Solve the following problem:
Q: A heat pump heats a house in the winter and then reverses to cool it in the summer. The interior temperature should be 20°C in the winter and 25°C in the summer. Heat transfer through the walls and ceilings is estimated to be 2400 kJ per hour per degree temperature difference between the inside and outside.
a. If the winter outside temperature is 0°C, what is the minimum power required to drive the heat pump?
b. For the same power as in part (a), what is the maximum outside summer temperature for which the house can be maintained at 25°C?