
134 The Principles of Thermodynamics
Clearly these are the proper equations of state in the sense of Callen; they relate the
intensive variables (T,P) of the first class to only the intensive variablesU
m
,V
m
of the
second class. The usual equations for ideal gases are easily recovered from them.
We see explicitly that there are only two degrees of freedom. It remains to evaluate
the third first class intensive variable
μ
and show that it is not really independent.
Evaluating the relevant partial derivative explicitly yields
μ
=
∂
U
∂
n
S,V
= U
m
(S
m
,V
m
)+
U
m
(S
m
,V
m
)
C
−
S
m
U
m
(S
m
,V
m
)
CR
= U
m
+PV
m
−TS
m
= G
m
(6.48)
Now we discuss the somewhat more involved example of the van der ...