A heat engine operates between reservoirs at 1000 and 300 K. Some of the power output from the heat engine drives a refrigerator which operates between 250 and 300 K. The heat-transfer input at 1000 K to the heat engine is 1000 kJ, and the heat transfer rejected from the refrigerator is 2700 kJ. (a) If the heat engine and refrigerator are both internally reversible devices, find the percentage of the heat-engine work output used to drive the refrigerator. (b) If the COP of the refrigerator is 80% of the value for an internally reversible device operating between the given temperatures, determine the actual work (kJ) required to operate the refrigerator. (c) In (b), what is the heat transfer rate from the heat engine to the cold reservoir assuming the thermal efficiency of the heat engine is 35%?