Existence of Caloric Equations of State in Thermodynamics

Abstract

Using the principle of equipresence, we treat the thermodynamics of continua sufficiently close to equilibrium so that the basic independent variables in constitutive equations can be taken to be the temperature, the temperature gradient, the deformation gradient (or the ``strain''), and the velocity gradient (or the ``rate of strain''). We derive a set of necessary and sufficient conditions on constitutive equations for the validity of the Clausius—Duhem inequality (i.e., the second law) in such continua. Most of these conditions are familiar; among our necessary conditions, however, is one which guarantees the existence of the caloric equation of state (or, equivalently, of the ``Gibbs relation'' for the entropy differential), and which has not previously been thought justifiable by purely macroscopic arguments. Specializing our general results to fluids, we discuss the thermodynamic restrictions on various possible generalizations and modifications of the classical theory of linearly viscous fluids with linear heat conduction.