Thermodynamics

Rankine Cycle Thermal Efficiency

The thermal efficiency of a basic Rankine cycle compares net turbine-minus-pump work with boiler heat input.

η_{th} = \frac{( h _{3} - h _{4} ) - ( h _{2} - h _{1} )}{h _{3} - h _{2}}

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Source & review

Difficulty

Intermediate

Read time

4 min

Prerequisites

Consistent SI units, algebra, and the physical assumptions listed below

Review statusNeeds review

Source

Teng-Jui Lin — Equation Sheets

Adapted from Teng-Jui Lin, Equation Sheets — Mechanical Engineering, under CC BY 4.0.

Adapted notation and added original explanations, variables, assumptions, applications, and a worked example. Renumbered states to pump 1→2, boiler 2→3, turbine 3→4, condenser 4→1, matching FormuLab's concept lesson.

Definition

Understanding the core concept

The thermal efficiency of a basic Rankine cycle compares net turbine-minus-pump work with boiler heat input. Keeping a single state-numbering convention prevents pump work or heat rejection from being placed on the wrong side of the balance.

Variables & Units

Understanding each component

Symbol	Meaning	Units
$η_{th}$	Cycle thermal efficiency as a fraction	$1$
$h_{1}$	Specific enthalpy at condenser exit / pump inlet	$kJ/kg$
$h_{2}$	Specific enthalpy at pump exit / boiler inlet	$kJ/kg$
$h_{3}$	Specific enthalpy at boiler exit / turbine inlet	$kJ/kg$
$h_{4}$	Specific enthalpy at turbine exit / condenser inlet	$kJ/kg$

Real-World Applications

Where this formula is used in practice

Steam-cycle balances

Compare net work output with heat supplied in the boiler.

Model checking

Confirm that pump input is subtracted from turbine output.

Worked Example

Step-by-step calculation with real numbers

Problem

Use illustrative enthalpies h₁ = 200, h₂ = 205, h₃ = 3200, h₄ = 2200 kJ/kg. They are supplied energy-balance values, not a steam-table lookup.

Given

h_{1} = 200, h_{2} = 205 [kJ/kg]

h_{3} = 3200, h_{4} = 2200 [kJ/kg]

Solution

η_{th} = \frac{( h _{3} - h _{4} ) - ( h _{2} - h _{1} )}{h _{3} - h _{2}}

η_{th} = \frac{( 3200 - 2200 ) - ( 205 - 200 )}{3200 - 205}

Final Answer

η_{th} = 0.332220

Formula Guide

Info

DifficultyIntermediate

Read Time4 min

PrerequisitesConsistent SI units, algebra, and the physical assumptions listed below

Tools

Source & review

StatusNeeds review

Last reviewedPending

Source

Teng-Jui Lin — Equation Sheets

Adapted from Teng-Jui Lin, Equation Sheets — Mechanical Engineering, under CC BY 4.0.

Assumptions

• The four steady-flow devices form a basic Rankine loop; neglect kinetic and potential energy changes.
• Pump and turbine are adiabatic; use consistent enthalpy references and units.
• The ideal Rankine model additionally makes pump and turbine isentropic; actual enthalpies may instead be supplied for a real-device energy balance.

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