A reversible heat engine receives the heat from a high-temperature source at \(810 \mathrm{~K}\) and release the same to a low-temperature sink at \(300 \mathrm{~K}\). Determine

(a) the thermal efficiency of the heat engine;

(b) the efficiency of the engine if the higher temperature is increased to \(1366 \mathrm{~K}\);

(c) the maximum efficiency of the engine, if the lower temperature is increased to \(344 \mathrm{~K}\) while the higher temperature is kept at \(810 \mathrm{~K}\).