Steam Power Cycles: Rankine

The Rankine cycle step by step, efficiency, superheat, reheat, regeneration and a complete 4 MPa worked example.

On this page

  1. The ideal Rankine cycle
  2. Worked example: 4 MPa and 400 °C
  3. Raising the efficiency
  4. The effect of condenser pressure
  5. Reheat and regeneration
  6. Real plants
  7. FAQ

The ideal Rankine cycle

The Rankine cycle is the basis of every steam power plant. Water goes round a loop with four steps, each handled by one device:

  1. 1 → 2 Pump: the liquid from the condenser is pumped to boiler pressure. Little work is needed because liquid is nearly incompressible: wp = vf (pboiler − pcond).
  2. 2 → 3 Boiler (and superheater): heat turns the water into steam at constant pressure: qin = h₃ − h₂.
  3. 3 → 4 Turbine: the steam expands to condenser pressure, producing the work wt = h₃ − h₄ (isentropic in the ideal cycle).
  4. 4 → 1 Condenser: the wet steam condenses to saturated liquid, rejecting qout = h₄ − h₁.
The Rankine cycleBoilerq in 3 018 kJ/kgTurbinew = 1 070 kJ/kgCondenserq out 1 952 kJ/kgPumpw = 4.0 kJ/kg2 h = 195.83 h = 3 213.64 h = 2 143.8 (x = 0.816)1 h = 191.8Enthalpies in kJ/kg. Net work 1 066 kJ/kg from 3 018 kJ/kg of heat: thermal efficiency 35.3 percent. Pump work isunder 0.5 percent of the turbine work.
The ideal Rankine cycle with the numbers of the worked example.

η = (wt − wp) ÷ qin = 1 − qout ÷ qin

Worked example: 4 MPa and 400 °C

Worked example: a steam plant with a 10 kPa condenser

Steam leaves the boiler at 4 MPa and 400 °C (h₃ = 3 213.6 kJ/kg, s₃ = 6.7690 kJ/kg·K) and is condensed at 10 kPa (hf = 191.81, hfg = 2 392.1, sf = 0.6492, sfg = 7.4996, vf = 0.00101).

  • Turbine exit (isentropic): s₄ = s₃, so x₄ = (6.7690 − 0.6492) ÷ 7.4996 = 0.8160; h₄ = 191.81 + 0.8160 × 2 392.1 = 2 143.8 kJ/kg.
  • Turbine work: wt = 3 213.6 − 2 143.8 = 1 069.8 kJ/kg.
  • Pump work: wp = 0.00101 × (4 000 − 10) = 4.03 kJ/kg, so h₂ = 191.81 + 4.03 = 195.84.
  • Heat added: qin = 3 213.6 − 195.84 = 3 017.8 kJ/kg; heat rejected qout = 2 143.8 − 191.81 = 1 952.0.
  • Net work = 1 069.8 − 4.03 = 1 065.8 kJ/kg; efficiency η = 1 065.8 ÷ 3 017.8 = 35.3 percent. The Carnot limit between 400 °C and 45.8 °C is 53 percent.
  • For a 50 MW plant: steam flow = 50 000 ÷ 1 065.8 = 46.9 kg/s (169 t/h); boiler heat 141.6 MW; condenser duty 91.6 MW, which needs about 2 188 kg/s of cooling water for a 10 K rise.

Notice that the condenser rejects more than 65 percent of the heat. That is the second law at work (see The Second Law, Entropy and Carnot), and the reason every power station has cooling towers or a river.

Raising the efficiency

Anything that raises the average temperature at which heat is added, or lowers the temperature at which it is rejected, helps:

  • Lower condenser pressure (a deeper vacuum): limited by the cooling water temperature and the wetness of the exhaust.
  • Higher boiler pressure: raises the heat-addition temperature, but makes the exhaust wetter unless you superheat or reheat.
  • Superheat to higher temperature: raises the average temperature and dries the exhaust; limited by metallurgy (about 540 to 600 °C in conventional plants, 600 to 620 °C in ultra-supercritical).
  • Reheat: expand part way, return the steam to the boiler to be reheated, then expand again.
  • Regeneration: bleed some steam from the turbine to preheat the feed water, so less heat is added at low temperature.

The effect of condenser pressure

Worked example: condenser at 50 kPa instead of 10 kPa

The same boiler, with the condenser at 50 kPa (Tsat = 81.3 °C), as in a district-heating plant that wants warm water out of the condenser.

  • x₄ = (6.7690 − 1.0912) ÷ 6.5019 = 0.8733; h₄ = 340.54 + 0.8733 × 2 304.7 = 2 353.1 kJ/kg.
  • wt = 860.5 kJ/kg; η = 29.9 percent against 35.3 percent at 10 kPa: the electricity falls, but the rejected heat is now useful at 81 °C.
  • This is the logic of combined heat and power: giving up some electrical efficiency to use the “waste” heat usually raises the overall fuel use effectiveness to 70 or 80 percent.

Reheat and regeneration

A modern station boiler at 16 to 25 MPa and 540 to 600 °C with one or two reheats and 6 to 8 feed-water heaters reaches 40 to 45 percent, and supercritical designs above 22 MPa about 45 to 48 percent. Open and closed feed-water heaters, a deaerator, and a boiler feed pump complete the real cycle. The principles are the same as the ideal cycle: more of the heat is added at high temperature.

Real plants

Real turbines (80 to 90 percent isentropic efficiency, see The Second Law, Entropy and Carnot), pipe pressure drops, boiler losses (see Combustion and Boiler Efficiency), auxiliary power and generator losses cut the plant efficiency to well below the ideal figure. With an 85 percent turbine and an 80 percent pump, the cycle above delivers 30.0 percent of the heat added, before boiler and generator losses. Small steam turbines for process plants and back-pressure sets exhaust at 2 to 10 bar into the process steam system instead of a condenser (see Steam Systems, Traps and Troubleshooting).

Related

FAQ

Why is Rankine used rather than Carnot?

A Carnot steam cycle would compress a wet mixture, which pumps cannot do well, and the efficiency gain is small. Rankine condenses completely, so a cheap pump handles only liquid.

Why is condenser pressure so low?

It lowers the temperature of heat rejection. A condenser at 5 to 10 kPa abs is a strong vacuum, kept by cooling water and air removal.

What limits boiler temperature?

Metal creep and oxidation. Higher alloys allow higher temperatures at higher cost.

What is the difference between steam rate and efficiency?

Steam rate is kg of steam per kWh (here 3 600 ÷ 1 065.8 = 3.38 kg/kWh). Efficiency is output per heat input. Both rank plants.

References

  • Çengel, Y. A. and Boles, M. A., Thermodynamics: An Engineering Approach, McGraw-Hill (vapor power cycles).
  • Wagner, W., Kretzschmar, H.-J., International Steam Tables (IAPWS-IF97), Springer.
  • Babcock and Wilcox, Steam: Its Generation and Use, 42nd edition.

Last reviewed: October 2026. Table values come from standard steam tables.