Rankine Cycle Efficiency Calculator

The Rankine cycle is the ideal thermodynamic cycle used to model steam power plants. Water is pumped to high pressure, boiled and superheated into steam, expanded through a turbine to produce work, then condensed back to liquid before the cycle repeats. Its thermal efficiency is eta = (Wturbine - Wpump) / Qin.

eta = ((h3-h4) - (h2-h1)) / (h3-h2), where h1 through h4 are the specific enthalpies in kJ/kg at the pump inlet, pump outlet, turbine inlet, and turbine outlet respectively. The numerator is net work output and the denominator is heat added in the boiler.

h1 is the enthalpy at the pump inlet, condenser exit, saturated liquid. h2 is the enthalpy at the pump outlet, boiler inlet, after the feedwater pump raises the pressure. h3 is the enthalpy at the boiler outlet, turbine inlet, usually superheated steam at high pressure and temperature. h4 is the enthalpy at the turbine outlet, condenser inlet, after expansion.

In practice, engineers look these enthalpies up from steam tables (or a steam property calculator) using the actual boiler pressure, condenser pressure, and superheat temperature of their system. This calculator intentionally takes enthalpies as direct input rather than pressures, since the steam-table lookup step is a separate, exact tabulated-data problem outside the scope of this tool.

Two reasons. First, real cycles have irreversibilities (friction, non-ideal expansion) that a Carnot cycle assumes away entirely. Second, and more fundamentally, heat addition in the boiler happens over a range of temperatures as water heats, boils, and superheats, not entirely at the single highest temperature the way an idealized Carnot cycle requires, so the average temperature of heat addition is lower than the peak temperature.

Lowering condenser pressure lowers the turbine outlet enthalpy h4, which increases turbine work (h3-h4) without changing the heat input Qin much, directly raising net work and efficiency. This is exactly why real power plant condensers operate under a vacuum, typically well below atmospheric pressure, rather than at atmospheric pressure or above.

Pumping a liquid (nearly incompressible) to higher pressure takes far less work than the pressure-volume work extracted from an expanding, low-density gas (steam) in the turbine. Pump work is often under 1 percent of turbine work, though this calculator still accounts for it explicitly since h2 and h1 are both required inputs.

In a saturated cycle, the boiler outlet (state 3) is saturated steam right at the boiling point for that pressure. In a superheated cycle, the steam is heated further past saturation before entering the turbine, raising h3 and generally increasing both net work and efficiency while also keeping the turbine exhaust drier (less moisture damage to turbine blades).

Steam power plants overwhelmingly use water as the working fluid because it is cheap, non-toxic, and has well-characterized thermodynamic properties, but the Rankine cycle itself is a general model. Organic Rankine cycles use other fluids with lower boiling points for waste-heat recovery and geothermal applications where source temperatures are too low for water to be practical.

The calculator shows an error, since h3 must exceed h2 for the boiler to actually be adding heat to the working fluid (Qin = h3-h2 must be positive). A Rankine cycle with zero or negative heat input is not physically meaningful.

No. The Rankine cycle operates between the same peak boiler temperature and condenser temperature, and the second law of thermodynamics guarantees the Carnot efficiency between those two temperatures is the absolute ceiling. Any correctly computed Rankine efficiency from valid steam-table enthalpies will always come out lower than the Carnot efficiency for the corresponding temperature range.