Chemical Engineering Thermodynamics
The necessary and sufficient condition for equilibrium between two phases is

The concentration of each component should be same in the two phases
The pressure should be same in the two phases
The temperature of each phase should be same
The chemical potential of each component should be same in the two phases

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Chemical Engineering Thermodynamics
On a P-V diagram of an ideal gas, suppose a reversible adiabatic line intersects a reversible isothermal line at point A. Then at a point A, the slope of the reversible adiabatic line (∂P/∂V)S and the slope of the reversible isothermal line (∂P/∂V)T are related as (where, y = Cp/Cv) )

(∂P/∂V)S = (∂P/∂V)T
(∂P/∂V)S = 1/y(∂P/∂V)T
(∂P/∂V)S = [(∂P/∂V)T]Y
(∂P/∂V)S = y(∂P/∂V)T

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