Entropy of systems with internal variables

Abstract

Two entropy functions are currently in use: the thermostatic entropy, defined by Carathéodory's theory, and the thermodynamic entropy, defined by the theory of irreversible processes. Both entropy concepts are confined to systems without internal variables, and both can be shown to be equal by substituting the respective balance of internal energy to which they are related by the integrating factor, 1/Θ. When irreversible internal phenomena are present, represented by internal coordinates and their conjugate affinities, they become part of the entropy production, but not of the energy balance, and the two entropies are no longer equal. It has been shown in the literature that by multiplication by a second integrating factor, an extended entropy function for systems with internal variables can be derived. It is the purpose of this paper to present a method for the determination of this integrating factor. Under certain conditions, the latter may be unity; such is shown to be the case with the Gibbs equation for gas mixtures.