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

The temperature of hot reservoir is 30.58 degrees Celsius.

Step-by-step 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=(T_c)/(T_h-T_c)`

`T_h` is the temperature of hot reservoir

`T_h-T_c=(T_c)/(CP)`

`T_h=(T_c)/(CP)+T_c`

`T_h=(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.