Abstract
Two different traditions of research emerged from Rudolf Clausius’s version of thermodynamics. While James Clerk Maxwell and Ludwig Boltzmann pursued the integration of thermodynamics with the kinetic theory of gases, others relied on a macroscopic and more abstract approach that set aside specific mechanical models. This second approach blossomed in about two decades in different countries of Europe and in the United States. François Massieu, Josiah Willard Gibbs, Hermann Helmholtz, and then Pierre Duhem explored the connections between the contents of thermodynamics and the formal structures of analytical mechanics. Others like the young Max Planck and Arthur von Oettingen pursued a sort of formal symmetry between thermal and mechanical variables. In the British Isles, Joseph John Thomson developed a dynamical approach to physics and chemistry, making use of the tools of abstract mechanics without excluding microscopic motions. Some developments were logically interconnected, as it was for Massieu’s, Gibbs’s, Helmholtz’s, and Duhem’s, even though they occurred in a largely independent manner. Duhem put forward the most original and most systematic reinterpretation of thermodynamics, which involved a bold upgrading of analytical mechanics and a bold mathematical unification of physics and chemistry. A strong commitment to unification was one of the hallmarks of all these theoretical researches.
Similar content being viewed by others
References
Bancroft W.D. 1897. Traité élémentaire de mécanique chimique, fondée sur la thermodynamique. P. Duhem. Vol. I. Science 120: 625–626
Bancroft W.D. 1898. Traité élémentaire de mécanique chimique, fondée sur la thermodynamique. By P. Duhem. Vol. II. Science 163: 214–215
Bancroft W.D. 1899. Traité élémentaire de mécanique chimique, fondée sur la thermodynamique. By P. Duhem. Vol. III. Vol. IV. Science 238: 81–82
Barus C. 1905. The Progress of physics in the Nineteenth Century. Science 22: 353–369
Bierhalter G. 1993. Helmholtz’s Mechanical Foundation of thermodynamics. in Cahan D. (ed.) 1993a, pp. 291–333
Boltzmann L. 1872. Weiteren Studien über das Wärmegleichgewicht unter Gasmolekülen. in Boltzmann L. 1909, I. Band, pp. 317–402
Boltzmann L. 1877. Über die Beziehung zwischen dem zweiten Hauptsatze der mechanischen Wärmetheorie und der Wahrscheinlichkeitsrechnung respektive den Sätzen über das Wärmegleichgewicht. in Boltzmann L. 1909, II. Band, pp. 164–223
Boltzmann L. 1909. Wissenschaftlichen Abhandlungen, Barth, Leipzig
Bordoni S. 2012a. Unearthing a Buried Memory: Duhem’s Third Way to thermodynamics. Part 1. Centaurus 54: 124–147
Bordoni S. 2012b. Unearthing a Buried Memory: Duhem’s Third Way to thermodynamics. Part 2. Centaurus 54: 232–249
Born M. 1948. Max Karl Ernst Ludwig Planck. 1858–1947. Obituary Notices of Fellows of the Royal Society 6: 161–188
Brenner A. 1990. Duhem. Science, réalité et apparence, Vrin, Paris
Brenner A. and R.J. Deltete. 2004. Essay Review on Duhem P. 2002, Foundations of Chemistry 6: 203–232
Bridgman P.W. 1961 (1941). The Nature of thermodynamics, Harper & Brothers, New York
Brouzeng P. 1981a. L’oeuvre scientifique de Pierre Duhem et sa contribution au développement de la thermodynamique des phénomènes irreéversibles, vol. 1, These (pour obtenir le grade de Docteur d’Etat ès Sciences), Université de Bordeaux I
Brouzeng P. 1981b. L’oeuvre scientifique de Pierre Duhem et sa contribution au développement de la thermodynamique des phénomènes irreéversibles, vol. 2 (documents annexes), These (pour obtenir le grade de Docteur d’Etat ès Sciences), Université de Bordeaux I
Brouzeng P. 1987. Duhem 1861–1916 – Science et Providence, Belin, Paris
Brown L., M. Riordan and M. Dresden (eds.), pp. 645–684
Buchwald J.Z. 1993. Electrodynamics in context: Object states, laboratory practice, and anti- romanticism. in Cahan D. (ed.) 1993a, pp. 334–373
Cahan D. (ed.) 1993a. Hermann von Helmholtz and the Foundations of Nineteenth-Century, University of California Press, Berkeley, Los Angeles, London
Cahan D. 1993b. Introduction: Helmholtz at the Borders of Science. in Cahan D. (ed.) 1993a, pp. 1–13
Clausius R. 1854. Ueber eine veränderte Form des zweiten Hauptsatzes der mechanischen Wärmetheorie. in Clausius R. 1864, pp. 127–154
Clausius R. 1862. Ueber die Anwendung des Satzes von der Aequivalenz der Verwandlungen auf die innere Arbeit. in Clausius R. 1864, pp. 242–279
Clausius R. 1864. Abhandlungen über die mechanische Wärmelehre, erste Abtheilung, Friedrich Vieweg und Sohn, Braunschweig
Clausius R. 1865. Ueber verschiedene für die Anwendung bequem Formen der Hauptgleichungen der mechanischen Wärmetheorie. in Clausius R. 1867, pp. 1–44
Clausius R. 1867. Abhandlungen über die mechanische Wärmelehre, zweite Abtheilung, Friedrich Vieweg und Sohn, Braunschweig
Darrigol O. 2002. Between Hydrodynamics and Elasticity Theory: The First Five Births of the Navier-Stokes Equation. Archive for History of Exact Sciences 56: 95–150
Darrigol O. 2003. Number and measure: Hermann von Helmholtz at the crossroads of mathematics, physics, and psychology. Studies in History and Philosophy of Science 34: 515–573
Darrigol O. 2010. James MacCullagh’s ether: An optical route to Maxwell’s equations?,. The European Physical Journal H 35: 133–172
Darrigol O. and J. Renn. 2003. La nascita della meccanica statistica. Storia della Scienza, Istituto della Enciclopedia Italiana, chapter xlv, pp. 496–507
Daub E.E. 1970. Entropy and Dissipation. Historical Studies in the Physical Sciences 2: 321–354
Deltete R. 1999. Helm and Boltzmann: Energetics at the Lübeck Naturforscherversammlung. Synthese 119: 45–68
Deltete R. 2000. Helm’s history of energetics: a reading guide. in Helm G. 2000, pp. 4–45
Deltete R.J. 2012. Planck, Ostwald, and the Second Law of thermodynamics. HOPOS 2: 121–146
Dugas R. 1937. La méthode physique au sens de Duhem devant la mécanique des quanta. Revue générale des Sciences pures et appliquées 48: 68–71
Duhem P. 1886. Le potentiel thermodynamique et ses applications à la mécanique chimique et à la théorie des phénomènes électriques, Hermann, Paris
Duhem P. 1891. Sur les équations générales de la Thermodynamique. Annales Scientifiques de l’Ecole Normale Supérieure, 3e série, tome VIII: 231
Duhem P. 1892. Commentaire aux principes de la Thermodynamique – Première partie, Journal de Mathématiques pures et appliquées, 4e série, tome VIII: 269
Duhem P. 1894a. Commentaire aux principes de la Thermodynamique – Troisième partie, Journal de Mathématiques pures et appliquées, 4e série, tome X: 203
Duhem P. 1894b. Sur les déformations permanentes et l’hystérésis. Mémoires présentées par divers savants étrangères et Mémoires couronnées par l’Académie de Belgique, Classe des Sciences, tome LIV: 1894
Duhem P. 1894c. Les théories de l’optique”, Revue des deux mondes 123: 94–125
Duhem P. 1895a. Sur les déformations permanentes et l’hystérésis – Deuxième mémoire: les modifications permanentes du soufre, Mémoires présentées par divers savants étrangères et Mémoires couronnées par l’Académie de Belgique, Classe des Sciences, tome LIV: 1895
Duhem P. 1895b. Sur les déformations permanentes et l’hystérésis – troisième mémoire: Théorie générale des modifications permanentes. Mémoires présentées par divers savants étrangères et Mémoires couronnées par l’Académie de Belgique, Classe des Sciences, tome LIV: 1895
Duhem P. 1896. Théorie thermodynamique de la viscosité, du frottement et des faux équilibres chimiques, Hermann, Paris
Duhem P. 2011, Commentary on the Principles of thermodynamics by Pierre Duhem, (Edited and Translated, with an Introduction by Paul Needham), Springer, Dordrecht, Heidelberg, London, New York
FitzGerald G.F. 1880. On the Electromagnetic Theory of the Reflection and Refraction of Light. Philosophical Transactions of the Royal Society 171: 691–711
Gibbs J.W. 1875-8. On the Equilibrium of Heterogeneous Substances, Transactions of the Connecticut Academy, in The Scientific Papers of J. Willard Gibbs, thermodynamics, Longmans, Green and Company, New York, Vol. I, pp. 55–349
Gibbs J.W. 1889. Rudolf Julius Emanuel Clausius. Proceedings of the American Academy, 16, pp. 458–65; reprinted in Gibbs J.W. 1906 2:261–267
Gibbs J.W. 1906. The Scientific Papers of J. Willard Gibbs, Longmans, Green, and Co., London, New York, and Bombay
Gillispie C.C. (ed.), 1970–80, Dictionary of Scientific Biography, Charles Schreibner’s Sons, New York
Hamilton W.R. 1834. On a General Method in Dynamics; .... Philosophical Transactions of the Royal Society, part II for 1834, pp. 247–308
Hankins T.L. 1980. Sir William Rowan Hamilton, The John Opkins University Press, Baltimore and London
Helm G. 1898. Die Energetik nach ihrer geschichtlichen Entwicklung, Verlag von Veit & Comp., Leipzig; reprinted in Helm G. 1981, Die Energetik nach ihrer geschichtlichen Entwicklung, Arno Press, New York; in Helm G. 2000, The Historical Development of Energetics (Translated, and with an Introductory Essay by R.J. Deltete), Kluwer Academic Publishers. Dordrecht, Boston, London
Helmholtz H. 1882. Die Thermodynamik Chemischer Vorgänge. Sitzungsberichte der Preussischen Akademie der Wissenschaften zu Berlin, (2 Febr. 1882) I: 22–39; in Helmholtz H. 1883, pp. 958–978
Helmholtz H. 1883. Wissenschaftliche Abhandlungen, II Band, Barth, Leipzig
Hertz H. 1894. Die Prinzipien der Mechanik (In neuem Zusammenhange dagerstellt), Barth, Leipzig; English translation in Hertz H. 1956, The Principles of mechanics, Dover, New York
Hoffmann D. 2008. Max Planck: Annalen Papers, Wiley-VCH, Weinheim
Jaki S.L. 1984. Uneasy Genius: the Life and Work of Pierre Duhem, Martinus Nijhoff Publishers, The Hague
Jellet J. and S. Haughton (eds.) 1880. The collected works of James MacCullagh, Hodges, Figgis & Co., Dublin, Longmans, Green & Co., London
Jouguet E. 1908. Lectures de Mécanique, Première partie – la naissance de la Mécanique, Gauthier-Villars, Paris
Jouguet E. 1917. L’œuvre scientifique de Pierre Duhem. in Revue générale des Sciences pures et appliquées, Paris, pp. 40–49
Klein M.J. 1969. Gibbs on Clausius. Historical Studies in the Physical Sciences 1: 127–149
Kragh H. 1993. Between physics and Chemistry: Helmholtz’s Route to a Theory of Chemical thermodynamics. in Cahn D. (ed.) 1993, pp. 403–431
Kragh H. 2008a. Entropic Creation – Religious Context of thermodynamics and Cosmology, Ashgate, Farnham (England)
Kragh H. 2008b. Pierre Duhem, Entropy, and Christian Faith. Physics in Perspective 10: 379–395
Kragh H. and S.J. Weininger. 1996. Sooner Silence than Confusion: The Tortuous Entry of Entropy into Chemistry. Historical Studies in the Physical and Biological Sciences 27: 91–130
Kuhn T.S. 1987. Black-Body Theory and the Quantum Discontinuity 1894-1912 (With a New Afterword), The University of Chicago Press, Chicago & London
Lagrange J.L. 1811. Mécanique analytique, tome premier, Courcier, Paris
Laidler K.J. 1993. The World of Physical Chemistry. Oxford University Press, Oxford, New York, Toronto
Lindsay R.B. 1937. Carl Barus: 1856–1935. Proceedings of the American Academy of Arts and Sciences 71: 484–489
MacCullagh J. 1848 (read 9 Dic. 1839). An essay towards the dynamical theory of crystalline reflexion and refraction. in Jellet J. and Haughton S. 1880 (eds.), part 1, pp. 145–184
Massieu F. 1869a. Sur les Fonctions caractéristiques des divers fluides. Comptes Rendus de l’Académie des Sciences LXIX: 858–862
Massieu F. 1869b. Addition au précédent Mémoire sur les Fonctions caractéristiques”, Comptes Rendus de l’Académie des Sciences LXIX: 1057–1061
Massieu F. 1876. Mémoire sur les Fonctions caractéristiques des divers fluides et sur la théorie des vapeurs. Mémoires des Savants étrangers twentiethII, pp. 1–92
Maxwell J.C. 1860. Illustrations of the Dynamical Theory of Gases; reprinted in Maxwell J.C. 1890 1: 377–409
Maxwell J.C. 1867. On the Dynamical Theory of Gases. Philosophical Transactions London, 157, pp. 49–88; reprinted in Maxwell J.C. 1890 2: 26–78
Maxwell J.C. 1878. Tait’s thermodynamics. Nature, pp. 257–9; reprinted in Maxwell J.C. 1890 2: 660–71
Maxwell J.C. 1890. The Scientific Papers of James Clerk Maxwell, (Niven W.D. ed.), 2 vols, University Press, Cambridge
McCormmach R. and C. Jungnickel. 1986. Intellectual Mastery of Nature, 2 vols., The University of Chicago Press, Chicago, London
Miller D.G. 1967. Pierre Duhem, un oublié. Revue des Questions Scientifiques, 138 (Octobre 1967), pp. 445–70; it was the French translation of Miller D.G. 1966, Ignored Intellect: Pierre Duhem. Physics Today 19: 47–53
Müller I. 2007. A History of Thermo-dynamics. The Doctrine of Energy and Entropy, Dover, New York
Müller I. and W. Weiss. 2012. Thermodynamics of irreversible processes – past and present. The European Physical Journal H 37: 139–236
Needham P. 2011. Introduction; in Duhem P. 2011, pp. v–xi
Norton Wise M. 1982. The Maxwell Literature and the British Dynamical Theory. Historical Studies in the Physical Sciences 13: 175–205
Oettingen A. 1885. Die thermodynamischen Beziehungen antithetisch entwickelt”, Mémoires de l’Académie impériale des Sciences de Saint-Pétersbourg, Tome twentieth XII: 1–70
Oettingen A.J. 1876. Ueber Temperatur und Adiabate. Annalen der Physik und Chemie, Ergänzungsband 7: 83–133
Ostwald W. 1896. Zur Energetik. Annalen der Physik und Chemie 58: 154–167
Planck M. 1879. Über der zweiten Hauptsatz der mechanischen Wärmetheorie, Ackerman, Munich
Planck M. 1880. Gleichgewichtszustände isotroper Körper in verschiedenen Temperaturen, Theodore Ackermann, München
Planck M. 1882. Verdampfen, Schmelzen und Sublimieren. Annalen der Physik und Chemie 15: 446–475
Planck M. 1889. A. von Oettingen. Die thermodynamischen Beziehungen antithetisch entwickelt. Annalen der Physik (Beiblätter), twentiethIII, pp. 466–9; reprinted in Hoffmann D. 2008, pp. 838–341
Planck M. 1893. Grundriss der Allgemeinen Thermochemie, Eduard Trewendt, Breslau
Planck M. 1897. Vorlesungen über Thermodynamik, Veit & Comp., Leipzig
Planck M. 1905. Vorlesungen über Thermodynamik, (zweite, verbesserte Auflage), Veit & Comp., Leipzig
Rankine W.J.M. 1851. On the Centrifugal Theory of Elasticity and its Connection with the Theory of Heat, in Rankine W.J.M. 1881, pp. 49–66.
Rankine W.J.M. 1853a. On the Mechanical Action of Heat, Section VI, in Rankine W.J.M. 1881, pp. 310–338
Rankine W.J.M. 1853b. On the General Law of the Transformation of Energy. in Rankine W.J.M. 1881, pp. 203–208
Rankine W.J.M. 1855. Outlines of the Science of Energetics”. in Rankine W.J.M. 1881, pp. 209–228
Rankine W.J.M. 1881. Miscellaneous Scientific Papers. Charles Griffin and Company, London
Serrin J. (ed.) 1986. New Perspectives in Thermodynamics. Springer-Verlag, Berlin, Heidelberg, New York, Tokyo
Servos J.W. 1990. Physical Chemistry from Ostwald to Pauling, Princeton University Press, Princeton
Stokes G.G. 1883. Mathematical and Physical Papers, vol. II, University Press, Cambridge
Tait P.G. 1877. Sketch of thermodynamics, second edition, David Douglas, Edinburgh
Tait P.G. 1880. Memoir. in Rankine W.J.M. 1881, pp. xix–xxxvi
Thomson J.J. 1888. Applications of Dynamics to physics and Chemistry, Macmillan and Co., London and New York
Timoshenko S.P. 1983. History of Strength of Materials, Dover, New York
Truesdell C. 1984. Rational thermodynamics. Springer-Verlag, New York, Berlin, Heidelberg, Tokyo
Truesdell C. 1986. What Did Gibbs and Carathéodory Leave Us About Thermodynamics?. in Serrin J. (ed.) 1986, pp. 101–124
Ugaglia M. 2004. Modelli idrostatici del moto da Aristotele a Galileo, Lateran University Press, Roma
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bordoni, S. Routes towards an abstract thermodynamics in the late nineteenth century. EPJ H 38, 617–660 (2013). https://doi.org/10.1140/epjh/e2013-40028-7
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjh/e2013-40028-7