A wing of the estate · the power house

The Engine Room

The estate's power house at the working edge, where heat is turned into work and the great flywheel never gives back quite all you put in — every machine obeys the same two laws: you cannot win, and you cannot break even. Each bench proves its own thermodynamics exact.

Hot surfaces · mind the firebox

The Heat Engines

cycles · work · the efficiency wall

The bay belted closest to the firebox, where a working gas is taken round a closed loop and comes back having done net work — but never all the heat you fed it. Here the Second Law has a face you can operate.

The Carnot Engine

Operate the most efficient heat engine that can exist. Drag the T–S rectangle — top edge T_h, bottom T_c, width the gas you let expand — and watch the four P–V corners re-solve, the gold work-area grow, and the efficiency rise toward a wall it can never cross: η = 1 − T_c/T_h. Reshape the loop and you feel the wall.

self-test 11/11 ✓ · two derivations agree · no cycle beats Carnot 👹

The Demon's Ledger

A sorting demon that seems to make order from chaos for free — reduced to one molecule, one recorded bit. Cash the bit into work (W = H·kT·ln2, the very same entropy() the Shannon bench counts with) and the bill comes due in erasure: Landauer's kT·ln2 of heat. One ledger, two units — and the Second Law always balances.

self-test 9/9 ✓ · one ledger, two units · cheating impossible ⚙️

The Brownian Ratchet

A microscopic ratchet-and-pawl that looks like it could turn random jiggling into useful work — and, run honestly, provably cannot, once both ends sit at the same temperature. Heat one end and it becomes a real engine, bounded by the very same carnotEfficiency() this wing's Carnot bench proves. Watch it twitch at equilibrium and never turn.

self-test 15/15 ✓ · ⟨ω⟩=0 at ΔT=0 · Carnot ceiling held 🔁

The Stirling Cycle

The same ceiling, a different machine. Carnot joins its isotherms with curved adiabats; this one joins them with straight isochores and a regenerator — a thermal sponge that catches the heat dumped on the way down and hands it back on the way up. Turn the regenerator's effectiveness ε to 1 and a wholly different loop reaches the very same wall, η = 1 − T_c/T_h.

self-test 11/11 ✓ · ∮P dV = Q_in−Q_out · ε→1 reaches Carnot

↓ The microscopic floor the engine is made of

Heat, temperature and pressure are bulk names for the chaos of countless colliding molecules. One wing over, in the Cavern, the Maxwell–Boltzmann gas is that very floor: hundreds of hard discs whose random collisions relax into the bell-curve of speeds that is temperature — the substance every engine here actually runs on.