wunder beta

📘 How do you analyze a Rankine cycle?

Intermediate case study of Rankine cycle thermodynamics

12
lessons
~30 min
to learn
Adults
level
Start the course →

What you’ll learn

  1. Selecting the Rankine Cycle CaseIdentify why the Rankine cycle is the dominant vapor power model and state its four principal components.The Rankine cycle models steam power plants with boiler, turbine, condenser, and pump. Its closed-loop design allows repeated use of the working fluid. Efficiency is limited by the temperatures at which heat is added and rejected.
  2. Steam Tables and Property EvaluationLocate and interpolate steam-table values for pressure, temperature, enthalpy, and entropy at key cycle states.Steam tables supply h, s, and v for compressed liquid, saturated mixture, and superheated vapor regions. Interpolation between tabulated pressures and temperatures yields the exact state properties needed for calculations.
  3. First Law on the BoilerApply the steady-flow energy equation to the boiler and compute heat input per unit mass.Neglecting kinetic and potential terms, q_in equals h_3 minus h_2. The calculation uses steam-table enthalpies at the boiler exit and economizer inlet. This step quantifies the largest energy transfer in the plant.
  4. Isentropic Turbine ExpansionCalculate turbine work and exit state for both ideal and actual expansions using the isentropic-efficiency definition.Isentropic efficiency relates actual work to the ideal work between the same inlet state and exit pressure. The actual exit enthalpy is found by rearranging the efficiency equation. Entropy generation appears as the difference between actual and ideal exit entropies.
  5. Condenser Heat RejectionDetermine condenser heat rejection and the minimum temperature difference permitted by the second law.The condenser duty equals the enthalpy drop from turbine exit to saturated-liquid exit. The second law sets the lower bound on rejection temperature through the entropy balance. Real condensers operate 5–10 °C above the cooling-water inlet temperature.
  6. Pump Work and Liquid CompressionCompute pump work using the incompressible-liquid approximation and compare it with turbine work.For incompressible flow, w_pump equals v times Delta P. The value is two orders of magnitude smaller than turbine work. The approximation holds because liquid specific volume changes little with pressure.
  7. Thermal Efficiency CalculationCalculate thermal efficiency from the first-law quantities already determined and identify the dominant loss.Efficiency equals 1 minus q_out over q_in. The condenser rejects the largest fraction of input energy. Increasing average heat-addition temperature raises efficiency while lowering rejected heat.
  8. T-s and P-v DiagramsSketch the ideal Rankine cycle on T-s and P-v diagrams and relate enclosed areas to work and heat transfers.On the T-s diagram, heat addition and rejection appear as horizontal lines while isentropic processes are vertical. Area under the upper line is q_in; area under the lower line is q_out. Net work is the enclosed area.
  9. Real Irreversibilities and LossesQuantify the effect of turbine and pump inefficiencies plus pressure drops on cycle performance.Each irreversibility increases exit entropy and therefore raises the condenser heat load. The resulting efficiency drop is calculated by repeating the energy balances with non-ideal component models. Entropy-generation terms locate the largest losses.
  10. Exergy Destruction BreakdownCalculate exergy destruction for each component and rank the components by loss magnitude.Exergy balance equates inlet exergy plus work to outlet exergy plus destruction. The boiler term dominates because combustion occurs far from the steam temperature. Condenser destruction is smaller because its temperature is closer to ambient.
  11. Cycle Optimization OptionsEvaluate the thermodynamic benefit and practical constraints of reheat, regeneration, and supercritical operation.Reheat reduces moisture in the low-pressure turbine and increases average heat-addition temperature. Regeneration preheats feedwater with extracted steam and reduces condenser load. Supercritical operation eliminates the boiling process and further raises efficiency.
  12. Environmental and Economic Trade-offsConnect thermodynamic efficiency to fuel consumption, emissions, and levelized cost of electricity.Higher efficiency directly reduces fuel burn and stack emissions. The marginal cost of advanced alloys and thicker walls eventually exceeds the value of saved fuel. The optimum design balances thermodynamic performance against capital and maintenance costs.

Questions this course answers

A new 300 MW waste-heat recovery plant must run continuously with minimal working-fluid loss. Which power-cycle architecture meets the requirement most directly?

Only the closed Rankine arrangement re-uses the same working fluid indefinitely, allowing continuous operation at utility scale without constant fluid replacement.

A boiler operates at 12 MPa and 520 °C. Which table region and lookup method gives the correct enthalpy?

At 12 MPa and 520 °C the steam is superheated, so the superheated-vapor table at exactly 12 MPa supplies h and s without interpolation.

Feedwater enters a boiler at 675 kJ/kg and leaves at 3475 kJ/kg. Neglecting kinetic and potential energy, what is the heat input per unit mass?

The steady-flow energy balance reduces to q_in = h3 − h2 when work, kinetic, and potential terms are negligible. Subtracting the inlet enthalpy from the outlet enthalpy directly supplies the required heat input.

A turbine has inlet conditions identical to the example but 90 % isentropic efficiency. Compared with the 85 % case, the actual exit enthalpy will be:

Higher efficiency means the actual work is closer to the ideal work, so less excess enthalpy remains at the exit and h4a is therefore smaller.

If the cooling-water inlet temperature were raised until it equalled the saturation temperature at 10 kPa, what would happen to the heat-rejection process?

The second law requires a finite temperature difference for irreversible heat transfer; if the cooling water reached the steam temperature, no driving force would exist and the required entropy decrease of the steam could not occur.

A pump compresses saturated liquid water from 8 kPa to 8 MPa. Using v = 0.001 m³/kg, what is the pump work?

w_pump equals v times ΔP, so 0.001 m³/kg times 7.992 MPa yields 8.0 kJ/kg.

Grounded in trusted sources

  • nist.gov
  • energy.gov
  • nasa.gov
  • Yunus A. Çengel and Michael A. Boles, Thermodynamics: An Engineering Approach — Rankine cycle
  • Michael J. Moran and Howard N. Shapiro, Fundamentals of Engineering Thermodynamics — steam tables / exergy
  • OpenStax University Physics / engineering thermo primers on vapor power cycles
  • IAEA / DOE vapor power cycle educational notes — efficiency and irreversibility context

Every Wunder lesson is built from real, reputable sources — never invented.

Related courses

📘How does relativity reshape spacetime?📘What does quantum theory actually claim?📘Atoms: Modern Physics📘Particle Physics: Modern Physics📘Modern Physics Essay: Modern Physics📘How did the solar system take shape?📘How do stars live and die?📘How do galaxies assemble over time?

Wunder is a personalized learn-anything platform — tell it any topic and it builds a beautiful, fact-checked course in minutes, with narration, a knowledge check, and a college-style University track.

All topics · Home

© 2026 Wunder Learning LLC · Terms & Privacy