Modern Engineering Thermodynamics

13.5 Operating Efficiencies 463
b. The maximum possible Rankine cycle thermal efficiency occurs when the piston-cylinder unit is reversible and the boiler
feed pump is isentropic (Figure 13.11):
T
1
h
4s
1
3,4s
2s
3
2s
s
s
FIGURE 13.11
Example 13.3, T–s diagram.
Station 1—Engine inlet
p 1 = 20:0 psia
x 1 = 1:00
h 1 = h g ð20:0 psiaÞ = 1156:4 Btu/lbm
Station 2s—Engine exit
p 2s = 14:7 psia
s 2s = s 1 = 1:7322 Btu/lbm . R
x 2s = s 2s –s f ð14:7 psiaÞ /sfg ð14:7 psiaÞ
s 1 = s g ð20:0 psiaÞ = 1:7322 Btu/lbm . R = ½1:7322 − 0:3122Š/1:4447 = 0:9829
Station 3—Condenser exit
p 3 = p 2s = 14:7 psia
x 3 = 0 s 4s = s 3
h 3 = h f ð14:7 psiaÞ = 180:1 Btu/lbm
v 3 = v f ð14:7 psiaÞ = 0:01672 ft 3 /lbm
h 2s = h f ð14:7 psiaÞ + x 2s h fg ð14:7 psiaÞ
= 180:1 + 0:9829ð970:4Þ
= 1133:9 Btu/lbm
Station 4s—Boiler inlet
p 4s = p 1 = 20:0 psia
Then, the isentropic efficiency of this system is given by Eq. (13.9b) as
ðη T Þ maximum
Rankine
= h 1 − h 2s − v 3 ðp 4 − p 3 Þ
h 1 − h 3 − v 3 ðp 4 − p 3 Þ
ð1156:4 − 1133:9 Btu/lbmÞ− 0:01672 ft 3 /lbm 20:0 − 14:7 lbf/in 2
144 in 2 /ft 2
118:16 ft . lbf/Btu
=
ð1156:4 − 180:1 Btu/lbmÞ− 0:01672 ft 3 /lbm 20:0 − 14:7 lbf/in 2
144 in 2 /ft 2
118:16 ft . lbf/Btu
= 0:0230 = 2:30%
Exercises
7. Determine the maximum Carnot cycle net power output in Example 13.3 if the boiler pressure is increased to 30.0 psia
from 20.0 psia. Assume all the other variables remain unchanged. Answer: (_W net ) Carnot = 16.2 W.
8. Determine the maximum Rankine cycle net power output in Example 13.3 if the boiler pressure is increased to 40.0 psia
from 20.0 psia. Assume all the other variables remain unchanged. Answer: (_W net ) max. Rankine = 22.2 W.
9. Determine the minimum power required to operate the boiler feed pump per unit mass flow of steam in Example 13.3
if the boiler pressure is 35.0 psia instead of 20.0 psia. Assume all the other variables remain unchanged.
Answer: j _W= _m j pump = 0.0184 W·h/(lbm).
The thermal efficiency calculated in part b of the previous example was for a reversible Rankine cycle engine
and, thus, is impossible to achieve with a real Rankine cycle engine. Considering the mechanical and thermal
inefficiencies of these relatively crude toy engines, it is easy to see why their actual operating thermal