Question

Suppose you want to operate an ideal refrigerator with a cold temperature of −11°C, and you would like it to have a coefficient of performance of 6.30. What is the hot reservoir temperature (in °C) for such a refrigerator?

Answer 1

Answer:

The temperature of hot reservoir is 30.58 degrees Celsius.

Explanation:

It is given that,

Temperature of the cold reservoir, $T_c=-11^{\circ}C=-11+273=262\ K$

Coefficient of performance, $CP=6.3$

We need to find the temperature of hot reservoir for such a refrigerator. The coefficient of performance is given by :

$CP=\dfrac{T_c}{T_h-T_c}$

$T_h$ is the temperature of hot reservoir

$T_h-T_c=\dfrac{T_c}{CP}$

$T_h=\dfrac{T_c}{CP}+T_c$

$T_h=\dfrac{262}{6.3}+262$

$T_h=303.58\ K$

or

$T_h=30.58^{\circ}C$

So, the temperature of hot reservoir is 30.58 degrees Celsius. Hence, this is the required solution.