linguistic:paraphrasing, structural:reformatting, information:classification
Carnot cycle

Carnot considered an idealized process in which heat from a thermal reservoir at a high temperature flows very slowly (and thus reversibly) into the gas contained in a cylinder enclosed by a movable piston. This gives an isothermal expansion of the gas that pushes out the piston and can be used to perform useful work. This does not yet constitute an engine because the piston must be returned to its original position in order for the machine to run cyclically.

Carnot then proposed reducing the temperature of the gas by an adiabatic expansion, during which the cylinder is thermally isolated so as to prevent heat from entering or leaving the gas. Once the temperature of the gas has reached the same value as that of the colder reservoir, the cylinder is put into thermal contact with that reservoir and the gas undergoes an isothermal compression, during which it very slowly (and thus reversibly) rejects heat into the reservoir.

To close the cycle, the temperature of the gas in the cylinder can be raised by adiabatic compression, until it reaches a value equal to the temperature of the hotter reservoir. This succession of isothermal expansion, adiabatic expansion, isothermal compression, and adiabatic compression can then be repeated as many times as desired, generating a net amount of work each time, at the expense of a transfer of heat from the hotter reservoir to the colder reservoir.

As Carnot explained, such a cycle constitutes the most efficient heat engine possible (given the temperatures of the two reservoirs), not only because of the (trivial) absence of friction, heat leakage, or other incidental wasteful processes: The main reason is that it involves no conduction of heat between parts of the engine at different temperatures. Carnot understood that the conduction of heat between bodies at different temperatures is a wasteful and irreversible process, which must be minimized if the heat engine is to achieve its maximum efficiency.

Because Carnot's cycle is reversible, it can also be used as a refrigerator: if an external agent supplies the needed mechanical work to move the piston, the sequence of transformations of the gas will absorb heat from the colder reservoir and reject it into the hotter reservoir. Carnot argued that no engine operating between reservoirs at two given temperatures could deliver more work than his reversible cycle. Otherwise, the more efficient engine could run Carnot's cycle in reverse as a refrigerator, thus returning all of the "caloric" from the colder back to the hotter reservoir, with some positive amount of work left over to perform a further useful task. Carnot assumed that such a process, in which no net "caloric" was consumed while positive work could be done forever, would be a perpetual motion and therefore forbidden by the laws of physics.

This argument led Carnot to conclude that

The motive power of heat is independent of the agents employed to realize it; its quantity is fixed solely by the temperatures of the bodies between which is effected, finally, the transfer of caloric.

Carnot understood that his idealized engine would have the maximum possible thermal efficiency given the temperatures of the two reservoirs, but he did not calculate the value of that efficiency because of the ambiguities associated with the various temperature scales used by scientists at the time:

In the fall of caloric, motive power undoubtedly increases with the difference of temperature between the warm and cold bodies, but we do not know whether it is proportional to this difference.