---
title: "Gas vs vapor cycles; Otto cycle efficiency"
subject: "Fundamental of Thermodynamics & Heat Transfer"
chapter: 6
key: "semester_2/fundamental_of_thermodynamics_and_heat_transfer:gas-vs-vapor-cycles-otto-efficiency"
source: https://www.bctengineer.com/q/semester_2/fundamental_of_thermodynamics_and_heat_transfer/gas-vs-vapor-cycles-otto-efficiency
site: BCT Engineering
---

# Gas vs vapor cycles; Otto cycle efficiency

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

- Asked in: 2070 Bhadra, 6 marks
- Video: [OTTO CYCLE & Internal Combustion Engines in 10 Minutes!](https://www.youtube.com/watch?v=q5vgBPb8gSc) — 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/gas-vs-vapor-cycles-otto-efficiency
- Whole chapter: https://www.bctengineer.com/md/semester_2/fundamental_of_thermodynamics_and_heat_transfer/chapter-6

## Question

Differentiate between gas and vapor cycles. Also derive an expression for the air standard efficiency of Otto cycle in terms of compression ratio.

## Short answer

Gas cycles work with a gaseous fluid without phase change (e.g., Otto, Brayton); vapor cycles involve phase change (e.g., Rankine). The Otto cycle air-standard efficiency is η = 1 - 1/r^(γ-1), derived from isentropic relations and constant-volume heat addition and rejection.

## Answer

#### Gas cycles and vapour cycles
| Point | Gas cycle | Vapour cycle |
|---|---|---|
| Working fluid | A gas (air) that stays gaseous throughout | A fluid that changes phase (liquid ⇄ vapour), usually water |
| Phase change | None | Evaporation and condensation occur |
| Examples | Otto, Diesel, Dual, Brayton, Stirling | Rankine, reheat, regenerative Rankine, vapour-compression refrigeration |
| Heat addition | Combustion in the cylinder or combustor | In the boiler |
| Heat rejection | Exhaust to atmosphere | In the condenser |
| Compression | Compressor takes much of the turbine work | Pump handles liquid, needs very little work |
| Equipment | Engines, gas turbines | Steam power plants, refrigerators |
| Property data | Ideal gas equations | Steam tables or charts |

#### Otto cycle efficiency
The Otto cycle is the ideal air-standard cycle of the spark-ignition engine:

- 1-2: isentropic compression
- 2-3: constant-volume heat addition
- 3-4: isentropic expansion
- 4-1: constant-volume heat rejection

```text
 P
 |   3
 |   |\
 |   | \
 |   |  '.
 |   |    '.
 |   2      '-.
 |    \        '-.
 |     '.         '-.
 |       '-.         '-. 4
 |          '-._         |
 |              '-.._    |
 |                   '-- 1
 +-----------------------> v
    v2                   v1
```

Let r = v₁/v₂ be the compression ratio. For air as an ideal gas with constant specific heats:

q_in = cv (T₃ − T₂), q_out = cv (T₄ − T₁)

η = 1 − q_out/q_in = 1 − (T₄ − T₁)/(T₃ − T₂)

Isentropic processes:
- 1-2: T₂/T₁ = (v₁/v₂)^(γ−1) = r^(γ−1)
- 3-4: T₃/T₄ = (v₄/v₃)^(γ−1) = (v₁/v₂)^(γ−1) = r^(γ−1)

So T₂/T₁ = T₃/T₄, which gives T₄/T₁ = T₃/T₂. Then

(T₄ − T₁)/(T₃ − T₂) = T₁/T₂ = 1/r^(γ−1)

**η_Otto = 1 − 1/r^(γ−1)**

The Otto efficiency depends only on the compression ratio r and on γ. Example: r = 8, γ = 1.4 gives η = 1 − 1/8^0.4 = 56.5 %.

## Related in Fundamental of Thermodynamics & Heat Transfer

- [Air standard cycle; diesel vs Otto](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Aair-standard-cycle-diesel-vs-otto) — Fundamental of Thermodynamics & Heat Transfer, chapter 6
- [Air standard assumptions; diesel cycle; Otto vs diesel](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Aair-standard-assumptions-diesel-vs-otto) — Fundamental of Thermodynamics & Heat Transfer, chapter 6
- [Ideal Otto cycle diagrams and efficiency](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Aotto-cycle-efficiency-compression-ratio) — Fundamental of Thermodynamics & Heat Transfer, chapter 6
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- [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
- [Air standard diesel: efficiency and mean effective pressure](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Adiesel-cycle-cutoff-2-efficiency-mep) — Fundamental of Thermodynamics & Heat Transfer, chapter 6

## Related in other subjects

- [Otto cycle efficiency and mean effective pressure](https://www.bctengineer.com/question.md?key=semester_6%2Finternal_combustion_engines%3Aotto-cycle-efficiency-numerical) — Internal Combustion Engines, chapter 1
- [Diesel cycle efficiency compared with Otto](https://www.bctengineer.com/question.md?key=semester_6%2Finternal_combustion_engines%3Adiesel-cycle-versus-otto-numerical) — Internal Combustion Engines, chapter 1
- [Diesel cycle with compression ratio 15:1](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_plant_equipment%3Adiesel-cycle-compression-15) — Power Plant Equipment, chapter 5
- [Gas turbine 5:1: power, efficiency, work ratio](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_plant_equipment%3Agt-5-1-work-ratio) — Power Plant Equipment, chapter 6