6-29
6-80E The sink temperature of a Carnot heat engine, the rate of heat rejection, and the thermal efficiency are given.
The power output of the engine and the source temperature are to be determined.
Assumptions The Carnot heat engine operates steadily.
Analysis (a) The rate of heat input to this heat engine is determined from the definition of thermal efficiency,
 th  1 
Q L
800 Btu/min

 0.75  1 

 Q H  3200 Btu/min

Q
Q
H
H
Then the power output of this heat engine can be determined from
W net,out   th Q H  0.753200 Btu/min   2400 Btu/min  56.6 hp
(b) For reversible cyclic devices we have
 Q H

 Q
 L

T
  H


 rev  TL




TH
HE
800 Btu/min
60°F
Thus the temperature of the source TH must be
 Q
TH   H
 Q
 L

 3200 Btu/min 
 TL  
 800 Btu/min 520 R   2080 R



 rev
6-81E The claim of an inventor about the operation of a heat engine is to be evaluated.
Assumptions The heat engine operates steadily.
Analysis If this engine were completely reversible, the thermal efficiency would be
 th,max
T
550 R
 1 L  1
 0.45
TH
1000 R
When the first law is applied to the engine above,
Q H  W net
 2544.5 Btu/h 
  15,000 Btu/h  27,720 Btu/h
 Q L  (5 hp)
1 hp


1000 R
Q H
HE
5 hp
15,000 Btu/h
550 R
The actual thermal efficiency of the proposed heat engine is then
 th 
W net
 2544.5 Btu/h 
5 hp

  0.459


27,720 Btu/h 
1 hp
QH

Since the thermal efficiency of the proposed heat engine is greater than that of a completely reversible heat engine which
uses the same isothermal energy reservoirs, the inventor's claim is invalid.
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