The turbine converts steam enthalpy into shaft work. In a perfect (isentropic) turbine, entropy stays constant as steam expands — all available energy becomes work. Real turbines lose energy to blade friction, flow separation, tip leakage, windage, and moisture erosion. The isentropic efficiency tells you what fraction of the ideal work you actually extract.

A value of η_t = 0.88 means 88% of the theoretically available work is extracted; 12% becomes heat that raises the exhaust enthalpy above the ideal value. This higher exhaust enthalpy (h₄ > h₄s) means more heat must be rejected in the condenser, directly reducing cycle thermal efficiency.

The pump raises water pressure from condenser to boiler pressure. In an ideal pump, only liquid incompressibility matters — the work equals v_f × ΔP (specific volume × pressure rise). Real pumps waste energy in fluid recirculation, cavitation, mechanical friction, and hydraulic losses. The pump efficiency tells you how much extra work must be supplied compared to the ideal.

Unlike the turbine where low efficiency means you get less output, low pump efficiency means you must supply more work. Because pump work is typically only 0.1–2% of turbine work in a Rankine cycle, pump efficiency has a small but measurable effect on the Back Work Ratio — the fraction of turbine work consumed by the pump.

The synchronous generator converts turbine shaft rotation into electrical power. Losses are copper losses (I²R heating in windings), iron losses (eddy currents and hysteresis in the stator core), mechanical losses (bearing friction, windage of the rotor), and excitation losses. Generators are among the most efficient machines ever built — losses are engineered to be tiny.

At η_g = 0.98, the generator converts 98% of shaft work to electricity. The remaining 2% heats the windings and must be removed by forced ventilation or hydrogen cooling in large machines. Generator efficiency is nearly constant across load, making it almost a fixed scaling factor on net power.

Boiler efficiency measures how much of the fuel's chemical energy is successfully transferred to the working fluid (steam). Losses include stack losses (hot flue gas exits with unused heat), radiation losses (heat lost through boiler walls), incomplete combustion (CO, unburned hydrocarbons), blowdown losses, and moisture in fuel. The HHV (Higher Heating Value) used in this calculator assumes all latent heat of water vapour in combustion products is recovered.

Boiler efficiency is typically the largest single source of loss in a power plant. A 10% improvement in boiler efficiency from 80% to 88% directly increases overall plant output by the same factor. Modern supercritical boilers achieve 92–95% efficiency by recovering heat from flue gas (economisers, air preheaters) and minimising excess air.

The thermal efficiency is the most fundamental measure of how well the thermodynamic cycle itself converts heat into work — before accounting for generator or boiler losses. It answers: "Of all the heat added in the boiler, what fraction became net shaft work at the turbine coupling?"

This is the standard metric used to compare different cycle configurations. A basic Rankine cycle running at 300°C / 3 MPa might achieve 28–32%. The same cycle with superheat to 560°C might reach 40–44%. Regenerative and reheat cycles can push this further. Thermal efficiency is always lower than the Carnot limit because real processes are irreversible — friction, heat transfer across finite temperature differences, and non-isentropic compression/expansion all generate entropy.

The Carnot efficiency is the maximum thermodynamically possible efficiency for any heat engine operating between two fixed temperature reservoirs. It is not a real cycle — no real process achieves it. Rather, it is a mathematical boundary derived from the Second Law of Thermodynamics.

Why must temperatures be in Kelvin? Because the Carnot formula uses the ratio T_C / T_H. This ratio only has physical meaning on an absolute temperature scale. On the Celsius scale, 0°C is not "zero heat energy" — it is 273.15 K. Using °C in the formula gives a physically wrong (and often absurd) result. The calculator always converts to Kelvin internally. In US mode, it converts to Rankine (°R = °F + 459.67), which is the US absolute scale.

In the Rankine cycle context, T_H is approximately the mean temperature at which heat is added (not the peak turbine inlet temperature) and T_C is the condenser saturation temperature. This is why the Carnot efficiency shown uses boiler and condenser temperatures — it is a useful comparison benchmark, not an exact calculation.

The Second Law efficiency answers: "How well does this cycle use its thermodynamic opportunity?" It is the ratio of what you achieve (thermal efficiency) to the maximum you could theoretically achieve (Carnot efficiency) for the same temperature limits.

A 2nd Law efficiency of 70% means your cycle extracts 70% of the maximum possible work from the available temperature difference. The remaining 30% is destroyed by irreversibilities — friction, heat transfer across temperature gradients, and mixing. This is a more meaningful comparison between cycles than thermal efficiency alone, because it normalises for the temperature conditions.

Real world-class steam plants achieve 2nd Law efficiencies of 75–85%. Simple cycles or older plants may be 55–65%. The difference is mostly turbine quality, boiler design, and use of regeneration and reheat.

The overall plant efficiency is the bottom-line number — it tells you how much of the fuel's total chemical energy ends up as electricity at the generator terminals. It multiplies the three major efficiency chains: how well the thermodynamic cycle converts heat to shaft work (η_th), how well the shaft drives the generator (η_g), and how much of the fuel's heat actually reached the working fluid (η_b).

This is the number used for carbon accounting, fuel cost calculations, and regulatory reporting. A plant with η_th = 42%, η_g = 98%, and η_b = 90% has overall plant efficiency of 42% × 98% × 90% = 37%. Of every 100 units of fuel energy burned, only 37 become electricity.

The Back Work Ratio is the Rankine cycle's great advantage over the gas turbine. In a gas turbine (Brayton cycle), compressing a gas requires enormous work — BWR is 40–80%. In the Rankine cycle, you pump liquid water, which requires almost no work because liquids are nearly incompressible. The BWR for Rankine cycles is typically only 0.1–3%.

This is why the Rankine cycle is the dominant technology for large-scale thermal power: almost all the turbine output is available as net work. The pump work is negligible in comparison. A BWR of 0.4% means only 4 units of every 1,000 turbine output units are used to drive the pump.

Heat rate is the standard industry metric for power plant performance, especially in the US. It tells you how many kilojoules (or BTU) of fuel energy are required to produce one kilowatt-hour of electricity. The relationship is simply the inverse of thermal efficiency, scaled to the unit of kWh.

A heat rate of 8,000 kJ/kWh means the plant is 45% efficient (3600/8000 = 0.45). World-class ultra-supercritical plants achieve heat rates of 7,200–7,800 kJ/kWh. Older subcritical plants may be 10,000–12,000 kJ/kWh. Every 1% reduction in heat rate saves approximately 1% on fuel costs — a critical economic metric.