The steam power plant that still makes most of the world's electricity: water pumped, boiled, expanded through a turbine, condensed, and pumped again — a closed loop across the vapour dome. Rendered, not quoted. The efficiency is built live from enthalpy differences, the pump work stays tiny because a liquid barely compresses, and the whole cycle is held below its Carnot ceiling.
source W. J. M. Rankine, A Manual of the Steam Engine and Other Prime Movers (Griffin, 1859) — 19th-c. facsimile scan, no canonical DOI, so AMBER.
Four steady-flow devices on one loop. Each is bookkept by the first law dU = dQ − dW as a specific enthalpy step:
| 1→2 pump (liquid) | wp=v·ΔP |
| 2→3 boiler (const P) | qin=h₃−h₂ |
| 3→4 turbine | wt=h₃−h₄ |
| 4→1 condenser (const P) | qout=h₄−h₁ |
Thermal efficiency η = wnet/qin = ((h₃−h₄) − (h₂−h₁)) / (h₃−h₂). Because the pump acts on a nearly incompressible liquid, wp ≪ wt.
A real closed cycle living under the-carnot-cycle: its efficiency can never exceed 1 − Tc/Th between condenser and boiler temperatures. It is the vapour cousin of the all-gas the-brayton-cycle — same pump/heat/expand/reject skeleton, but Rankine crosses the saturation dome and boils, which is exactly what makes the pump work vanish.
Re-derives η from the current engine state on every tick and compares it to the sealed boot value. Green while faithful; flips red the instant the RED-team tamper (window 6) changes the sign of the pump term.
witness idle
Steam-table working point (3 MPa boiler, 10 kPa condenser, superheat to 350 °C):
| h₁ sat-liquid @10 kPa | 191.81 kJ/kg |
| v₁ liquid specific vol | 0.00101 m³/kg |
| P₁=P₄ condenser | 10 kPa |
| P₂=P₃ boiler | 3000 kPa |
| h₃ superheated @3 MPa | 3115.3 kJ/kg |
| h₄ turbine exit (s₄=s₃) | 2135.8 kJ/kg |
| Tc / Th (sat) | 318.96 / 507.0 K |
| wpump = v·(P₂−P₁) | – |
| wturbine = h₃−h₄ | – |
| wnet = wt − wp | – |
| qin = h₃−h₂ | – |
| wp / wt ratio | – |
| ηRankine | – |
| ηCarnot ceiling | – |
Proven result at boot, after the fail-loud selfcheck:
η pending…
η ≈ 33.4 % — a third of the boiler heat becomes work, the rest is dumped to the condenser at constant pressure. Below the Carnot ceiling, and the pump costs three parts in a thousand.
"Superheat and reheat forever — just keep raising η toward 1." Wrong at the wall: the cycle is capped by 1 − Tc/Th. Metallurgy fixes the turbine-inlet temperature and the condenser cannot fall below ambient, so Th and Tc are pinned. Real plants also lose to irreversible expansion (turbine isentropic efficiency < 1) and to moisture eroding the last turbine stages once quality drops.
"The pump work is negligible, drop it entirely."
→ Small (≈3 kJ/kg here) but not zero; at supercritical pressures it grows and must stay in the ledger, or η is overstated.
"Rankine can equal Carnot with enough superheat."
→ No. Heat is added over a range of temperatures, so mean-add temperature stays below Th; η is strictly less than the Carnot value.
"Boiler and condenser change the pressure as they add heat."
→ Both exchange heat at essentially constant pressure; that is what the flat 2→3 and 4→1 legs mean.
The planted void: flip the pump term's sign so wnet = wt + wp — energy from nowhere, η overstated. The witness (7) catches it live.