Advertisement

On The Axiomatic Foundations of Temperature

  • M. Pitteri

Abstract

When the pioneers of thermodynamics deal with temperature, they presume the reader to have an intuitive idea of what temperature is and to be already familiar with the body of common experience with gases upon which much of classical thermometry is based1. From that experience we extract the concept of an ideal gas, that is, of a gas whose pressurep, volumeV and temperatureθ obey the thermal equation of state
$$pV = R\theta ,{\text{ R = const}}{\text{.,}}$$
(G6.1)
for all positivep, V andθ. Real gases, air for instance, are good approximations to an ideal gas at temperatures which are not too low, and the best way to measure temperature in a wide range of circumstances is to use the air thermometer. The concept of ideal gas is important in classical thermodynamics and the air thermometer is regarded as giving the ideal-gas temperature most nearly. TRUESDELL [28, §§11B, 11H] discusses this matter and points out that KELVIN [12], who was perhaps the first to conceive that thermometers other than the air thermometer could be used to formulate thermodynamics, “seems to have perceived that the basic ideas of the theory of heat should be independent of the choice of thermometer. He seems also to have wished to excise the concept of ideal- gas temperature”. The latter wish was expressed later by MACH [15], who introduced the concept ofhotness as primitive in thermodynamics.

Keywords

Thermal Equilibrium Sensory Experience Thermodynamic System Mechanical Concept Classical Thermodynamic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    J. B. Boyling, “An axiomatic approach to classical thermodynamics”,Proceedings of the Royal Society(London) A 329 (1972): 35 – 70.MathSciNetGoogle Scholar
  2. [2]
    A. Bressan, “Metodo di assiomatizzazione in senso stretto della meccanica classica. Applicazione di esso ad alcuni problemi di assiomatizzazione non ancora completamente risolti”Rendiconti del Seminario Matematico, Uni- versita di Padova 32 (1962): 55–212.MATHGoogle Scholar
  3. [3]
    A. Bressan, “On the usefulness of modal logic in axiomatization of physics”, Proceedings of the 1972Biennial Meeting of the Philosophy of Science Association, edited by K. S. Shaffner & R. S. Cohen, Dordrecht, Reidel, 1974.Google Scholar
  4. [4]
    A. Bressan, “On physical possibility” and “Supplement 1979”,Italian Studies in Philosophy of Science, edited by M. L. DALLA CHIARA, Dordrecht & Boston, Reidel, 1980.Google Scholar
  5. [5]
    A. Bressan, “Substantial uses of physical possibility in principles or definitions belonging to well-known classical theories of continuous media”,Atti Accademia Nazionale Lincei, Scienze Fis., Mat. Nat. (8) 17 (1984): 137 – 162.MathSciNetMATHGoogle Scholar
  6. [6]
    A. Bressan, A General Interpreted Modal Calculus, New Haven, Yale University Press, 1972.MATHGoogle Scholar
  7. [7]
    C. Carathèodory, “Untersuchungen über die Grundlagen der Thermodynamik”,Mathematische Annalen67 (1909): 355 – 386.MathSciNetCrossRefGoogle Scholar
  8. [8]
    S. Carnot,Réflexions sur la Puissance Motrice du Feu et sur les Machines Propres a developper cette Puissance, Paris, Bachelier, 1824 =Annales scientifiques de l’Ecole Normale Supérieure(2) 1 (1872): 393 – 457.MathSciNetGoogle Scholar
  9. [9]
    G. G. Emch,Algebraic Methods in Statistical Mechanics and Quantum Field Theory, New Yorketc, Wiley-Interscience, 1972.Google Scholar
  10. [10]
    M. Feinberg, R. Lavine, “Thermodynamics based on the Hahn-Banach theorem: the Clausius inequality”,Archive for Rational Mechanics and Analysis82 (1983): 203 – 293.MathSciNetADSMATHCrossRefGoogle Scholar
  11. [11]
    J. W. Gibbs, “Graphical methods in the thermodynamics of fluids”, inCollected Works, Volume 1, New Haven, Yale University Press, 1928, variously reprinted.Google Scholar
  12. [12]
    W. Thomson (Lord Kelvin), “On the absolute thermometric scale founded on Carnot’s theory of the motive power of heat; and calculated from Reg- nault’s observations”,Proceedings of the Cambridge Philosophical Society1 (1843/1868), no. 5:66 – 71.Google Scholar
  13. [13]
    H. J. Kreuzer,Non-equilibrium Thermodynamics and its Statistical Foundations, Oxford, Clarendon Press, 1981.Google Scholar
  14. [14]
    E. Mach,Die Mechanik in ihrer Entwickelung. Historisch-kritisch dargestellt, Leipzig, F. A. Brockhaus, 1883.Google Scholar
  15. [15]
    E. Mach,Die Prinzipien der Wärmelehre, Historisch-kritisch Entwickelt, Leipzig, F. A. Brockhaus, 1896.Google Scholar
  16. [16]
    C.-S. Man,Critical Studies in Some Thermodynamic Problems, M. Phil, thesis in mathematics, University of Hong Kong, 1976.Google Scholar
  17. [17]
    A. Messiah,Quantum Mechanics, Volume 1, Amsterdam, North-Holland, 1961.Google Scholar
  18. [18]
    P. PainlevÉ,Les Axiomes de la Mécanique, Paris, Gauthier-Villars, 1922.Google Scholar
  19. [19]
    [19]AB Pippard,The Elements of Classical Thermodynamics, Cambridgeetc, Cambridge University Press, 1964.Google Scholar
  20. [20]
    M. Pitteri, “Classical thermodynamics of homogeneous systems based upon Carnot’s General Axiom”,Archive for Rational Mechanics and Analysis80 (1982):333–385.MathSciNetADSMATHCrossRefGoogle Scholar
  21. [21]
    M. Pitteri, “On a definition of temperature based upon mechanical concepts alone”, to appear as a memoir inAtti Accademia Nazionale Lincei.Google Scholar
  22. [22]
    J. B. Serrin,Foundations of Classical Thermodynamics, Lecture Notes, Department of Mathematics, University of Chicago, 1975.Google Scholar
  23. [23]
    J. B. Serrin, “The concepts of thermodynamics”, inContemporary Developments in Continuum Mechanics and Partial Differential Equations, edited by G. M. De La Penha & L. A. Medeiros, Amsterdam, North-Holland, 1978.Google Scholar
  24. [24]
    J. B. Serrin,Mathematical Foundations of Thermodynamics, notes of lectures delivered at the University of Naples, Summer, 1980.Google Scholar
  25. [25]
    C. Truesdell & S. Bharatha,The Concepts and Logic of Classical Thermo-dynamics as a Theory of Heat Engines, Rigorously Constructed upon the Foundation Laid by S. Carnot and F. Reech, New Yorketc, Springer-Verlag, 1977.Google Scholar
  26. [26]
    C. Truesdell, “Some challenges offered to analysis by rational thermo- mechanics”, inContemporary Developments in Continuum Mechanics and Partial Differential Equations, edited by G. M. De La Penha & L. A. Medeiros, Amsterdam, North-Holland, 1978.Google Scholar
  27. [27]
    C. Truesdell, “Absolute temperatures as a consequence of Carnot’s General Axiom”,Archive for History of Exact Sciences20 (1979): 357–380.MathSciNetCrossRefGoogle Scholar
  28. [28]
    C. Truesdell,The Tragicomical History of Thermodynamics, 1822–1854, New York etc., Springer-Verlag, 1980.MATHGoogle Scholar
  29. [29]
    G. Whaples, “Carathéodory’s temperature equations”, Journal of Rational Mechanics and Analysis1 (1952): 301 – 307.MathSciNetMATHGoogle Scholar
  30. [30]
    MW Zemanski,Heat and Thermodynamics, New Yorketc, McGraw-Hill, 1968.Google Scholar

Copyright information

© Springer-Verlag New York Inc 1984

Authors and Affiliations

  • M. Pitteri

There are no affiliations available

Personalised recommendations