Chemical Engineering Thermodynamics
The Maxwell relation derived from the differential expression for the Helmholtz free energy (dA) is

(∂T/∂V)S = -(∂P/∂S)V
(∂S/∂P)T = -(∂V/∂T)P
(∂V/∂S)P = (∂T/∂P)S
(∂S/∂V)T = (∂P/∂T)V

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Chemical Engineering Thermodynamics
A reasonably general expression for vapour-liquid phase equilibrium at low to moderate pressure is Φi yi P = Yi xi fi° where, Φ is a vapor fugacity component, Yi is the liquid activity co-efficient and fi° is the fugacity of the pure component i. the Ki value (Yi = Ki xi) is therefore, in general a function of

Temperature and pressure only
Temperature only
Temperature, pressure and liquid composition xi only
Temperature, pressure, liquid composition xi and vapour composition yi

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