The basic “tools” are the set of fundamental differentials, Eqs. (154B), (161)–(163),
and the set of the Maxwell relations, Eqs. (167)–(170). The former equations are
written in the following forms by considering, for instance, U as a function of any
pair of independent variables x and y:
@U
@x
y
¼ T
@S
@x
y
À p
@V
@x
y
ð171Þ
The rest of the three equations can be similarly written as
@H
@x
y
¼ T
@S
@x
y
þ V
@p
@x
y
ð172Þ
@A H
@x
y
¼ ÀS
@T
@x
y
À p
@V
@x
y
ð173Þ
@G
@x
y
¼ ÀS
@T
@x
y
þ V
@p
@x
y
ð174Þ
Equations (171)–(174) and Eqs. (167)–(170) enable the determination of thermodynamic properties as shown in the following.
9.5.2 Examples
Before the demonstration by examples, recall the following definitions of molar
heat capacity and other derivative forms of properties:
c p ¼
1
N
@H
@T
p
¼
@h
@T
p
¼ T
@S
@T
p
c V ¼
1
N
@U
@T
V
¼
@u
@T
V
¼ T
@S
@T
V
b
1
V
@V
@T
p
¼ À
1
V
@S
@p
T
in view of (170)
j T
À1
V
@V
@p
T
One of the most common examples of property relationships is the construction
of V ¼ Vðx; yÞ and w ¼ wðx; yÞ, where x and y can be any pair of independent
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9 Applications to Special States of Thermodynamic Equilibrium …