238 SOLUTIONS
Therefore,
Equating (S.4.104.3) and (S.4.104.11), we can find the chemical potential
for an intrinsic semiconductor:
If then the chemical potential is in the middle of the band gap:
4.105 Adiabatic Demagnetization (Maryland)
We now want to produce a Maxwell relation whose independent variables
are T and H. Write an equation for the free energy F:
a) We start with the usual relation and substitute
MdH for P dV, since the work done in this problem is magnetic rather
than mechanical. So