MechanicalThermodynamics

Ideal Rankine Cycle

Follow water through a pump, boiler, turbine, and condenser

Difficulty

Intermediate

Read time

6 min

Review status

Needs review

Concept sketch

Ideal Rankine Cycle

Illustrative model, not experimental data

Overview

The Rankine cycle models a steam power plant by separating heat transfer from work transfer in four steady-flow devices. Following the same state numbering through the loop makes the energy balance much easier to organize.

How to read it

Track the same kilogram of fluid around the four devices.
Distinguish work output from work input.
Check that net work equals heat input minus heat rejection.

When to use it

Organizing a basic steam-cycle calculation.
Interpreting the effect of turbine and pump losses.

Number the states around the loop

State 1 is saturated liquid leaving the condenser. The pump raises it to boiler pressure at state 2. The boiler adds heat until state 3 at the turbine inlet. The turbine expands the steam to state 4, then the condenser returns it to state 1.

What ideal means here

Treat pump and turbine as adiabatic and internally reversible, so their ideal paths are isentropic. Neglect pipe pressure drops and changes in kinetic and potential energy. Boiler and condenser heat transfer occur at approximately constant pressure. Real devices require efficiency and loss corrections.

Use enthalpy differences per kilogram

With h in kJ/kg, the turbine work output is h₃ − h₄, pump work input is h₂ − h₁, and boiler heat input is h₃ − h₂. Subtract pump input from turbine output before calculating efficiency.

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

Property values come from the state

Use consistent steam tables or a water-property model for pressure, temperature, entropy, and phase. The ideal-gas equation is not a substitute in the saturated liquid–vapor region. Convert pressure units before estimating pump work from v Δp.

Worked example

For an illustrative four-state cycle, take h₁ = 200, h₂ = 205, h₃ = 3200, and h₄ = 2200 kJ/kg. These supplied values are for an energy-balance exercise, not a steam-table lookup.

1.Separate turbine output, pump input, and boiler heat.
$w_{t} = 1000 w_{p} = 5 q_{in} = 2995 [kJ/kg]$
2.Find net work and thermal efficiency.
$w_{net} = 995 kJ/kg η_{th} = \frac{995}{2995} = 0.3322$
3.Check conservation of energy.
$q_{out} = 2200 - 200 = 2000 2995 - 2000 = 995 [kJ/kg]$

The illustrative cycle converts 33.2% of supplied heat into net work.

Key takeaways

The cycle produces net work by adding and rejecting heat.
Each state needs a physically consistent property description.
Thermal efficiency uses net work, not turbine work alone.

Common mistakes

Ignoring pump work without checking its size.
Mixing kJ/kg with J/kg.
Using saturation quality outside the two-phase region.

Related formulas

First Law of Thermodynamics Carnot Efficiency

Related concepts

Rankine Reheat Cycle Vapor-Compression Refrigeration

Source

Aiman Amri — rankine_cycle.ipynb

Adapted from the notebook model under MIT. Explanations, diagrams, and worked examples were created for FormuLab.

Adapted from Aiman Amri, Mechanical Engineering Calculations.

MIT license and copyright notice

Rewritten as a concept lesson with explicit assumptions, original diagrams, and a new worked example. External images, executable code, and notebook outputs are not included.

Ideal Rankine Cycle

Ideal Rankine Cycle

How to read it

When to use it

Number the states around the loop

What ideal means here

Use enthalpy differences per kilogram

Property values come from the state

Worked example

Product

Company

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