A heat engine operates between two TERs at 1000oC and 20oC respectively. Two-thirds of the work output is used to drive a heat pump that removes heat from the cold surroundings at 0oC and transfers it to a house kept at 20oC. If the house is losing heat at a rate of 60,000 kJ/h, determine
(a) The minimum rate of heat supply to the heat engine.
(b) What-if Scenario: What would the minimum heat supply be if the outside temperature dropped to -10oC?