The gas turbine and the jet engine: air drawn in, compressed, burned at constant pressure, expanded through a turbine — in a continuous flow, not a bang. Two adiabats and two isobars. Its efficiency is one clean law in the pressure ratio, η = 1 − rp(1−γ)/γ, and it hides a brutal secret: a huge slice of the turbine's output is spent just to keep the compressor turning. The blue team builds and defends it; the red team tries to break it.
source G. B. Brayton, Improvement in Gas Engines, U.S. Patent 125,166 (Apr. 2, 1872) — the "Ready Motor," continuous constant-pressure combustion; the ideal air-standard form is the Joule / Brayton cycle. patents.google.com/patent/US125166A. Rendered, not quoted.
Air-standard, ideal gas, γ = 7/5. Four reversible legs around the loop:
1→2 isentropic compression (the compressor), pressure up by rp. 2→3 heat added at constant pressure (the burner). 3→4 isentropic expansion (the turbine). 4→1 heat rejected at constant pressure.
Each adiabat multiplies temperature by rp(γ−1)/γ, so the efficiency collapses to η = 1 − rp(1−γ)/γ = 1 − T₁/T₂ — it depends on the pressure ratio alone, not on the peak temperature.
Live states for the current settings:
| state | P | T (K) |
|---|
Brayton's 1872 constant-pressure combustion is the exact opposite choice from Otto's constant-volume bang. That single decision — burn while flowing — is what makes a continuous machine possible: the gas turbine, and then the jet engine.
It is the gas cousin of the-rankine-cycle (steam), and like every heat engine it sits under the-carnot-cycle ceiling, 1 − Tc/Th. Each sphere is the next one's premise.
The blue team's live check: recompute η across the whole ladder of pressure ratios and confirm it rises, hits ≈0.482 at rp=10, keeps a heavy back-work ratio, and stays under Carnot. If red tampers, this badge is where it shows.
Three numbers enter the machine: the pressure ratio rp across the compressor, the turbine-inlet temperature T₃ (how hot the burner runs), and the intake temperature T₁. The adiabatic ratio γ = 7/5 is fixed for diatomic air.
Everything else — every state, the work of each stroke, the efficiency — is derived, never entered. Feed them into the panel below.
Every stroke's work is computed from the ideal-gas law on the spot, never looked up.
P–V loop · area enclosed = net work
What the machine proves, at rp=10, γ=7/5: the efficiency is η ≈ 0.482 = 1 − rp(1−γ)/γ, it rises with rp, heat crosses at constant pressure, the back-work ratio ≈ 0.41 (the compressor eats 41% of the turbine's output — a steam plant's pump takes ~1%), and the whole cycle stays below the Carnot limit 1 − Tc/Th ≈ 0.786.
The blue team's witness (left) confirms these live; the red team (right) tries to make them wrong.
The ideal formula also ignores pressure drop in the burner (heat is not perfectly isobaric in practice), variable specific heats at 1500 K, and combustion irreversibility. η = 1 − rp(1−γ)/γ is a ceiling for the ideal cycle, not a promise for the machine on the test stand.
"Higher pressure ratio is always better." Cut. η rises with rp, but net work per unit mass peaks and falls: push rp too high and T₂ approaches T₃, choking the heat you can add. Aircraft engines trade efficiency against power density — they do not chase η alone.
"Efficiency depends on how hot the burner runs." Cut. Ideal Brayton η depends on rp only — T₃ sets the work and the back-work ratio, not the efficiency. Raising T₃ buys power, not thermal efficiency (in the simple cycle).
"It's just Otto with different numbers." Kept, corrected. Otto adds heat at constant volume, Brayton at constant pressure — a different geometry and a far heavier back-work ratio. Same second law, different loop.
The red team's move: flip the exponent sign to η = 1 − rp(γ−1)/γ. Now "efficiency" falls as pressure rises and goes negative — physically absurd. The blue team's witness (window 7) is watching.
Flip the sign and η(rp=10) is no longer 0.482 and no longer rises with rp — the witness recomputes, disagrees with the known physics, and turns red. Nothing is faked; the attack is real and it is caught.