A heat pump is used to maintain a living space at 22 °C when the outside air temperature is 2 °C. The room loses heat at an average rate of 6000 kJ per hour. Electricity costs Rs 6.0 per kWh. Answer the following questions:
(i) Calculate the maximum possible COP of the heat pump operating between these two temperatures.
(ii) Determine the minimum electrical power input (in kW) required to supply the needed heat to the room.
(iii) Estimate the minimum monthly cost (30 days of continuous operation) of running such an ideal heat pump at this load.
(iv) State any two practical reasons why the actual monthly cost of operating a real heat pump would be higher than the value calculated in part (iii).