How can a reversible heat engine run backward as a refrigerator?

A reversible heat engine can function as a refrigerator when its cycle is operated in reverse. In a standard heat engine, the system absorbs heat from a high-temperature reservoir, performs work, and exhausts waste heat to a low-temperature reservoir.123

When this process is perfectly reversible—meaning the net entropy change of the system and its surroundings is zero—an infinitesimal change in the operating conditions allows the cycle to be inverted. In this reversed state, the machine consumes work to extract heat from a cold reservoir and rejects it into a warmer environment.132

This transition is rooted in the second law of thermodynamics, which dictates that while heat does not spontaneously flow from a colder to a hotter region, it can be forced to do so if external work is applied to the system. By reversing the Carnot cycle, the engine effectively acts as a refrigerating engine, utilizing mechanical energy to maintain a temperature difference against the natural direction of heat flow.12