---
title: "Rankine cycle plots and efficiency"
subject: "Fundamental of Thermodynamics & Heat Transfer"
chapter: 6
key: "semester_2/fundamental_of_thermodynamics_and_heat_transfer:rankine-cycle-efficiency"
source: https://www.bctengineer.com/q/semester_2/fundamental_of_thermodynamics_and_heat_transfer/rankine-cycle-efficiency
site: BCT Engineering
---

# Rankine cycle plots and efficiency

Fundamental of Thermodynamics & Heat Transfer · Chapter 6: Thermodynamic Cycles

- Asked in: 2075 Baisakh, 6 marks
- Video: [Thermodynamics RANKINE CYCLE in 10 Minutes!](https://www.youtube.com/watch?v=AwLpST3vlS4) — Less Boring Lectures
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_2/fundamental_of_thermodynamics_and_heat_transfer/rankine-cycle-efficiency
- Whole chapter: https://www.bctengineer.com/md/semester_2/fundamental_of_thermodynamics_and_heat_transfer/chapter-6

## Question

Sketch the Rankine cycle on p-v and T-s plots when the state of steam at the boiler outlet is saturated and superheated vapor respectively. Derive an expression for the efficiency of Rankine cycle.

## Short answer

The Rankine cycle consists of isentropic pump and turbine, constant‑pressure boiler and condenser. Efficiency: η = [(h₃−h₄)−(h₂−h₁)]/(h₃−h₂) ≈ (h₃−h₄)/(h₃−h₁). Superheat raises average heat‑addition temperature, improving efficiency. p‑v and T‑s diagrams show the four processes including evaporation and superheat.

## Answer

The Rankine cycle is the ideal cycle of a steam power plant. It has four processes:

- 1-2: isentropic compression of saturated liquid in the pump
- 2-3: constant-pressure heat addition in the boiler (and superheater)
- 3-4: isentropic expansion in the turbine
- 4-1: constant-pressure heat rejection in the condenser (to saturated liquid)

#### Diagrams
**(a) Saturated vapour at boiler outlet**

```text
 T-s diagram                        P-v diagram
 T                                  P
 |           .-'''-.                |  2 _________________ 3 (sat. vapour)
 |         .'       '.              |  |                    \
 |   2'  /____________3             |  |                     '.
 |      /             |\            |  |                       '-.
 |     /              | \           |  1 ______________________ 4
 |  2 /               |  \          +-------------------------------> v
 |  1/________________4   \
 |  /                      \
 +-----------------------------> s
 (2 lies just above 1; 2-2' liquid heating, 2'-3 boiling)
```

**(b) Superheated vapour at boiler outlet**

```text
 T-s diagram                        P-v diagram
 T                                  P
 |                       3          |  2 ____________________ 3
 |           .-'''-.   .'|          |  |                       \
 |         .'       '.'  |          |  |                        '.
 |   2'  /____________3' |          |  |                          '-.
 |      /              \ |          |  1 _________________________ 4
 |     /                \|          +----------------------------------> v
 |  2 /                  |\
 |  1/___________________4 \
 |  /                       \
 +-----------------------------> s
 (2 lies just above 1; 2'-3' boiling, 3'-3 superheating)
```

#### Efficiency derivation
Per kg of steam (steady flow, kinetic and potential energies neglected):

- Pump work: w_p = h₂ − h₁ = v_f (P₂ − P₁)
- Heat added: q_in = h₃ − h₂
- Turbine work: w_t = h₃ − h₄
- Heat rejected: q_out = h₄ − h₁

Net work: w_net = w_t − w_p = (h₃ − h₄) − (h₂ − h₁)

**η_Rankine = w_net/q_in = [(h₃ − h₄) − (h₂ − h₁)]/(h₃ − h₂) = 1 − (h₄ − h₁)/(h₃ − h₂)**

The pump work is very small compared with the turbine work, so approximately η ≈ (h₃ − h₄)/(h₃ − h₁).

The efficiency rises with higher boiler pressure, higher superheat temperature and lower condenser pressure.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Pump work in the Rankine cycle is:
   A. v_f (P2 - P1)
   B. h4 - h1
   C. cp (T2 - T1)
   D. h3 - h4
   Answer: A. For incompressible liquid, w_p = h2 - h1 = v_f (P2 - P1). (Key point: Pump work)

2. Which is the Rankine efficiency?
   A. (h3 - h2)/(h3 - h4)
   B. (h3 - h4)/(h4 - h1)
   C. [(h3 - h4) - (h2 - h1)]/(h3 - h2)
   D. (h4 - h1)/(h3 - h2)
   Answer: C. eta = w_net/q_in with w_net = w_t - w_p and q_in = h3 - h2. (Key point: Efficiency expression)

3. Why can pump work be neglected?
   A. It is cancelled by boiler
   B. It is very small compared with turbine work
   C. It equals condenser heat
   D. It is zero for liquids
   Answer: B. Liquid is nearly incompressible, so eta is approximately (h3 - h4)/(h3 - h1). (Key point: Pump approximation)

4. Which change raises Rankine efficiency?
   A. Higher condenser pressure
   B. Lower superheat
   C. Lower boiler pressure
   D. Higher boiler pressure or superheat, lower condenser pressure
   Answer: D. These raise mean heat-addition temperature or lower mean rejection temperature. (Key point: Improving efficiency)

## Related in Fundamental of Thermodynamics & Heat Transfer

- [Rankine cycle 2 MPa: efficiency vs Carnot](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Arankine-cycle-2mpa-efficiency-vs-carnot) — Fundamental of Thermodynamics & Heat Transfer, chapter 6
- [Gas vs vapor cycles; Otto cycle efficiency](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Agas-vs-vapor-cycles-otto-efficiency) — Fundamental of Thermodynamics & Heat Transfer, chapter 6
- [Define moisture content, superheated vapor, etc.](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Amoisture-superheated-definitions) — Fundamental of Thermodynamics & Heat Transfer, chapter 3
- [Define saturation temp, saturated vapor, quality, subcooled liquid, critical point](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Asaturation-temp-saturated-vapor-subcooled-defs) — Fundamental of Thermodynamics & Heat Transfer, chapter 3
- [Simple Rankine plant 2 MPa / 20 kPa: efficiency, power](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Arankine-2mpa-20kpa-50kgs) — Fundamental of Thermodynamics & Heat Transfer, chapter 6
- [Vapor compression refrigeration cycle p-h and T-s](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Avapor-compression-refrigeration-ph-ts) — Fundamental of Thermodynamics & Heat Transfer, chapter 6

## Related in other subjects

- [Boiler efficiency with superheated steam](https://www.bctengineer.com/question.md?key=semester_3%2Fapplied_thermodynamics%3Aboiler-efficiency-superheated-steam) — Applied Thermodynamics, chapter 1
- [Throttled reheat cycle with 50 bar steam](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_plant_equipment%3Athrottled-reheat-50-bar) — Power Plant Equipment, chapter 7
- [Reheat Rankine cycle: 20 MPa, 500°C](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_plant_equipment%3Arankine-reheat-20mpa) — Power Plant Equipment, chapter 7
- [Rankine efficiency and impulse versus reaction](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_plant_equipment%3Arankine-efficiency-impulse-reaction) — Power Plant Equipment, chapter 7