Rankine Cycle Thermal Efficiency (Simplified)
Rankine Cycle Thermal Efficiency (Simplified)
The Rankine cycle is the thermodynamic backbone of most steam power plants — water is boiled, expanded through a turbine to generate work, condensed, and pumped back to the boiler — and its thermal efficiency, how much of the heat input actually becomes net electrical output, is the single number utilities use to compare plant designs and fuel costs. While a full Rankine analysis tracks enthalpy at each of the four cycle points from steam tables, the same first-law result can be reached directly from the heat added in the boiler and the heat rejected in the condenser, since whatever heat is not rejected must have left as net work.
By the first law, the thermal efficiency is eta = 1 - Qc/Qh, one minus the ratio of heat rejected to heat added. where Qh is the heat added to the working fluid in the boiler (per unit mass) and Qc is the heat rejected in the condenser (per unit mass).
Inputs
Q_h := 2500 kJ/kg=2.5e+06 m^2/s^2
Q_c := 1600 kJ/kg=1.6e+06 m^2/s^2
Since energy entering as boiler heat either leaves as condenser heat or as net turbine work, the fraction not rejected is exactly the fraction converted to usable work — the cycle efficiency.
eta_rankine := 1 - Q_c/Q_h=0.36
Results
An efficiency of 36% is a realistic value for a simple subcritical Rankine cycle, well below the Carnot limit between the same boiler and condenser temperatures because of the irreversibilities in real expansion and heat transfer. Real power plants push efficiency higher — often into the low-to-mid 40s percent — through reheat, regenerative feedwater heating, and higher boiler pressures, none of which are captured in this simplified heat-in/heat-out bookkeeping. Any Qc/Qh ratio close to 1 would signal a cycle barely producing net work, which in practice would point to a condenser or boiler operating far closer together in temperature than a real plant would allow.
Assumptions & limitations
- First-law (energy balance) estimate only, not a full steam-table cycle analysis.
- Ignores pump work, which is normally small compared to turbine work.
- No reheat or regenerative feedwater heating included.
- Steady-state, closed-cycle operation with no working-fluid losses.