The Rankine Cycle — How Steam Powers the World
The Rankine Cycle — How Steam Powers the World
About 80% of the world's electricity — from coal and gas plants to nuclear reactors — is generated by a single thermodynamic cycle: the Rankine cycle. Water is converted to steam, expanded through a turbine to generate electricity, condensed back to liquid, and pumped back to pressure. Round and round, 24 hours a day, powering civilisation.
The Four Stages
- 1 → 2: Pump. Liquid water is pumped from condenser pressure to boiler pressure. Pumping a liquid requires very little work — this is why the Rankine cycle is so efficient compared to the Brayton cycle.
- 2 → 3: Boiler (Heat Addition). Water is heated at constant pressure until it becomes superheated steam. The heat source can be burning fuel, nuclear fission, concentrated solar, or geothermal energy.
- 3 → 4: Turbine. Steam expands through the turbine, doing work (generating electricity). The turbine is the heart of the power plant — modern steam turbines exceed 90% isentropic efficiency.
- 4 → 1: Condenser (Heat Rejection). Spent steam is condensed back to liquid water, rejecting heat to a river, cooling tower, or the sea.
Rankine Cycle Efficiency
The ideal (isentropic) thermal efficiency compares net work to heat input:
$$\eta_{th} = \frac{W_{turbine} - W_{pump}}{Q_{boiler}} = 1 - \frac{Q_{condenser}}{Q_{boiler}}$$
The Carnot efficiency sets the upper limit for any heat engine operating between temperatures $T_H$ (boiler) and $T_L$ (condenser):
$$\eta_{Carnot} = 1 - \frac{T_L}{T_H}$$
Real Rankine cycles achieve 35–46% thermal efficiency, while the Carnot limit at typical steam conditions is around 50–60%. The gap arises from irreversibilities in the turbine, heat transfer, and condenser.
Back Work Ratio — Why Steam is Better Than Gas
The back work ratio is the fraction of turbine output consumed by the pump:
$$BWR = \frac{W_{pump}}{W_{turbine}}$$
For the Rankine cycle, $BWR \approx 1$–$3\%$ — almost all turbine work is available as net output. Compare this to the Brayton cycle where $BWR \approx 40$–$50\%$! Liquids are vastly easier to pump than gases to compress. This is the fundamental thermodynamic advantage of steam power.
Boiler: $T_H = 550°$C $= 823$ K. Condenser: $T_L = 40°$C $= 313$ K. Turbine efficiency $\eta_t = 88\%$. Estimate thermal efficiency.
- Carnot limit: $\eta_C = 1 - 313/823 = 61.9\%$
- Ideal Rankine would achieve roughly 42% at these conditions (using steam tables).
- With $\eta_t = 88\%$, actual thermal efficiency $\approx 0.88 \times 42 \approx 37\%$.
- This means for every 100 MJ of coal burned, 37 MJ becomes electricity and 63 MJ is rejected as waste heat — mostly to the condenser cooling water.
Supercritical and ultra-supercritical coal plants push steam to 600°C and 250+ bar, achieving efficiencies above 45%. Combined-cycle gas plants pair the Brayton cycle with a Rankine cycle to exceed 60% — nearly double the efficiency of a simple steam plant from the 1950s.