Question

An office uses a heat pump to receive 500 kJ/day heat in winter to maintain its temperature at 300 K. The ambient temperature is 280 K. If the COP of the heat pump is 60% of its theoretical maximum value, the ratio of actual work input to the minimum theoretical work input to the heat pump is $____________$ (rounded off to one decimal place).

Hint:

Always compare actual COP with Carnot COP to determine how much extra work is needed.

Answer 1

Correct Answer: 1.6

Step 1: Carnot COP of heat pump. \[ COP_{Carnot} = \frac{T_H}{T_H - T_L} = \frac{300}{300 - 280} = 15 \]
Step 2: Actual COP. \[ COP_{act} = 0.6 \times 15 = 9 \]
Step 3: Work ratio. Work = $\dfrac{Q_H}{COP}$. \[ \frac{W_{act}}{W_{min}} = \frac{Q/COP_{act}}{Q/COP_{Carnot}} = \frac{COP_{Carnot}}{COP_{act}} = \frac{15}{9} = 1.7 \] Final Answer: \[ \boxed{1.7} \] % Quicktip