the first Clausius theorem yields
Z
AP I B
dQ
T
¼
Z
AP II B
dQ
T
along any arbitrary reversible path from A to B. That is to say, there exists a state
variable denoted by S and known as entropy which is defined by
S B À S A ¼
Z B
A
dQ
T
0
@
1
A
Reversible
ð62Þ
Correspondingly,
dS ¼
dQ
T
Reversible
ð62AÞ
or,
dQ
ð Þ reversible ¼ TdS
Like any thermodynamic state variable, the state-variable entropy can be
expressed in the form of functions of state: for instance, S = S(T, V) or S = S(T,
p) or S = S(p, V). If the two end states differ from each other only infinitesimally,
the change of dS may be expressed as
A
B
II
I
Fig. 5.2 Depiction of a cyclic process: the first leg may be reversible (as considered in this
section) or irreversible, but the second leg is reversible as considered here as well as in Sect. 5.4
5.3 The Entropy, a New State Variable
97