Rankine Efficiency

Overview

The Rankine cycle is the ideal cycle for steam power plants. It describes the conversion of heat into work using water/steam as the working fluid.

Formula

$\eta = \frac{W_{net}}{Q_{in}} = \frac{(h_1 - h_2) - (h_4 - h_3)}{h_1 - h_4}$

Calculator

Notes

• Results are approximate and should be verified for critical applications
• Input values should be within reasonable engineering ranges

Rankine vs Carnot Cycle

The Rankine cycle addresses a practical limitation of the Carnot cycle. In a Carnot cycle, steam is only partially condensed, requiring a large compressor to handle the two-phase mixture. The Rankine cycle improves upon this by fully condensing the steam to liquid before compression, enabling the use of a smaller, more efficient feed pump.

Efficiency Formula

The Rankine cycle efficiency is defined as:

$\mu_R = \frac{H_i - H_e}{H_i - h_c}$

Where:

• $\mu_R$ — Rankine cycle efficiency (dimensionless)
• $H_i$ — Specific enthalpy at turbine inlet (kJ/kg)
• $H_e$ — Specific enthalpy at turbine outlet (kJ/kg)
• $h_c$ — Sensible heat (specific enthalpy) of saturated liquid in the condenser exhaust (kJ/kg)

The numerator $(H_i - H_e)$ represents the work extracted by the turbine, while the denominator $(H_i - h_c)$ represents the total heat input to the cycle from the boiler.

Key Characteristics

Parameter	Carnot Cycle	Rankine Cycle
Compression medium	Liquid-vapor mixture	Saturated liquid only
Pump size	Large	Small
Condensation	Partial	Complete
Practical application	Theoretical limit	Practical power plants

Notes

The Rankine cycle is the foundational thermodynamic cycle for steam-based power generation, including coal, nuclear, and concentrated solar power plants. The key advantage over the Carnot cycle is the reduction in pumping work, as compressing a liquid requires significantly less energy than compressing a two-phase mixture.

References

• Original Source