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Question

A Carnot refrigerator A works between 10C and 27C, while Carnot refrigerator B works between 27C and 17C, both removing heat equal to 200 J from the freezer. Then which of the following is the correct option regarding the coefficient of performance (β) of both the refrigerators?

A
βA<βB
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B
βA>βB
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C
βA=βB=0
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D
βA=βB0
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Solution

The correct option is B βA>βB
For refrigerator A,
Temperature of sink, T2=10+273=263 K
Temperature of source, T1=27+273=300 K
Coefficient of performance for a Carnot refrigerator is,
βA=T2T1T2=263300263=7.1
Simlarly for refrigerator B,
Temperature of Sink, T2=27+273=246 K
Temperature of source, T1=17+273=290 K
Coefficient of performance,
βB=T2T1T2=246290246=5.6
βA>βB

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