The Carnot cycle is the most efficient engine possible between two temperatures. Follow its four steps — heat in, expand, heat out, compress — on the heat engine and the P–V diagram, and see why the loop's enclosed area is the net work you get out.
The Carnot cycle is an idealised heat engine — a repeating four-step process that turns a temperature difference into useful work. Its working substance is a gas that is alternately heated, expanded, cooled and compressed inside a cylinder. Because every step is carried out perfectly, with no friction or wasted energy, it reaches the greatest efficiency any engine can achieve between two given temperatures.
Real engines — power stations, car engines, jet turbines — all fall short of the Carnot limit, but that limit is the yardstick they are measured against. Seeing the cycle clearly explains why efficiency depends on the two temperatures rather than on the fuel or the working gas, and why you can never convert all the heat you put in into work.
The gas is held against the hot reservoir and allowed to expand. Because it stays at the reservoir's temperature, heat flows in freely with no extra warming — the absorbed heat Q_H is what pushes the piston out and does work. On the P–V diagram this is the top curve of the loop.
The gas keeps expanding, but now it is insulated from both reservoirs so no heat enters or leaves. The work it does has to come out of its own internal energy, so its temperature falls from the hot level to the cold one.
The gas is now pressed against the cold reservoir and squeezed. Held at the cold temperature, it gives up heat Q_C to the reservoir — the energy that the cycle cannot turn into work. This is the lower curve of the loop.
With the reservoirs removed again, the gas is compressed the rest of the way. No heat is exchanged, so the work done on the gas warms it back from the cold temperature to the hot one, returning it exactly to its starting state.
Going round the loop, the work produced during expansion is bigger than the work spent during compression. The difference — drawn as the area enclosed by the loop — is the net work out, W = Q_H − Q_C. Its efficiency depends only on the two temperatures: hotter hot, colder cold, better engine.
It is an idealised four-step heat-engine cycle: isothermal expansion, adiabatic expansion, isothermal compression and adiabatic compression. It is the most efficient cycle that can run between two fixed temperatures, so it sets the theoretical ceiling that real engines can only approach.
Heat can only be taken in or given out usefully when the working gas is at the same temperature as the reservoir, so the heating steps must be isothermal. The other two steps change the temperature between the hot and cold levels, and doing that with no heat exchange at all (adiabatically) avoids wasting any energy.
Because its efficiency depends only on the two temperatures — 1 minus the cold temperature over the hot temperature — and not on the working substance. Reversible operation means no energy is thrown away, so any real engine, which always has friction and irreversible losses, can only match it in the limit.
It is the net work done per cycle. The loop is traced clockwise, so the work done during expansion is larger than the work spent during compression; the difference — the enclosed area — is the useful work output.
Yes. Run in reverse it becomes the ideal refrigerator or heat pump: it takes in work to move heat from the cold reservoir to the hot one. Real refrigerators and heat pumps try to follow this same reverse pattern.
Because it would have to run infinitely slowly to stay reversible and lose no energy to friction, giving almost no power for its size. Real plants use the Rankine cycle, which trades some efficiency for a useful rate of work.