That is, for isobaric processes we have the general expression
S B À S A ¼
Z B
A
C p T
ð Þ
T
dT
ð63CÞ
We shall consider the full implication of this general equation in detail in the
following chapters, especially in Chap. 9.
5.3.3 The Entropy of Ideal Gases
Here, we consider its application to ideal gases to determine the ideal gases entropy
expression in terms of T, p, and V. Rewrite Eq. (64)
dS ¼
dU þ pdV
T
¼
dU þ d pV
ð Þ À Vdp
T
¼
dH À Vdp
T
ð65Þ
Substitution of Eqs. (34) and (35), p/T = NR/V, and V/T = NR/p into the equation
above leads to the following results, respectively,
dS ¼ Nc V
dT
T
þ NR
dV
V
ð66Þ
dS ¼ Nc p
dT
T
À NR
dp
p
ð67Þ
Integration of both equations yields
S T; V
ð
Þ ¼Nc V lnT þ NRlnV þ const
ð68Þ
S B À S A ¼ Nc V ln
T B
T A
þ NRln
V B
V A
ð68AÞ
and
S T; p
ð
Þ ¼ Nc p lnT À NRlnp þ const
ð69Þ
S B À S A ¼ Nc p ln
T B
T A
À NRln
p B
p A
ð69AÞ
Making use of the thermal equation of state of an ideal gas, either Eq. (68A) or
(69A) yields
5.3 The Entropy, a New State Variable
99