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

Ax₁
Ax₁²
A . x₂²
Ax₂

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Chemical Engineering Thermodynamics
It is desired to bring about a certain change in the state of a system by performing work on the system under adiabatic conditions.

The amount of work needed is independent of path
More information is needed to conclude anything about the path dependence or otherwise of the work needed
Work alone can not bring out such a change of state
The amount of work needed is path dependent

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