Abstract: Elementary thermodynamics has been much neglected as an object of inquiry both by mathematicians and engineers. The basic concepts of heat and hotness can, however, be given a precise structure consistent with the foundations of classical continuum mechanics, and it is possible to develop a rigorous notion of absolute temperature and a rigorous discussion of the Clausius inequality. In this view entropy is a derived concept, and the existence of internal energy and entropy must be established for any given class of materials. To complete the fundamental notions of thermodynamics one must in addition consider the problem of stability of rest states, and the question of internally constrained materials. To illustrate the problems involved in the foundations of the thermodynamics we give examples of a material obeying the Clausius inequality which does not have a unique entropy function, and of an unstable material satisfying the Clausius-Duhem inequality which is cooled by the addition of heat. We also examine the thermodynamic structure of an internally constrained material whose density is a function of temperature, and finally show how a heat-conducting compressible Navier-Stokes fluid can be introduced as a thermodynamic entity without using either the notion of internal energy or of entropy.
Publication Year: 1978
Publication Date: 1978-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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Cited By Count: 29
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