Question

An inventor claims to have developed a food freezer that at steady state requires a power input of 0.25 kW to extract energy by heat transfer at a rate of 3000 J/s from freezer contents at 270 K. Investigate this claim for an ambient temperature of 293 K.

Answer 1

Answer:

The claim is false. ($COP_{real} > COP_{ideal}$).

Explanation:

The real coefficient of performance of the food freezer is:

$COP_{real} = \frac{\dot Q_{L}}{\dot W}$

$COP_{real} = \frac{3\,kW}{0.25\,kW}$

$COP_{real} = 12$

The ideal coefficient of performance, that is, when freezer has a reversible process, is:

$COP_{ideal} = \frac{T_{L}}{T_{H}-T_{L}}$

$COP_{ideal} = \frac{270\,K}{293\,K-270\,K}$

$COP_{ideal} = 11.739$

A real freezer has a coefficient of performance lesser than or equal to ideal coefficient of performance. Since supposed real coefficient of performance is greater than ideal coefficient of performance. The claim is proved to be false.