On Thermodynamics and the Nature of the Second Law. I. Single Phase Continua.

The contents of this paper represent a new approach to continuum thermodynamics and are chiefly concerned with a a procedure for obtaining restrictions on constitutive equations, b an appropriate mathematical statement of the second law and c the nature of restrictions placed by the latter on thermo-mechanical behavior of single phase continua. The point of departure is the introduction of a balance of calory or entropy and the use of the energy equation as an identity for all motions and all temperature distributions. This is in contrast to the approach adopted in most of the current literature on continuum thermodynamics based on the use of the clausius-Duhem inequality. In order to gain some insight into the nature of the procedure, a study was made of an elastic material, which includes that of an ideal fluid as a special case, prior to the consideration of the second law. The existing statements of the second law or thermodynamic irreversibility are discussed along with a postulation of an inequality which reflects the fact that not all heat supplied to the body can be transformed into useful mechanical work. Since the latter inequality is stated for spatially homogeneous temperature fields, the restriction on the heat conduction vector is considered separately and is confined here to equilibrium cases in which heat flow in steady. The remainder of the paper deals mainly with the nature of thermodynamic restrictions on the thermo-mechanical response of a variety of deformable media, including elastic-plastic materials and simple materials with fading memory.