Thermodynamics, Statistical Physics, and Quantum Mechanics

THERMODYNAMICS AND STATISTICAL PHYSICS 153

where we used

So, we obtain

Substituting into (S.4.50.2) yields

b,c) We cannot determine the temperature dependence of but we
can find as follows:

Similarly,

where Fisthe Helmholtz free energy, and we used

From (S.4.50.4) and the equation of state, we have

and from (S.4.50.5),