THE STIRLING ENGINE

Two isotherms, two isochores, and a regenerator that hands heat from one leg to the next. Rejected on the cooling leg, returned on the heating leg — so it never touches the fuel bill. With an ideal regenerator the closed-cycle engine reaches the Carnot ceiling; switch it off and the same hardware collapses to a fraction of it. Rendered, not quoted.

source Stirling, R. — British Patent No. 4081 (1816), "Improvements for Diminishing the Consumption of Fuel..."; first description of the regenerator ("economiser"). No stable digital facsimile of the original specification — AMBER. Cycle facts cross-checked against hotairengines.org/stirling-1816 and Stirling cycle.

Blue team · builds & defends
3

THE MODEL

One mole of a diatomic ideal gas, γ = 7/5, cycled clockwise:

1 → 2isothermal expand @ Th
2 → 3isochoric cool → regenerator
3 → 4isothermal compress @ Tc
4 → 1isochoric heat ← regenerator

Isothermal legs trade heat with the reservoirs: Q = nRT ln(V2/V1). Constant-volume legs trade heat only with the regenerator: Q = nCvΔT, Cv = R/(γ−1) = 2.5R.

5

THE LINEAGE

The regenerator engine — Stirling 1816. Isotherms and isochores stitched by a heat-storing mesh that lets a closed cycle touch the-carnot-cycle efficiency in the ideal limit.

It is the closed-cycle counterpoint to the-otto-cycle: Otto burns and vents; Stirling seals the gas and recycles the intermediate heat internally instead of throwing it away.

7

THE WITNESS

Re-runs the engine's law live against the panel state. Confirms while honest; flips red the instant the regenerator is faked.

witness idle

Checks: with regenerator ⇒ η = 1 − Tc/Th; without ⇒ strictly lower; reported η never exceeds Carnot.

The machine
4

DATA IN in ▼

▼ the machine ▼
0

THE PANEL LIT

Qh in (isothermal @ Th)—
regenerator store = return—
Wnet = enclosed area—
heat charged to hot reservoir—
efficiency η = Wnet/Qin—
Carnot ceiling 1 − Tc/Th—
▼ proven out ▼
8

DATA OUT out ▼

With the regenerator installed the closed cycle reaches the Carnot ceiling exactly:

η = —

Boot value, set only after selfcheck() returns true. The regenerator's constant-volume heat cancels leg-for-leg, so the fuel pays for the hot isotherm alone.

Red team · attacks & breaks
1

THE ADVERSARY WALL

"Closed cycle at Carnot efficiency? Then a real Stirling engine outruns the second law." — No. Carnot is the ceiling, not a bonus. The ideal Stirling ties it only because the regenerator makes the constant-volume heat internal and reversible. Any real regenerator has dead volume, finite ΔT, and pumping loss, so real η sits well below this number. The wall is the reservoir pair: no closed cycle beats 1 − Tc/Th.
2

THE GRAVEYARD

"The isochoric legs make free heat, so η > Carnot."
→ The regenerator only recycles heat between two legs of the same gas; it creates none. It cancels, it does not credit.

"Without a regenerator the Stirling still runs near Carnot."
→ Then the constant-volume heating draws from the hot reservoir; η falls to ~19.6% here — a factor of three.

"Compression ratio sets efficiency like in Otto."
→ Ideal Stirling η depends on Tc/Th only; V2/V1 moves the work, not the ratio.

6

THE TAMPER

The disclosed planted void: pull the regenerator but keep charging the fuel bill for the hot isotherm only — counting the constant-volume heat as free, so the reported η jumps to Carnot while the real one has collapsed.

The WITNESS (7) recomputes the honest denominator and catches the overstatement live.