Thermodynamic relations for two phases containing two components in equilibrium under generalized stress

Abstract

The application of thermodynamics to cases of other than hydrostatic pressure is important in connection with the swelling and flow and fracture of solids under generalized stress. In the present paper the methods of Gibbs are applied to the case of two phases containing the same two component substances in equilibrium with each other. The problem is first considered in its most general form, each phase being under generalized stress and each containing each component. The more particular problem in which one of the components is absent from one of the phases is then considered, and the particular case in which one of the phases is fluid and, therefore, able to withstand only hydrostatic pressure, is dealt with in some detail. The cases of a two-component fluid phase in equilibrium with a one-component solid phase and a one-component fluid phase in equilibrium with a two-component solid phase are treated together. These cases correspond respectively to what are often called solution and swelling, although there is no logical reason for this nomenclature. The derivatives of pressure on the fluid phase for changes of temperature and changes of each of the components of generalized stress on the solid phase are given. When suitably interpreted, the same formulae apply to both solution and swelling. Formulae for entropy changes with stress and temperature are also given, and the use of other independent variables such as strain, force, and displacement instead of stress is discussed.