2-37 Show that the magnetic moment, M, of a paramagnetic material is a state function by showing that dM is an exact differential.

In general if a differential , dz is exact if

Equation of state is given by:

So dM is given by

dM will be exact if

So first find and

and

Now we take the mixed 2^nd partials and

and

Obviously

dM is an exact differential and hence M is a state function.