An irreversible heat pump is designed to remove heat at 7 C from the atmosphere and supply 43,200 kJ/h to an industrial process at 420 K . The COP of the actual heat pump is 60% of that of an internally reversible heat pump operating between the same two temperatures. The heat pump is driven, through a transmission, by the output of a heat engine which receives heat transfer from a reservoir at 1050 K and rejects heat to the same industrial process at 420 K. The thermal efficiency of the heat engine is 75% of that of an internally reversible heat engine operating between the same two temperatures. The transmission which delivers the power to the heat pump from the heat engine has an efficiency of 80%. Determine (a) the power output required for the heat pump (kW), (b) the rate of heat input to the heat engine (kW), and (c) the heat transfer rate from the heat engine to the industrial process (kW)