9. A heat pump is required for heating a house. The heat pump is using the cold outdoor air and operating between temperatures of -15 C and 35 C. The house is estimated to lose heat at a rate of 80000 kJ/hour (a) Determine the minimum power required to run this heat pump and briefly explain why minimum power cannot be achieved in the real heat pump. (6 marks) (b) Determine the power required to heat the house with an electrical heater to maintain the same temperature and compare your result to (a). Which device will be cheaper to operate and why? (3 marks) (c) Produce separate pressure-molar volume (P-V) diagrams for the heat pump, labelling the heat supplied and removed and the network supplied, to illustrate the ideal process: () operating between the temperatures indicated above, (1) if the low operating temperature is decreased, (iii) if the rate of heat loss from the house is reduced. (8 marks) (d) An inventor claims to have produced a heat pump for the house with a coefficient of performance COP = 8. Is their claim valid? Explain your answer with reference to the second law of thermodynamics and entropy. (8 marks)