CHAP. 3: FUNDAMENTALS OF THERMODYNAMICS [CONTENTS] 84
By comparing (3.33) and (3.37) we obtain
(
∂U
∂S)V=T ,
(
∂U
∂V)S=−p. (3.38)In a similar way we obtain forH=f(S, p),F=f(T, V),G=f(T, p)
(
∂H
∂S)p= T ,
(
∂H
∂p)S= V , (3.39)
(
∂F
∂T)V= −S ,
(
∂F
∂V)T= −p , (3.40)
(
∂G
∂T)p= −S ,
(
∂G
∂p)T= V. (3.41)
3.4.3 Maxwell relations
By applying the equalities of mixed derivatives (3.26) to the Gibbs equations (3.33) through
(3.36), i.e. to the total differentials of the functionsU,H,F,G, we obtain the so-called Maxwell
relations
(
∂T
∂V
)S= −
(
∂p
∂S)V, (3.42)
(
∂T
∂p)S=
(
∂V
∂S)p, (3.43)
(
∂p
∂T)V=
(
∂S
∂V)T, (3.44)
(
∂V
∂T)p= −
(
∂S
∂p)T. (3.45)
Maxwell relations, in particular (3.44) and (3.45), rank among the major thermodynamic rela-
tions. They are used to derive many other equations.