Equilibrium thermodynamic properties of two-component and two phase mixtures

Abstract

We develop a general thermodynamic framework for determining the equilibrium thermodynamic and thermophysical properties of systems composed of two constituents or two phases. The formulation does not require the introduction of a specific equation of state for the constituent phases or for the mixture and can therefore be applied using either analytical equations of state, tabulated thermodynamic data, or experimental measurements of the constituent properties. Two classes of systems are considered. The first consists of two immiscible constituents in complete thermodynamic equilibrium, with no mass transfer between them. The second consists of two phases of the same substance in equilibrium, with mass exchange between the phases, as occurs in liquid--vapor systems and blackoil models. For both classes of systems, we derive expressions for the mixture compressibility, equilibrium speed of sound, thermal expansion coefficients, heat capacities, and Gr\"uneisen coefficient in terms of the corresponding properties of the individual constituents or phases. Particular attention is given to two-phase equilibrium, for which pressure and temperature are constrained by the coexistence relation and cannot be treated as independent variables. The resulting expressions provide a consistent alternative to simple arithmetic averaging of thermophysical properties and can be applied directly to experimentally measured or tabulated phase properties. The framework is illustrated for ideal-gas mixtures and for liquid--vapor equilibrium, including asymptotic limits relevant to cavitating flows.