A refrigerator using helium gas operates on the reversed cycle shown in the foll

Question

A refrigerator using helium gas operates on the reversed cycle shown in the following figure. Assume that T1 = -24?C and T2 = -71?C.

What is the refrigerator's coefficient of performance?

What is the refrigerator's power input if it operates at 64 cycles per second?

K-P19.58.jpg

A refrigerator using helium gas operates on the reversed cycle shown in the following figure. Assume that T1 = -24?C and T2 = -71?C. What is the refrigerator's coefficient of performance? What is the refrigerator's power input if it operates at 64 cycles per second?

Explanation / Answer

The efficiency of a Carnot engine operating between reservoirs at absolute temperatures Tc and Th is
? = 1 - Tc/Th

n=1-24/71=0.66

The coefficient of carnot heat pump operating at same temperatures for purpose of cooling is:
COP = Tc / (Th - Tc) = (Tc/Th) / (1 - (Tc/Th))

The temperature ratio Tc/th can expressed using the given efficiency:
Tc/Th = 1 - ?
=> 0.33
COP = (1 - ?) / ? = (1/?) - 1 = 1.55-1= 0.55

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