11.a heat engine operates between two reservoirs at 800 and 20°c. one-half of the work output of the heat engine is used to drive a carnot heat pump that removes heat from the cold surroundings at 2°c and transfers it to a house maintained at 22°c. if the house is losing heat at a rate of 62,000 kj/h, determine the minimum rate of the heat supply to the heat engine required to keep the house at 22°c.