General information on equations of state on the basis of the thermostatic theory of stability

Abstract

Based on considerations similar to those used byGyarmati concerning the entropy function, it is shown that, in a special case, a sufficient condition for “stability in the large” of the homogeneous equilibrium state is conditiond 4 u>0 together with the condition of “local stability”d 2 u>0 (where the internal energy function is denoted byu). The concave behaviour of thermostatic coefficients of stability $$\lambda _t \equiv (\partial \Gamma _t /\partial a_t )\Gamma _1 ,...,\Gamma _{t - 1, } a_{t + 1} ,...,a_n $$ as function ofa t follows from the first condition, here the intensive quantity characteristic of interactioni is denoted byΓ i , while the corresponding molar extensive quantity is denoted bya i. On the basis of this fact and ofSemenchenko’s Theorem of States of Maximal Stability one can deduce inequalities from which conditions are obtained for the sign of the first and second derivatives of the functions describing the temperature dependence of the isobaric heat capacity and of the pressure dependence of the isothermal compressibility. Relations can be obtained for the dependence on the mole fraction of a component 1 of the component’s chemical potential μ1 in binary ideal and regular mixtures. All these relations are in accordance with empirical data available, and they can find applications in practice.