From optimal engines to minimal refrigerators: the Carnot case

The Carnot limit defines the maximum efficiency for reversible heat engines. However, when applied to reversible refrigerators operating within a fixed temperature range, the Carnot cycle corresponds—counterintuitively—to the minimum possible performance. While this fact is established in formal thermodynamics, it is frequently overlooked or misunderstood by students. This paper presents a physical explanation for this asymmetry without explicitly relying on entropy formalism. A direct, simple mathematical demonstration of this result is provided, along with a concrete illustrative example.