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On the definition of the absolute temperature—a reconciliation of the classical method with that of Carathéodory

Published online by Cambridge University Press:  14 November 2011

Johann Walter
Johann Walter
Affiliation:
Institut für Mathematik der R. W. T. H. Aachen
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Extract

In this paper a combination is given of the two methods mentioned in the title with the aim of optimising the definition of the absolute temperature with respect to physical transparency and mathematical simplicity. The mathematical tools used are the elements of vector analysis, i.e. “usual” mathematics (“normale” Mathematik) in the sense of Born [1, p. 162, cf. also 22, p. 579].

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 82 , Issue 1-2 , 1978 , pp. 87 - 94
Copyright
Copyright © Royal Society of Edinburgh 1978

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References

1Born, M.. Ausgewählte Abhandlungen 1 (Göttingen: Vandenhoeck & Ruprecht, 1963).Google Scholar
2Boyling, J. B.. An axiomatic approach to classical thermodynamics. Proc. Roy. Soc. London Ser. A 329 (1973), 35–70.Google Scholar
3Bryan, G. H.. Allgemeine Grundlagen der Thermodynamik (abgeschlossen im Januar 1903). Enzyklopädie der mathematischen Wissenschaften, V3 (Leipzig: Teubner 1903-1921).Google Scholar
4Carathéodory, C.. Gesammelte mathematische Schriften 2 (München: C. H. Beck, 1955).Google Scholar
5Cooper, J. L. B.. The foundations of thermodynamics. J. Math. Anal. Appl. 17 (1967), 172–193.CrossRefGoogle Scholar
6Eisenschitz, R.. The principle of Carathéodory. Sci. Prog. 43 (1955), 246–260.Google Scholar
7Finkelstein, R. J.. Thermodynamics and statistical physics (San Francisco: W. H. Freeman, 1969).Google Scholar
8Guggenheim, E. A.. Thermodynamics, classical and statistical. Handbuch der Physik, III/2 (Berlin: Springer, 1959).Google Scholar
9Helmholtz, H. von. Studien zur Statik monozyklischer Systeme. J. Reine Angewandte Math. 97 (1884), 111–140.CrossRefGoogle Scholar
10Jauch, J. M.. On a new foundation of equilibrium thermodynamics. Found. Phys. 2 (1972), 327–332.CrossRefGoogle Scholar
11Jauch, J. M.. Analytical thermodynamics. I Thermostatics - General theory. Found. Phys. 5 (1975), 111–132.CrossRefGoogle Scholar
12Kestin, J.. A course in thermodynamics (Waltham, Mass.: Blaisdell, 1966).Google Scholar
13Landé, A.. Axiomatische Begründung der Thermodynamik durch Carathéodory. Handbuch der Physik IX 281–300 (Berlin: Springer, 1926).Google Scholar
14Landsberg, P. T.. Main ideas in the axiomatics of thermodynamics. Pure Appl. Chem. 22 (1970), 215–227.CrossRefGoogle Scholar
15Päsler, M.. Phaenomenologische Thermodynamik (Berlin: Walter de Gruyter, 1975).CrossRefGoogle Scholar
16Planck, M.. Physikalische Abhandlungen und Vorträge 2 (Braunschweig: Vieweg, 1958).Google Scholar
17Sears, F. W.. A simplified simplification of Carathéodory's treatment of thermodynamics. Amer. J. Phys. 31 (1963), 747–752.CrossRefGoogle Scholar
18Serrin, J.. Foundations of classical thermodynamics. Chicago Univ. Dept. Math. Lecture Notes (1975).Google Scholar
19Sommerfeld, A.. Vorlesung über theoretische Physik V: Thermodynamik und Statistik 1st edn (Wiesbaden: Dieterich, 1952).Google Scholar
20Stepanov, W. W.. Lehrbuch der Differentialgleichungen (Berlin: VEB Deutscher Verlag der Wissenschaften, 1956).Google Scholar