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A comparison and criticism of two axiomatic systems for classical thermodynamics Erickson, Arvon Donald

Abstract

This thesis is a comparison and criticism of two approaches to classical thermodynamics, that due to P. Rastall in the "Journal of Mathematical Physics", Volume 11, Number 10, October 1970, page 2955, and that due to H.A. Buchdahl and W. Greve in "Zeitschrift für Physik" 168, 1962, page 316 and page 386. Rastall's approach is somewhat more general and appeals because of his generally careful attention to the explicit, orderly statement of the assumptions and rigorous proofs based only on these assumptions. However, his approach is significantly improved by substituting the main assumption of the Buchdahl-Greve paper for two of his assumptions. The Buchdahl-Greve assumption is fundamentally appealing and as well as leading to a more natural proof of a crucial theorem, it also allows a straightforward proof for the continuity of the entropy function, which Rastall assumes ad hoc. The proof given in the Buchdahl-Greve paper for the continuity of the entropy function is shown to be circular but a correct proof based on the Buchdahl-Greve assumption is possible and one is given in an appendix. Suggestions are also made concerning how one might improve this combined Buchdahl-Rastall approach.

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