Sadi Carnot formulated the theorem that no engine can be more efficient than a reversible engine operating between the same reservoirs. The principle is known as Carnot’s theorem or Carnot’s rule.
Carnot presented the underlying idea in 1824 in Reflections on the Motive Power of Fire. He argued that an ideal engine’s maximum performance depends on the temperatures of its hot and cold reservoirs, not on whether it uses steam, air, or another working substance.
The theorem has two closely related consequences: no irreversible engine can outperform a reversible one between the same reservoirs, and all reversible engines working between the same two reservoirs have equal efficiency. The limiting value is ηmax = 1 − TC/TH, with temperatures measured on an absolute scale.
Carnot reasoned using the caloric theory of heat, which was later abandoned. Even so, his reversible-cycle analysis survived and became a foundation of the second law of thermodynamics. Clausius and Kelvin subsequently placed the result within the modern framework of entropy and thermodynamic temperature.