My thermodynamics book suggests that the Maxwell Relations must be used when dealing with a single-phase system. The equations come right after the section Mathematical Relations for the Homogeneous Phase, in which the following is stated:
In the following sections we'll develop many expressions to calculate differences of properties in a single phase, compressible and homogeneous (applicable to the vapor, liquid and solid phases).
Perhaps that is only to make a clear distinction between them and the Clapeyron equation, introduced right before. In any case, I don't agree with this view. To me, since the equations come from definitions of thermodynamic potentials, which are valid at any state, they must be valid anywhere.
I'll give a simple example of validity. There's this Maxwell Relation, of which I take the inverse: $$-\left(\partial s \over \partial p \right)_T = \left(\partial v \over \partial T \right)_p \Rightarrow -\left(\partial p \over \partial s \right)_T = \left(\partial T \over \partial v \right)_p$$
We know that, in saturation, $p = p(T)$ and $T = T(p)$. Therefore, both sides of the last equation are zero. Therefore, this Maxwell Relation holds in two-phase (saturation).
I know that this one example of validity does not mean that all relations are valid in saturation. But are they?
