Carnot cycle explained
When no engine can be complete, what remains as the best is a cycle joined from two isothermal legs and two adiabatic legs. Carnot wrote that efficiency as (η = 1 - TCTH), and a real engine sitting between the same two reservoirs does not beat this value. Whatever gas does the work, the ceiling stays fixed by the two temperatures alone.
The stretches that trade heat on the hot side stay at a fixed temperature, and the stretches where heat does not cross move only the temperature, with no exchange at all. All four stretches have to be walked very slowly so the gas remains near equilibrium, and a real engine that carries friction plus a finite temperature gap never quite reaches that slow round trip. Each slow step is what keeps the gas from being driven far from the state the diagram assumes. Friction and a finite temperature gap are what keep a real engine off that slow round trip.
The efficiency is fixed as η = 1 - TCTH alone, so the working gas does not matter at all. A plant that runs on steam at 800 K and rejects heat to an environment at 300 K has a ceiling near 60 percent, and because the cold side cannot be lowered to absolute zero it never reaches 100 percent. Absolute zero stays out of reach, so the ceiling stays strictly below the whole of the heat taken in. Because the cold side cannot reach absolute zero, the ceiling stays strictly below the whole of the heat.
In a reversible cycle QCQH = TCTH, so QHTH = QCTC. Heat moves in proportion to temperature and the quotient Q/T stays conserved, and that quotient receives the name entropy in the next chapter. The two bars of heat and temperature therefore move together, and whatever ratio you set, the equality is the thing that stays put. That conserved quotient is why the next chapter can give the exchange a name instead of leaving it as a loose proportion. That conserved quotient is what the next chapter will name, once the loop has brought it back to itself.
A real engine stays only under the ceiling, and if some engine sat above it you could pair it with a reversed twin and carry heat from the cold side to the hot side with no work at all, a perpetual machine that would break law 2. That impossibility is what pins the ceiling where it is. Engineers treat anything drawn above that line as a drawing error rather than a design, and the proof does not depend on the fuel or the metal. The impossibility of a work-free uphill heat flow is what holds the ceiling where it is.
The efficiency hangs only on TCTH, it is a ceiling nobody can cross, and the equality QHTH = QCTC is the seed of the next chapter, entropy. In practice one lifts the ceiling by raising TH as far as the materials can bear, which is why jet engines and power plants push the combustion temperature. Raising the hot temperature is the lever a builder still has. Pushing the combustion temperature as far as the materials bear is how a builder lifts that ceiling.