Suppose you want to operate an ideal refrigerator with a cold temperature of − 13.5 °C , and you would like it to have a coefficient of performance of at least 7.75. What is the maximum hot reservoir temperature for such a refrigerator?

292.984 K or 19.98 °C

Explanation:

Using,

η = Tc/(Th-Tc) Equation 1

Where η = coefficient of performance, Tc = cold temperature of the refrigerator, Th = hot temperature of the refrigerator.

Make Th the subject of the equation

η (Th-Tc) = Tc

η Th-η Tc = Tc

Th = (Tc+ηTc)/η Equation 2

Given: Tc = -13.5°C+273 = 259.5 °C, η  = 7.75

Substitute into equation 2

Th = (259.5+7.75×259.5)/7.75

Th = (259.5+2011.125)/7.75

Th = 2270.625/7.75

Th = 292.984 °C or 19.98 °C

Hence the maximum hot reservoir temperature = 292.984 °C or 19.98 °C

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