= 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 that
$$
\frac{Q_c}{Q_h}=\frac{T_c}{T_h}.
$$
Fixing one reference value defines the <thermodynamic temperature> scale, and the reversible efficiency is
$$
\boxed{\eta_{\rm rev}=1-\frac{T_c}{T_h}}.
$$
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