Question

A heat pump is used to maintain a house at a constant temperature of ${22}^{o}C$. The house is losing heat to the outside air through the walls and windows at a rate of 40 MJ/J, while energy generated within the house from the people, lights and appliances amount to 6000kJ/h. For a COP of 2.4, the power input to the heat pump is

• A. 3.13 kW
• B. 4.25 kW
• C. 3.93 kW
• D. 5.13 kW

Answer 1

The correct option is C 3.93 kW

$\text{Heat lost by house}=\frac{40\times {10}^3}{3600}=11.11kW$

$\text{Heat generated in the house}=\frac{6000}{3000}=1.67kW$

$\text{Net heat lost by house}=11.11-1.67=9.44kW$

$COP=\frac{\text{Heat added}}{\text{Power input}}$

$\text{Power input}=\frac{9.44}{2.4}=3.93kW$