A heat engine operates between two reservoirs at 800 and 200C . One half of the work output of the engine is used to drive a carnot heat pump that removes heat from the cold surroundings at 20C and transfer it to a house maintained at 220C. If the house is losing heat at a rate of 62000 kJ/h, determine the minimum rate of heat supply to the heat engine required to keep the house at 220C.
