A reversible heat engine operates between two reservoirs at temperatures, \(700^{\circ} \mathrm{C}\) and \(50^{\circ} \mathrm{C}\). The engine drives a reversible refrigerator which operates between reservoirs at temperature of \(50^{\circ} \mathrm{C}\) and \(-25^{\circ} \mathrm{C}\). The heat transfer to the engine is \(2500 \mathrm{~kJ}\) and the net work output of the combined refrigerator plant is \(400 \mathrm{~kJ}\).

(a) Determine the net heat transfer to the reservoir at \(50^{\circ} \mathrm{C}\).

(b) Reconsider (a) given that the efficiency of the heat engine and the COP of the refrigerator are each \(45 \%\) of their maximum possible values.