Bordoni New Preprint MPIWG 2013

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Bordoni New Preprint MPIWG 2013
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  MAX-PLANCK-INSTITUT FÜR WISSENSCHAFTSGESCHICHTE Max Planck Institute for the History of Science 2013 PREPRINT 443 Stefano Bordoni Looking for a Rational Thermodynamics in the late XIX century      Looking for a Rational Thermodynamics in the late XIX century *   Stefano Bordoni ABSTRACT. From Rudolf Clausius’ classical version of Thermodynamics two different traditions of research really emerged. If James C. Maxwell and Ludwig Boltzmann pursued the integration of thermodynamics with the kinetic theory of gases, others relied on a macroscopic and more abstract approach, which set aside specific mechanical models. Starting from 1869, the French engineer François Massieu was able to demonstrate that thermodynamics could be based on two “characteristic functions” or potentials. Josiah W. Gibbs and Hermann von Helmholtz exploited the structural analogy between Mechanics and Thermodynamics: from a mathematical point of view, Helmholtz’s “free energy” was nothing else but Gibb’s first potential. In the meantime, in 1880, the young German physicist Max Planck aimed at filling the gap between thermodynamics and the theory of elasticity. Five years later Arthur von Oettingen put forward a formal theory, where mechanical work and fluxes of heat represented the starting point of a dual mathematical structure. In 1891 Pierre Duhem generalized the concept of “virtual work” under the action of “external actions” by taking into account both mechanical and thermal actions. Between 1892 and 1894 his design of a generalized Mechanics based on thermodynamics was further developed: ordinary mechanics was looked upon as a specific instance of a more general science. KEY WORDS: Mechanics, Thermodynamics, Potentials, Work, Heat, Energy, Lagrange’s equations, General equations.  Introduction 1. Mechanical models 2. The roots of a formal analogy 3. A family of Potentials 4. Physical and mathematical symmetries 5. The general equations of Thermodynamics Concluding remarks *  I should like to thank the Max-Planck-Institut für Wissenschaftsgeschichte (Berlin), and in particular Jürgen Renn, Massimiliano Badino and Christoph Lehner, for having given me the opportunity to discuss some contents of the present paper. Parts of sections 3 and 5 can also be found in my previous Preprint 428, although within a different historiographical framework.
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