Which, in the limit of
R
DG¼0
A
_
Ex D dt ¼ 0 becomes,
W ¼
Z
DG¼0
A
_
Wdt ¼ ÀDG
the same relation as (109).
We now consider an open chemical system with chemical reactants input at
T A ¼ T 0 and p A ¼ p 0 . This can be an idealized fuel-cell system operating at
steady-state operation, @=@t ¼ 0. The system is subject to the additional
assumptions
_
Q j ¼ 0 thermally isolated
ð
Þ
1
2
mv
2
¼ 0
mgz ¼ 0
The general exergy equation for a control volume is
@Ex cv
@t
¼
X
j
1 À
T 0
T j
_
Q j À _
W shaft þ
X
i
_
m i fe i À
X
e
_
m e fe e À _
Ex D
Under the assumptions, the equation and the flow exergy expression reduce to
0 ¼ À _
W shaft þ
X
i
_
m i fe i À
X
e
_
m e fe e À _
Ex D
and
fe ¼ h À h 0
ð
ÞÀT 0 s À s 0
ð
Þ¼g À g 0
That is,
0 ¼ À _
W shaft þ
X
i
_
m i g À g 0
ð
Þ i À
X
e
_
m e g À g 0
ð
Þ e À _
Ex D
7.5 Chemical Exergy and Exergy of Heat and Cold
181