T
0
6 ¼ T System
For the present quasi-static cycles, (72) cannot be replaced by
I
dQ System
T System 0
Therefore, a serious ambiguity exists in the application of Inequality since T′ in
Eq. (72) is ill-defined.
We may now establish the corresponding entropy change for the general thermodynamic process of a system following a similar reasoning in Sect. 5.3: Consider again two end equilibrium states of a system, A and B, and two different paths
I and II, each connecting A to B (using the same Fig. 5.2)—note, however, here
only path II is restricted to be reversible. Let path I be represented by AP I B (which
is irreversible) and path II by AP II B (which is reversible). Now, imagine a cyclic
process of AP I BP II A and consider the cyclic integration along this cycle
I
AP I BP II A
dQ
T 0 ¼
Z
AP I B
dQ
T 0 þ
Z
BP II A
dQ
T
0
Since path II is reversible, the following equality holds:
Z
BP II A
dQ
T
¼ À
Z
AP II B
dQ
T
Therefore,
Z
AP I B
dQ
T 0 À
Z
AP II B
dQ
T
0
i.e.,
Z
AP I B
dQ
T 0
Z
AP II B
dQ
T
Since the integral along the reversible path AP II B equals the entropy change S B – S A
S B À S A !
Z B
A
dQ
T 0
0
@
1
A
quaisstatic
ð73Þ
5.4 Entropy Change in a System Undergoing an Irreversible Process
101