A Carnot heat engine receives heat at 527 C and rejects the waste heat to the environment at 22 C. The entire work output of the heat engine is used to drive a Carnot refrigerator that removes heat from the cooled space at -15C at a rate of 8 kW and rejects it to the same environment at 22 C. Determine: (a) The work output of the heat engine. (b) The rate of heat supplied to the heat engine. (c) The total rate of heat rejection to the environment