Question

It is proposed to use a heat pump to heat a home in a cold winter, when the surrounding temperature is -23°C to maintain the room at +22°C. If the power rating of the heat pump is 5 kW, the maximum heat transfer rate that can be provided to the home is  
1. 11 kW
2. 22 kW
3. 33 kW
4. 44 kW

Answer 1

Correct Answer - Option 3 : 33 kW

Concept:

The maximum heat transfer rate is possible for a reversible heat pump whose COP is given by

\(cop = \frac{{\mathop T\nolimits_H }}{{\mathop T\nolimits_H - \mathop T\nolimits_L }}\)

Calculation:

Given:

T_H = 22°C = 295 k

T_L=-23°C = 250 k

work input, W_inp = 5 kW

\(\begin{array}{l} cop = \frac{{\mathop T\nolimits_H }}{{\mathop T\nolimits_H - \mathop T\nolimits_L }} = \frac{{\mathop H\nolimits_R }}{{\mathop W\nolimits_{inp} }}\\ cop = \frac{{295}}{{295 - 250}} = \frac{{\mathop H\nolimits_R }}{{5 \times \mathop {10}\nolimits^3 }}\\ \mathop H\nolimits_R = 33~kW \end{array}\)