Brayton Cycle.

The Brayton cycle takes its working fluid through 4 processes and returns it to the state it began in. In order, those are:

1. Adiabatic compression
2. Constant-pressure combustion
3. Adiabatic expansion
4. Constant-pressure heat rejection

You will find it in jet engines and power-station gas turbines. At the standard set-up above — pressure ratio 12, peak temperature 1,500 K, intake temperature 300 K — it reaches a thermal efficiency of 50.83%, against a Carnot limit of 80.00% for the same temperature span. The net work is 454.4 kJ/kg, from 893.8 kJ/kg of heat in and 439.5 kJ/kg rejected.

Its efficiency has a closed form: η = 1 − 1/rₚ^((γ−1)/γ). The simulator above does not use it — it solves the state points and divides net work by heat in — but the two agree to machine precision, and the test suite behind this page checks that on every build.

Switch the diagram pane between P–v and T–s and watch the same cycle change costume. On the pressure–volume plot the area inside the loop is the net work per kilogram of working fluid, because work is the integral of P dv. On the temperature–entropy plot the area inside the loop is the net heat, because heat in a reversible process is the integral of T ds.

Those two areas are the same number. That is the first law applied to a closed loop: the fluid ends where it started, so its internal energy has not changed, so everything that went in as heat came out as work. Two different pictures, one arithmetic.

The T–s view is the more revealing of the two once you are comfortable with it, because it shows the temperature at which heat crossed the boundary — and that, not the amount, is what decides how much of it can become work.

George Brayton built a constant-pressure combustion engine in the 1870s. It was a piston machine, and it was not a commercial success. What survived is the cycle: steady compression, heat added at constant pressure, steady expansion — which turned out to describe something Brayton never built.

A gas turbine has no pistons, no crank and no flywheel. Air flows continuously through a compressor, into a combustor that burns fuel in it at roughly constant pressure, and out through a turbine that extracts work. Nothing reciprocates. It is the same cycle as Brayton’s engine, in a completely different machine.

Look at the back work ratio on the panel. In a piston engine, compression and expansion happen in the same cylinder at different times, and the flywheel carries the energy across. In a gas turbine they happen at the same instant in different components, and the turbine has to drive the compressor continuously through a shaft before it drives anything else. At a pressure ratio of 12 that is roughly 40% of the turbine's gross output, gone before the machine produces anything at all.

This is why the gas turbine took so long to arrive. The thermodynamics were understood in the nineteenth century; the problem was that early compressors were inefficient enough that the turbine could not both drive them and produce useful work. The engine had to wait for aerodynamics.

Efficiency here rises with pressure ratio and with nothing else — set the peak temperature anywhere and the efficiency card will not move. But peak temperature decides the work per kilogram of air, which decides how big the engine has to be for a given output, so every generation of gas turbine has pushed turbine inlet temperature as hard as materials allow.

They have pushed it past the melting point of the alloys. Modern first-stage turbine blades are grown as single crystals to remove grain boundaries that would creep, coated in ceramic thermal barriers, and shot through with internal passages that bleed cooler compressor air out over the surface as a film. The gas is hotter than the metal could survive standing still in it.