Page 143 - Advanced thermodynamics for engineers

6.3 EFFICIENCY OF COMBINED CYCLE INTERNALLY REVERSIBLE HEAT 129

From Eqns (6.18) and (6.28),
" ( )!#
1 Q _ 1 Q _
_ 2 C
Q ¼ C H T H þ þ T C (6.29)
H
s 1 C 2 s 2 T C
Rearranging Eqn (6.29) gives,
Q _ H Q _ H Q _ H 1 T C !
¼ 1 ; (6.30)
C H T H C 2 T H C C T H s 1 s 2 T H
which can be written as

Q _ H ðs 1 s 2 T C =T H Þ
¼ : (6.31)

C H T H C H C H
s 1 s 2 1 þ þ
C 2 C C
The power output of engine E H can be obtained from Eqn (6.31) as
_ _
W H Q H ðs 1 s 2 T C =T H Þ
¼ ð1 s 1 Þ¼ ð1 s 1 Þ: (6.32)

C H T H C H T H C H C H
s 1 s 2 1 þ þ
C 2 C C
_
In a similar manner W C =C H T H can also be evaluated as
_ _
W C Q H ðs 1 s 2 T C =T H Þð1 s 2 Þs 1
¼ s 1 ð1 s 2 Þ¼ ; (6.33)

C H T H C H T H
s 1 s 2 1 þ C H þ C H
C 2 C C
_
W H ð1 s 2 Þ
¼ s 1 : (6.34)
C H T H ð1 s 1 Þ
It can be seen from Eqns (6.32) and (6.34) that it is possible to split the power output of the two
engines in an arbitrary manner, dependent on the temperature drops across each engine. The ratio of
work output of the two engines is
_
W H 1 ð1 s 1 Þ
¼ : (6.35)
_
W C s 1 ð1 s 2 Þ
This shows that if the temperature ratios across the high-temperature and the low-temperature
engines are equal (i.e. s 1 ¼ s 2 ), the work output of the low-temperature engine will be

_ _
W C ¼ s 1 W H (6.36)
Hence the work output of the low-temperature engine will be lower than that of the high-
temperature engine for the same temperature ratio. The reason comes directly from Eqns (6.32)
and (6.33), which show that the work output of an engine is directly proportional to the temperature of
the ‘heat’ at entry.