R., On the behavior of carbonic acid in relation to pressure volume and temperature, Philosophical Magazine, 9, 303-408 (1880)
[15]	Coffey, P., Chemical free energy and the third law of thermodynamics, Historical Studies in the Physical and Biological Sciences, 36, 365-396 (2006)
[16]	Coy, D. C. 1993. Visualizing thermodynamic stability and phase equilibrium through computer graphics. Ph.D. Dissertation, Iowa State University.
[17]	Cropper, WH, Walther Nernst and the Last Law, Journal of Chemical Education, 64, 1-8 (1987)
[18]	Cropper, WH, Great physicists. The life and times of leading physicists from Galileo to hawking, 106-123 (2004), Oxford: Oxford University Press, Oxford
[19]	Dais, P., The double transfer of thermodynamics: from physics to chemistry and from Europe to America, Studies in History and Philosophy of Science, 77, 54-63 (2019)
[20]	Darrigol, O., Atoms, mechanics, and probability: Ludwig boltzmann’s statistico-mechanical writings—An exegesis (2018), Oxford: Oxford University Press, Oxford · Zbl 1382.83003
[21]	Darrigol, O., The Gibbs Paradox: Early history and solutions, Entropy, 20, 1-54 (2018)
[22]	Daub, EE, Gibbs’ phase rule: A centenary retrospect, Journal of Chemical Education, 53, 747-751 (1976)
[23]	Deltete, RJ; Brenner, A., Review. Pierre Duhem: Mixture and chemical combination and related essays, Foundations of Chemistry, 6, 203-230 (2004)
[24]	Donnan, FG; Haas, A., Commentary on the scientific writings of J. Willard Gibbs (1936), New Haven, Connecticut: Yale University Press, New Haven, Connecticut
[25]	Duhem, P., Sur le potentiel thermodynamique et la théorie de la pile voltaïque, Comtes Rendus de l’Académie des Sciences, 99, 1113-1115 (1884)
[26]	Duhem, P., Le potentiel thermodynamique et ses applications à la mécanique et à l’étude des phénomènes électriques (1886), Paris: Hermann A, Paris
[27]	Duhem, P., Sur les ėquations gėnėral de thermodynamique, Annales Scientifiques de l’Ecole Normale Supėrieure, 3e Sėrie, 8, 231-266 (1891) · JFM 23.1172.01
[28]	Duhem, P., Commentaire aux principes de la thermodynamique-premier Partie, Journal de Mathėmatiques Pures et Appliquėes, 4e Serie, 8, 269-330 (1892) · JFM 24.1096.03
[29]	Duhem, P., Notation atomique et hypothѐses atomistiques. Revue des questions scientifiques, 31, 391-457. Translated by Needham, P. (2000). Atomic Notation and Atomistic Hypotheses, Foundations of Chemistry, 2, 127-180 (1892)
[30]	Duhem, P., Introduction a la mechanique chimique (1893), Paris: George Carré, Paris
[31]	Duhem, P., Commentaire aux principes de la Thermodynamique-Deuxiѐme partie, Journal de Mathėmatiques Pures et Appliquėe 4e Serie, 9, 293-473 (1893) · JFM 25.1778.01
[32]	Duhem, P. 1893c. L’Ècole anglaise et les thėories physiques: Á propos d’un livre rėcent de W. Thomson. Revue des Questions Scientifiques, 34: 345-378. Edited and translated by Ariew, R., and P. Barker as Duhem, P. (1996). The English School and Physical Theories: On a Recent Book by W. Thomson. In Essays in the History and Philosophy of Science. Indianapolis: Hackett. · JFM 25.0110.03
[33]	Duhem, P., Commentaire aux principes de la thermodynamique—Troisième partie: Les équations générales de la thermodynamique, Journal de Mathématiques Pures et Appliquées, 10, 207-285 (1894)
[34]	Duhem, P. 1895, 1898, 1902. Sur les déformations permanents et l’hystérésis. In: 4e and 5e mėmoire de l’Académie de Belgique, tome. LIV, tome. LVI, tome. LXII.
[35]	Duhem, P., Théorie thermodynamique de la viscosité, du frottement et des faux équilibres chimiques, Mémoires de la Société des Sciences physiques et naturelles de Bordeaux, 5e série, 2, 99-126 (1896) · JFM 29.0770.02
[36]	Duhem, P., Thermochimie à propos d’un livre récent de Marcellin Berthelot, Revue des questions scientifiques Ser 2, 7, 361-392 (1897)
[37]	Duhem, P. 1897b. Traité Élémentaire de Mécanique Chimique fondée sur la Thermodynamique Livre II; tome. I, Paris: Librairie Scientifique A. Hermann. · JFM 29.0775.04
[38]	Duhem, P., Les théories électriques de J, Clerk Maxwell. Étude historique et critique, Annales de la Societe Scientifique de Bruxelles, 4, 239-253 (1900) · JFM 31.0821.02
[39]	Duhem, P., Recherches sur l’Hydrodynamique, Annales de la Faculté des Sciences eo Toulouse, Série 2, 3, 379-431 (1901) · JFM 33.0770.01
[40]	Duhem, P., Les theories electriques de J. Clerk Maxwell. Premiere Partie: Les electrostatiques de Maxwell, Annales de la Societe Scientifique de Bruxelles, 25, 1-90 (1901)
[41]	Duhem, P., Les theories electriques de J. Clerk Maxwell. Seconde Partie: L’electrodynamique de Maxwell, Annales de la Societe Scientifique de Bruxelles, 25, 293-417 (1901)
[42]	Duhem, P. 1902a. Le mixte et la combinaison chimique. Éssai sur l’évolution d’une idée. Paris, C. Naud, Editeur, 208 pp. Edited and translated, with an Introduction by Paul Needham. 2002. Mixture and Chemical Combination and Related Essays. Dordrecht: Springer.
[43]	Duhem, P. 1902b. Thermodynamique et Chimie, leçons élémentaires à l’usage des chimistes. Leçons XVIII. XIX et XX, Paris: Librairie Scientifique A. Hermann.
[44]	Duhem, P. 1902c. Les théories électriques de J. Clerk Maxwell. Étude historique et critique. Paris: A. Hermann. 228 pp. Edited and translated by Aversa, A. 2015. The Electric Theories of J. Clerk Maxwell_A Historical and Critical Study. New York: Springer. · JFM 33.0906.06
[45]	Duhem, P., Thermodynamics and chemistry. A non-mathematical treatise for chemists and students of chemistry (1903), New York: Wiley, New York
[46]	Duhem, P., L’évolution de la mécanique, 348 (1905), Paris: Librairie Scientifique A. Hermann, Paris
[47]	Duhem, P., Josiah-Willard Gibbs, à propos de la publication de ses mémoires scientifiques, 43 (1908), Paris: Librairie Scientifiquc, A. Hermann, Paris · JFM 39.0028.04
[48]	Duhem, P., La science Allemande, 144 (1915), Paris: A. Hermann et Fils, Paris · JFM 45.1215.07
[49]	Dunn, E.; Fosdic, RL, The Morphology and Stability of Material Phases, Archive for Rational Mechanics and Analysis, 74, 1-99 (1980)
[50]	Fisher, ME; Caldi, DG; Mostow, GD, Phases and phase diagrams: Gibbs’s legacy today, Proceedings of the Gibbs Symposium, 39-72 (1989), Providence: American Mathematical Society, Providence
[51]	Garber, EW, James Clerk Maxwell and thermodynamics, American Journal of Physics, 37, 146-155 (1969)
[52]	Garber, EW, Clausius and Maxwell’s Kinetic theory of gases, Historical Studies in the Physical Sciences, 2, 299-319 (1970)
[53]	Gibbs, JW, Graphical methods in the thermodynamics of fluids, The Transactions of the Connecticut Academy of Arts and Science, 2, 309-342 (1873) · JFM 05.0585.01
[54]	Gibbs, JW, A method of geometrical representation of the thermodynamic properties of substances by means of surfaces, The Transactions of the Connecticut Academy of Arts and Science, 2, 309-342 (1873) · JFM 05.0585.02
[55]	Gibbs, JW, On the equilibrium of heterogeneous substances, The Transactions of the Connecticut Academy of Arts and Science, 3, 108-248 (1876) · JFM 08.0559.03
[56]	Gibbs, JW, On the equilibrium of heterogeneous substances, The Transactions of the Connecticut Academy of Arts and Science, 3, 343-524 (1878) · JFM 10.0759.01
[57]	Gibbs, JW, On the vapor-densities of peroxide of nitrogen, formic acid, acetic acid, and perchloride of phosphorus, American Journal of Science, Series, 3, 18, 371-387 (1879) · JFM 11.0783.01
[58]	Gibbs, JW, Elementary principles in statistical mechanics developed with especial reference to the rational foundation of thermodynamics (1902), New York: Dover Publications, New York · JFM 33.0708.01
[59]	Guggenheim, EA, Modern-thermodynamics by the methods of Willard Gibbs (1933), London: Methuen & Co., Ltd, London · JFM 59.0785.08
[60]	Helmholtz, H. F. (1882). Die Thermodynamik Chemisher Vergänge. Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften zu Berlin, Erster Halbband, Januar bis Mai, 22-39 pp. Translated in English under the direction of the Physical Society of London. Helmholtz, H. F. 1888. The thermodynamics of chemical processes. Physical memoirs selected and translated from foreign sources, Vol. I. Part II, pp. 43-62. London: Taylor and Francis.
[61]	Hiebert, EN; Gillispie, CC, Nernst, Hermann walther, Dictionary of scientific biography, 432-453 (1981), New York: Charles Scribner Sons, New York
[62]	Horstmann, A., Theorie der Dissociation. Annalen der Chemie und Pharmacie 170:192-210. An English translation appears as Horstmann, A. (2009). The theory of dissociation, Bulletin for the History of Chemistry, 34, 76-82 (1873)
[63]	Jaki, SL, Uneasy genius: The life and work of Pierre Duhem (1984), The Hague: Martinus Nijhoff Publishers, The Hague
[64]	Jensen, WB, August Hortsmann and the origin of chemical thermodynamics, Bulletin of the History of Chemistry, 34, 83-91 (2009)
[65]	Jolls, KR; Caldi, DG; Mostow, GD, Gibbs and the art of thermodynamics, Proceedings of the Gibbs symposium, 39-72 (1989), Providence, RI: American Mathematical Society, Providence, RI
[66]	Jolls, KR, Understanding thermodynamics through interactive computer graphics, Chemical Engineering Progress, 85, 64-69 (1989)
[67]	Kipnis, A.; Martinas, K.; Ropolyi, L.; Szegedi, P., Early chemical thermodynamics: Its duality embodied in Van ‘t Hoff and Gibbs, Thermodynamics, history, and philosophy, facts, trends, and debates, 492-507 (1991), London: World Scientific Publishing Co, London
[68]	Klein, MJ; Aris, A.; Davis, HT; Stewers, RH, The scientific style of Josiah Willard Gibbs, Essays of founders of modern science, 142-162 (1984), Minneapolis: University of Minnesota Press, Minneapolis
[69]	Klein, MJ; Caldi, DG; Mostow, GD, The physics of J. Willard Gibbs in his time, Proceedings of the Gibbs symposium, 5-8 (1989), Providence, Rl: American Mathematical Society, Providence, Rl
[70]	Klein, MJ; Garber, E., Duhem on Gibbs, Essays in honor of Robert Schofield, 52-67 (1990), London: Associated University Press Inc, London
[71]	Kragh, H.; Weininger, SJ, Sooner Silence than confusion: The Tortuous entry of entropy into chemistry, Historical Studies in the Physical and Biological Sciences, 27, 91-130 (1996)
[72]	Lewis, GN; Randall, M., Thermodynamics and the free energy of chemical substances (1923), New York: McGraw-Hill Company, New York
[73]	Manville, O. 1928. L’Oeuvre scientifique de Pierre Duhem. Memoires de la Societe scientifique des sciences physiques et naturelles de Bordeau, Paris: Blanchard. · JFM 53.0029.09
[74]	Massieu, F. 1869. Sur les fonctions caractéristiques des divers fluides et sur la théorie des vapeurs. Comptes Rendus 69: 858-862, and 1057-1061.
[75]	Massieu, F., Thermodynamique: Mémoire sur les fonctions caractéristiques des divers fluides et sur la théorie des vapeurs, Académie des Sciences de L’Institut National de France, 22, 1-92 (1876)
[76]	Mathias, PM, The Gibbs-Helmholtz equation for chemical process and technology, Industrial and Engineering Chemistry Research, 55, 1076-1087 (2016)
[77]	Maugin, G., Continuum mechanics through the eighteenth and nineteenth century. Historical perspectives from John Bernoulli (1727) to Ernst Hellinger (1914) (2014), Cham Heidelberg: Springer, Cham Heidelberg · Zbl 1303.74003
[78]	Maxwell, JC, Theory of heat (1872), London: Longmans, Green, and Co, London
[79]	Maxwell, JC, On the dynamical evidence of the molecular constitution of bodies, Nature, 11, 357-359 (1875)
[80]	Maxwell, JC, On the equilibrium of heterogeneous substances, Philosophical Magazine, Series, 6, 16, 818-824 (1876) · JFM 08.0710.02
[81]	Maxwell, JC, Theory of heat (1902), London: Longmans, Green, and Co, London
[82]	Meyerhoffer, W., Die Phasenregel und ihre Anwendungen, 72 (1893), Leipzig: Franz Deuticke, Leipzig
[83]	Miller, DG, Duhem and the Gibbs-Duhem equation, Journal of Chemical Education, 40, 648 (1963)
[84]	Miller, DG, Ignored intellect: Pierre Duhem, Physics Today, 19, 47-53 (1966)
[85]	Miller, DG; Gillispie, CC, Duhem Pierre-Maurice-Marie, Dictionary of scientific biography, 225-233 (1981), New York: Charles Scribner’s Sons, New York
[86]	Moore, CE; von Smolinski, A.; Jaselskis, H., The Ostwald-Gibbs correspondence: An interesting component in the history of the energy concept, Bullerin of the History of Chemistry, 2, 114-127 (2002)
[87]	Müller, I., A history of thermodynamics. The doctrine of energy and entropy, 127-164 (2006), Berlin: Springer, Berlin
[88]	Needham, P., Commentary of the principles of thermodynamics by Pierre Duhem (2011), Dordrecht: Springer, Dordrecht
[89]	Nernst, W. 1893. Theoretische Chemie, vom Standpunkte der Avogadroschen Regel und der Thermodynamik. Stuttgart: Verlag von Ferdinand Enke. Translated by Lehfeldt, R. A., Nernst, W. 1904. Theoretical Chemistry from the standpoint of Avogadro’s Rule and Thermodynamics. Fourth edition, London: Macmillan and Co.
[90]	Nernst, W. 1906. Über die Berechnung Chemischer Gleichgewichte aus Thermischen Messungen. Nachrichten von der Königlichen Gesebchn/t der Wimenscholten. zu Göttingen Mathematisch-Physikalische Klasse. Verlag von Wilhelm Knapp, Halle (Saale) 1924.
[91]	Nernst, W. 1918. Die theoretischen und experimentellen Grundlagen des neuen Wärmesatzes. Halle: Verlag von Wilhelm Knapp. Translated in English: Nernst, W. 1969. The New heat theorem. Its foundation in theory and experiment. New York: Dover Publications Inc. · JFM 46.1154.04
[92]	Partington, JR, A Text-book of thermodynamics (with special reference to Chemistry) (1913), London: Constable and Company Ltd, London · JFM 44.1047.08
[93]	Rocke, AI, The quiet revolution Hermann Kolbe and the science of organic chemistry (1993), Berkeley: University of California Press, Berkeley
[94]	Root-Bernstein, R.S. 1980. The ionists: Founding physical chemistry 1872-1890. Ph.D. dissertation, Ann Arbor: Princeton University.
[95]	Saurel, P., On the critical state of a one component system, The Journal of Physical Chemistry, 6, 474-491 (1902)
[96]	Servos, JW, A disciplinary program that failed: Wilder D. Bancroft, The Journal of Physical Chemistry, 1896-1933, 73, 207-232 (1982)
[97]	Servos, JW, Physical chemistry from Oswald to Pauling The making of a science in America (1990), Princeton, NJ: Princeton University Press, Princeton, NJ
[98]	Stokes, GG; Larmor, J., Memoir and scientific correspondence of the late Sir George Gabriel Stokes (1907), Cambridge: Cambridge University Press, Cambridge
[99]	Thomson, J., Considerations on the abrupt change at boiling or condensing in reference to the continuity of the fluid state of matter, Proceedings of the Royal Society, 20, 278-286 (1871)
[100]	Truesdell, C., The mechanical foundations of elasticity and fluid dynamics, Journal of Rational Mechanics and Analysis, 1, 125-300 (1952) · Zbl 0046.17306
[101]	Truesdell, C., Rational thermodynamics (1984), New York: Springer, New York · Zbl 0598.73002
[102]	Truesdell, C.; Serrin, J., What did Gibbs and Caratheodotory leave us about thermodynamics?, New perspectives in thermodynamics, 101-113 (1986), Berlin: Springer, Berlin
[103]	Van der Waals, JD, Over de continuiteit van den gas- en vloeistoftoestand (1873), Leiden: Sijthoff, A.W, Leiden · JFM 05.0515.01
[104]	van’t Hoff, J. H. 1884. Études de Dynamique Chimique. Amsterdam: Frederic Muller & Co. Revised and enlarged by Cohen E., and translated in English by Ewan T. van’t Hoff, J. H. 1896. Studies in chemical dynamics. Amsterdam: Frederic Muller & Co.
[105]	van’t Hoff, J. H. 1887. Die Rolle des osmotischen Druckes in der Analogie zwischen Lösungen und Gasen, Zeitscbrift für Physikalische Chemie 1: 481-508. Translated in English, van’t Hoff, J. H. 1995. The role of osmotic pressure in the analogy between solutions and gases. Journal of Membrane Science 100: 39-44.
[106]	van’t Hoff, JH, Physical chemistry in the service of the sciences. The Decennial Publications of the University of Chicago (1903), Chicago: Chicago University Press, Chicago
[107]	van’t Hoff, JH, Die chemischen Grundbegriffe nach Menge, Mass und Zeit (1912), Braunschweig: Vieweg, & Sohn, Braunschweig · JFM 43.0920.18
[108]	Wheeler, IP, Josiah Willard Gibbs the history of a great mind (1962), New York: Yale University Press, New York · Zbl 0045.14711
[109]	Wilson, EB; Donnan, FG; Haas, A., Papers I and II as Illustrated by Gibbs’ lectures on thermodynamic, Commentary on the scientific writings of J. Willard Gibbs, 19-59 (1936), New Haven, Connecticut: Yale University Press, New Haven, Connecticut
[110]	Wisniak, J., Hendrik-Willem Bakhuis Roozeboom: Equilibrium and phase topology, Journal of Phase Equilibria, 24, 422-430 (2003)