A heat engine operates on a Carnot cycle that runs clockwise between a reservoir at \(340 \mathrm{~K}\) and a reservoir at \(280 \mathrm{~K}\). One cycle moves enough energy from the hightemperature reservoir to raise the temperature of \(1.0 \mathrm{~kg}\) of water by \(1.0 \mathrm{~K}\). How much work is done by the engine in one cycle?