Chemical Engineering Thermodynamics
The molar excess Gibbs free energy, gE, for a binary liquid mixture at T and P is given by, (gE/RT) = A . x₁. x₂, where A is a constant. The corresponding equation for ln y₁, where y₁ is the activity co-efficient of component 1, is

A . x₂²
Ax₁²
Ax₂
Ax₁

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

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