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Unformatted text preview: 41. The eﬃciency of the engine is deﬁned by ε = W/Q1 and is shown in the text to be ε = (T1 − T2 )/T1 ,
so W/Q1 = (T1 − T2 )/T1 . The coeﬃcient of performance of the refrigerator is deﬁned by K = Q4 /W
and is shown in the text to be K = T4 /(T3 − T4 ), so Q4 /W = T4 /(T3 − T4 ). Now Q4 = Q3 − W , so
(Q3 − W )/W = T4 /(T3 − T4 ). The work done by the engine is used to drive the refrigerator, so W is
the same for the two. Solve the engine equation for W and substitute the resulting expression into the
refrigerator equation. The engine equation yields W = (T1 − T2 )Q1 /T1 and the substitution yields
Q3
Q3 T1
T4
=
−1=
− 1.
T3 − T4
W
Q1 (T1 − T2 )
Solve for Q3 /Q1 :
Q3
=
Q1 T4
+1
T3 − T4 T1 − T2
T1 = T3
T3 − T4 T1 − T2
T1 = 1 − (T2 /T1 )
.
1 − (T4 /T3 ) ...
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This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.
 Fall '08
 SPRUNGER
 Physics

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