The definition of a Carnot engine does not specify whether the engine’s working substance is a gas or a liquid. It makes no difference. Our argument that a perfectly reversible engine is the most efficient possible heat engine depended only on the engine’s reversibility. Consequently, any Carnot engine operating between and must have exactly the same efficiency as any other Carnot engine operating between the same two energy reservoirs. If we can determine the thermal efficiency of one Carnot engine, we’ll know the efficiency of all Carnot engines. Because liquids and phase changes are complicated, we’ll analyze a Carnot engine that uses an ideal gas.