A reversible heat engine working between two thermal reservoirs at \(875 \mathrm{~K}\) and \(315 \mathrm{~K}\) drives a reversible refrigerator which operates between the same \(315 \mathrm{~K}\) reservoir and a reservoir at \(260 \mathrm{~K}\). The engine is supplied \(2000 \mathrm{~kJ}\) of heat and the network output from the composite system is \(350 \mathrm{~kJ}\). Calculate the heat transfer to the refrigerator and the net heat interaction with the reservoir at \(315 \mathrm{~K}\) temperature.