Question

A domestic food freezer is to be maintained at temperature of - 15 deg. C. The ambient air temperature is 30 deg. C. If the heat leaks into the freezer at the continuous rate of 1.75 kJ/s, find the power required to pump out the heat continuously.
Ans = 0.305 kJ

Answer 1

Given:

T_{L} = -15°C

T_{H} = 30°C

Leak = 175 kJ/s = 175 kW.

To find:

Least power to pump out heat.

Calculation:

Carnot COP (coefficient of performance)

$\sf{ = \dfrac{T_{L}}{T_{H} - T_{L}} }$

$\sf{ = \dfrac{( - 15 + 273)}{(30 + 273)- ( - 15 + 273)} }$

$\sf{ = \dfrac{258}{303 - 258} }$

$\sf{ = \dfrac{258}{45} }$

$= 5.73 \:$

Actual COP of refrigerator:

$\sf{ = \dfrac{Q}{P} }$

$\sf{ = \dfrac{1.75 }{P} }$

For minimum power to pump out heat:

$\therefore \: \sf{ \dfrac{1.75 }{P} = 5.73 }$

$\sf{ = > P = 0.305 \: kW }$

So, final answer is:

$\boxed{ \rm{ P = 0.305 \: kW }}$