Thermodynamic Potentials and the Laws

For the pressure-volume work done by a gas expanding reversibly (through a succession of equilibrium states)  

PHASE EQUILIBRIA, PHASE DIAGRAMS. AND PHASE MODELING 

All of the quantities introduced thus far, U, W, q, P, and V, ate thermodynamic state variables. 

The other state variable, entropy, S, is actually defined by the second law of thermodynamics  

The second law of thermodynamics then states that the entropy of an isolated system (a system with constant U and constant V) increases (d5 0) for a spontaneous processes or stays constant (d5 = 0) at equilibrium. In Eq. 11.9, no internal processes ate considered S is normally regarded as an external variable even though it is not possible to control its value externally without knowledge of the properties of the system). If internal processes are considered, an internal variable must be included, namely, /a, the chemical potential (to be discussed shortly). 

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