 Solution

The Carnot theorem states that no engine between two fixed heat reservoirs can be more efficient than a reversible engine, and that all reversible engines between those reservoirs have the same efficiency. Thus the heat ratio of a reversible engine depends only on the two reservoirs. Its multiplicative consistency for three reservoirs permits a state variable $T$, unique up to an overall scale, such thatFixing one reference value defines the thermodynamic temperature scale, and the reversible efficiency is