Rankine Cycle Efficiency (Ideal)

First-cut thermal efficiency, work, and heat for an ideal Rankine steam power cycle from your four state enthalpies.

Inputη = wₙₑₜ / qᵢₙ = [(h₁−h₂) − (h₄−h₃)] / (h₁−h₄) , BWR = wₚ / wₜ

h₁ — turbine inlet enthalpy (kJ/kg)or enter Btu/lb — converts to kJ/kgh₂ — turbine exit enthalpy (kJ/kg)or enter Btu/lb — converts to kJ/kgh₃ — pump inlet (sat. liquid) enthalpy (kJ/kg)or enter Btu/lb — converts to kJ/kgh₄ — pump exit (boiler inlet) enthalpy (kJ/kg)or enter Btu/lb — converts to kJ/kgMass flow rate (optional, for power) (kg/s) — optionalor enter lb/s — converts to kg/s

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The engineering

The Rankine cycle is the workhorse of steam power: pump liquid to boiler pressure (3→4), add heat to make superheated steam (4→1), expand through the turbine (1→2), then reject heat in the condenser (2→3). Feed the four state enthalpies from your steam tables and this card returns the per-kilogram work and heat terms plus overall thermal efficiency. Add a mass flow to get actual plant power and boiler duty.

The back work ratio is the giveaway that steam beats gas: pump work is typically under 1% of turbine work because you're compressing an incompressible liquid, so a gas turbine's 40–80% BWR dwarfs a steam plant's ~0.4%. If your efficiency lands above the Carnot limit set by boiler and condenser temperatures, or your pump work is a large fraction of turbine work, recheck which enthalpy went where.

This is the ideal (isentropic) cycle — real turbines and pumps carry isentropic efficiencies, so use h₂ and h₄ at the actual (not ideal) exit states if you want the actual efficiency.

Where this math comes from

William John Macquorn Rankine, a Glasgow engineering professor, laid out the thermodynamics of the vapor power cycle in his 1859 Manual of the Steam Engine and Other Prime Movers — the first textbook to treat steam engines as a rigorous energy-balance problem rather than a craft. He gave working engineers the entropy-and-enthalpy bookkeeping that let them predict, not just build, an engine's performance.

The cycle that carries his name codified what Watt, Trevithick, and a century of millwrights had done by feel. Every modern coal, nuclear, geothermal, and concentrating-solar plant still runs a Rankine cycle, and the analysis in this card is exactly the four-point energy balance taught from Moran & Shapiro's Fundamentals of Engineering Thermodynamics.

1824Sadi CarnotEstablishes the maximum efficiency bound any heat cycle can approach.
1859W. J. M. RankinePublishes the vapor-cycle analysis in his steam-engine manual.
1865Rudolf ClausiusFormalizes entropy, giving the isentropic turbine/pump steps their footing.
1934Mollier / steam-table lineageh–s diagrams and standardized steam tables make state-point lookup routine.
2018Moran, Shapiro et al.9th-edition FEE Thermodynamics cements the four-state teaching form this card uses.

See the full timeline of the math behind every calculator →

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