E 2 À E 1 ¼
Z 2
1
dQ À
Z 2
1
dW ¼
Z 2
1
dQ À W
ð22AÞ
dS ! d E S ¼
Z
A
ÀJ Q
T
dA
2
4
3
5 dt
ð89AÞ
which may be written if a single value T is defined for the system as
S 2 À S 1 !
Z 2
1
dQ
T
One may introduce entropy generation or entropy growth, S G , as
S 2 À S 1 ¼
R 2
1
dQ
T
þ S G . The Clausius inequality becomes
S G ! 0
and the system entropy balance becomes
S 2 À S 1 ¼
Z 2
1
dQ
T
b
þ S G
ð89DÞ
The exergy balance for a closed system is developed by substituting (118) into
(22A)
Ex 2 À Ex 1
ð
ÞÀp 0 V 2 À V 1
ð
ÞþT 0 S 2 À S 1
ð
Þ¼
Z 2
1
dQ À W
With the replacement of S 2 À S 1 by using Eq. (89D) in the above equation
Ex 2 À Ex 1 ¼
Z 2
1
1 À
T 0
T
dQ À W À p 0 V 2 À V 1
ð
Þ
½
Š
8
<
:
9
=
;
À T 0 S G
ð119Þ
The term on the left side of Eq. (119) is the exergy change of the closed system.
The terms on the right side represent the breakdown of the system exergy change
dependent on processes: The first group represents two kinds of exergy transfers.
The exergy transfer associated with the transfer of heat, E q , is
7.4 Thermodynamic Processes and Exergy Balance
175