Suppose you want to operate an ideal refrigerator with a cold temperature of - 15.5 °C, and you would like it to have a coefficient of performance of at least 8.25. What is the maximum hot reservoir temperature for such a refrigerator?

15.65 °C

Explanation:

cold temperature (Tc) = - 15.5 degree C = 273.15 - 15.5 = 257.65 kelvin

minimum coefficient of performance (η) = 8.25

find the maximum hot reservoir temperature of such a generator (Th)

η = / frac{Tc}{Th-Tc}

Th = Tc x (/frac{1}{η} + 1)

Th = 257.65 x (/frac{1}{8.25} + 1)

Th = 288.8 K

Th = 288.8 - 273.15 = 15.65 °C