Question

An actual refrigerator operates with a COP that is half the Carnot COP. It removes 10 kW of heat from a cold reservoir at 250 K and dumps the waste heat into the atmosphere at 300 K. (a) Determine the net work consumed by the refrigerator. (b) What-if Scenario: How would the answer change if the cold storage were to be maintained at 200 K without altering the rate of heat transfer

Answer 1

Step-by-step explanation:

Given

`\left ( COP\right )_(actual)=0.5\left ( COP\right )_(ideal)`

`T_L=250 K`

`T_H=300 K`

ideal COP
`=(T_L)/(T_H-T_L)=(250)/(300-250)=5`

`\left ( COP\right )_(actual)=2.5`

Also
`COP=(Desired\ effect)/(Power\ supplied)`

`2.5=(10)/(W_(in))`

`W_(in)=4 kW`

(b)if
`T_L=200 K`

`\left ( COP\right )_(actual)=0.5* (200)/(300-200)=1`

thus
`W_(in)=10 kW`