What cycle is the most efficient possible heat engine cycle?

The Carnot cycle is the most efficient possible heat-engine cycle operating between two fixed temperatures. Its efficiency sets an ideal upper limit for all real engines.

Proposed by French engineer Sadi Carnot in 1824, the cycle consists of four reversible stages: isothermal expansion, adiabatic expansion, isothermal compression, and adiabatic compression. During the isothermal expansion, the working substance absorbs heat from the hot reservoir; during isothermal compression, it releases heat to the cold reservoir.

For reservoir temperatures measured in kelvins, its ideal efficiency is η = 1 − Tc/Th, where Th is the hot-reservoir temperature and Tc is the cold-reservoir temperature. Efficiency therefore depends only on the two reservoir temperatures, not on whether the working substance is a gas, vapour, or another material.

No practical engine exactly follows a Carnot cycle because real processes involve friction, heat losses, finite temperature differences, and other irreversibilities. Brayton, Diesel, and Otto cycles can be useful in particular machines, but none can exceed Carnot efficiency between the same temperatures.