Imagine an irreversible engine I and a Carnot engine R operating between the same two reservoirs....

Imagine an irreversible engine I and a Carnot engine R operating between the same two reservoirs. Suppose that they absorb different amounts of heat from the high temperature reservoir, perform different amounts of work, but reject the same amounts of heat to the low-temperature reservoir. Prove Carnot's theorem with the aid of the Kelvin-Planck statement of the second law.