A heat engine operating between two reservoirs at \(1000 \mathrm{~K}\) and \(300 \mathrm{~K}\) is used to drive a heat pump which extracts heat from the reservoir at \(300 \mathrm{~K}\), at a rate twice that at which engine rejects heat to it. If efficiency of the engine is \(40 \%\) of the maximum possible and the co-efficient of performance of the heat pump is \(50 \%\) of the maximum possible, make calculations for the temperature of the reservoir to which the heat pump rejects heat. Also workout the rate of heat rejection from the heat pump if the rate of supply of heat to the engine is \(50 \mathrm{~kW}\).