The work term, _
W, is treated, in the context of exergy analysis, as in Sect. 7.2
W ¼ W shaft þ W normal
where W normal is the system mass expansion work. In the context of exergy analysis,
we consider the useful work portion of this expansion work by dealing with the
combination of W normal and Àp 0 DV. That is, the useful work exerted by the normal
surface of a system mass is
W normal À p 0 DV
Now, consider its rate. Between t and t þ Dt, the change in volume of the system
mass is
DV ¼ m e v e
and exergy transfer accompanying work is
W normal À p 0 m e v e
Rate of exergy transfer accompanying work is
lim
Dt!0
W normal
Dt
À lim
Dt!0
m e
Dt
p 0 v e
Noting that W normal ¼ m e p e v e , as Dt ! 0, we can write “rate of exergy transfer
accompanying normal work” as
_
m e p e v e À p 0 v e
ð
Þ
The mass specific exergy equals
ex ¼ u À u 0
ð
Þþp 0 v À v 0
ð
ÞÀT 0 s À s 0
ð
Þþ
1
2
v
2
þ gz
Correspondingly,
Z
cs
q ex
ð Þ ~ Vd ~ A ¼ À
X
i
_
m i ex i þ
X
e
_
m e ex e
Note that the combination of pv À p 0 v
ð
Þand u À u 0
ð
Þþp 0 v À v 0
ð
Þ
½
Š becomes
u þ pv À u þ pv
ð
Þ 0 ¼ h À h 0
7.4 Thermodynamic Processes and Exergy Balance
177