Proof that the Clausius-Serrin inequality is equivalent to a strengthened "Kelvin's law"
Man, Chi-Sing
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti, Tome 68 (1980), p. 399-409 / Harvested from Biblioteca Digitale Italiana di Matematica
Access to full text
Full (PDF)
Full (DjVu)

A partire da una formulazione precisa della «disuguaglianza di Clausius» per i processi ciclici, in termini della funzione di accumulazione di Serrin, viene data una dimostrazione matematica esatta del fatto che la disuguaglianza di Clausius correttamente formulata (ovvero la disuguaglianza di Clausius-Serrin) è equivalente a una versione rafforzata della «legge di Kelvin». L’introduzione di un gas ideale con calore specifico costante fornisce alla dimostrazione qui presentata una notevole semplicità ed eleganza. Lo strumento matematico usato non richiede più della convergenza uniforme e delle proprietà elementari dell’integrale di Riemann-Stieltjes.

Publié le : 1980-12-01
@article{RLINA_1980_8_69_6_399_0,
     author = {Chi-Sing Man},
     title = {Proof that the Clausius-Serrin inequality is equivalent to a strengthened "Kelvin's law"},
     journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti},
     volume = {68},
     year = {1980},
     pages = {399-409},
     mrnumber = {0690307},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RLINA_1980_8_69_6_399_0}
}

Man, Chi-Sing. Proof that the Clausius-Serrin inequality is equivalent to a strengthened "Kelvin's law". Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti, Tome 68 (1980) pp. 399-409. http://gdmltest.u-ga.fr/item/RLINA_1980_8_69_6_399_0/

[1] Serrin, J. (1978) - The concepts of thermodynamics, pp. 411—451 of G.M. De La Penha and L.A. Medeiros (eds.), Contemporary Developments in Continuum Mechanics and Partial Differential Equations, Amsterdam etc., North-Holland Publishing Company. | Zbl 0433.73003

[2] Serrin, J. (1979) - Conceptual analysis of the classical second laws of thermodynamics, «Arch. Rational Mech. Anal.», 70, 355-371.

[3] Man, C.-S. - Thermodynamics based on a work inequality, forthcoming in «Arch. Rational Mech. Anal.».

[4] Man, C.-S. - A generalized Kelvin's law for systems with approximate restorability, in preparation.

[5] Clausius, R. (1865) - Über verschiedene für die Anwendung bequeme Formen der Hauptgleichungen der mechanischen Wärmetheorie, «Annalen der Physik und Chemie» (2) 125, 353-400. Transl. R.B. Lindsay, On different forms of the fundamental equations of the mechanical theory of heat and their convenience for application, pp. 162-193 of The Second Law of Thermodynamics, ed. J. Kestin, Stroudsburg (Pa.), Dowden, Hutchinson and Ross, 1976.

[6] Serrin, J. (1975) - Foundations of Classical Thermodynamics, Lecture Notes, Department of Mathematics, University of Chicago.

[7] Man, C.-S. - Proof of the Clausius-Serrin inequalities under the thermometric axiom, in preparation.

[8] Thomson, W. (later Lord Kelvin) (1850-1853) - On the dynamical theory of heat, with numerical results deduced from Mr. Joule's equivalent of a thermal unit, and Mr Regnault's observations on steam, Parts I-III, «Transactions of the Royal Society of Edinburgh», 20, Part 2, 261-268, 289-298.

[9] Pippard, A.B. (1964) - The Elements of Classical Thermodynamics, Cambridge etc., Cambridge University Press.

[10] Truesdell, C. and Bharatha, S. (1977) - The Concepts and Logic of Classical Thermodynamics as a Theory of Heat Engines, Rigorously Constructed upon the Foundation Laid by S. Carnot and F. Reech, New York etc., Springer-Verlag. | Zbl 0379.73001

[11] Truesdell, C. and Toupin, R. (1960) - The classical field theories, pp. 226-793 of «Encyclopedia of Physics», Volume 3, Part 1, ed. S. Flügge, Berlin etc., Springer-Verlag.