Chemical Engineering Thermodynamics
For a multicomponent system, the term chemical potential is equivalent to the

Partial molar free energy
Molal concentration difference
Molar free energy
Molar free energy change

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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.

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

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