engineering thermodynamics and mechanical engineering thermodynamics. Consider, first, the system rate version of Eq. (119), i.e., Eq. (119A),
dEx
dt
¼
X
j
1 À
T 0
T j
_
Q j À _
W À p 0
dV
dt
À _
Ex D
where
Ex ¼ U À T 0 S þ p 0 V
½
Š A À U À T 0 S þ p 0 V
½
Š 0 þ
1
2
mv
2
þ mgz
Specifically, we have a chemical closed system at T A ¼ T 0 and p A ¼ p 0 , and the
system is subject to the additional assumptions:
_
Q j ¼ 0 thermally isolated
ð
Þ
dV=dt ¼ 0 constant volume
ð
Þ
1
2
mv
2
¼ 0
mgz ¼ 0
The exergy expression and exergy equation can be reduced to
Ex ¼ U À T 0 S þ p 0 V
½
Š A À U À T 0 S þ p 0 V
½
Š 0 ¼ U À TS þ pV
½
Š A À U À TS þ pV
½
Š 0
¼ ÀDG A (the Gibbs free energy)
dEx
dt
¼
d ÀDG
ð
Þ
dt
¼ À _
W À _
Ex D or À
d ÀDG
ð
Þ
dt
¼ _
W þ _
Ex D
That is,
ÀDG A ¼
Z
DG¼0
A
_
Wdt þ
Z
DG¼0
A
_
Ex D dt
180
7 Free Energy, Exergy, and Energy …