--- title: "Air standard assumptions; diesel cycle; Otto vs diesel" subject: "Fundamental of Thermodynamics & Heat Transfer" chapter: 6 key: "semester_2/fundamental_of_thermodynamics_and_heat_transfer:air-standard-assumptions-diesel-vs-otto" source: https://www.bctengineer.com/q/semester_2/fundamental_of_thermodynamics_and_heat_transfer/air-standard-assumptions-diesel-vs-otto site: BCT Engineering --- # Air standard assumptions; diesel cycle; Otto vs diesel Fundamental of Thermodynamics & Heat Transfer · Chapter 6: Thermodynamic Cycles - Asked in: 2069 Bhadra, 6 marks - Video: [Thermodynamics DIESEL CYCLE in 10 Minutes!](https://www.youtube.com/watch?v=TMAJMGCl-tI) — 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/air-standard-assumptions-diesel-vs-otto - Whole chapter: https://www.bctengineer.com/md/semester_2/fundamental_of_thermodynamics_and_heat_transfer/chapter-6 ## Question Write the assumptions of an air standard analysis. Sketch an ideal diesel cycle on P-v and T-s diagrams. Also compare Otto and diesel cycle. ## Short answer Air-standard assumptions: fixed mass of ideal gas, reversible processes, constant specific heats, heat addition replaces combustion. Diesel cycle: isentropic compression, constant-pressure heat addition, isentropic expansion, constant-volume rejection. At same compression ratio Otto has higher efficiency; at same maximum pressure Diesel is more efficient. ## Answer #### Assumptions of air standard analysis 1. The working fluid is a fixed mass of air, circulating in a closed loop, and always behaves as an ideal gas. 2. All processes are internally reversible. 3. Combustion is replaced by a heat addition process from an external source; the exhaust is replaced by heat rejection to the surroundings that restores the initial state. 4. The air has constant specific heats, evaluated at 25 °C (cold air standard: cp = 1.005, cv = 0.718 kJ/kg·K, γ = 1.4). 5. Changes in kinetic and potential energy are neglected; there is no friction or heat loss. #### Ideal diesel cycle Processes: 1-2 isentropic compression; 2-3 constant-pressure heat addition; 3-4 isentropic expansion; 4-1 constant-volume heat rejection. ```text P-v diagram T-s diagram P T | 2 _______ 3 | 3 | | \ | .'| | | '. | .' | | | '. | .' | | \ '-. | 2 _.' | | \ '-. 4 | | 4 | '. | | | .' | '-. | | | .' | '-._ | | | .' | '--.._ | | 1.-' | '--- 1 | +-------------------------> v +--------------------> s v2 v1 1-2 isentropic compression 2-3 constant-P heat addition 3-4 isentropic expansion 4-1 constant-v heat rejection ``` η_Diesel = 1 − (1/r^(γ−1)) × (r_c^γ − 1)/(γ (r_c − 1)) #### Comparison of Otto and Diesel cycles | Point | Otto cycle | Diesel cycle | |---|---|---| | Used in | Spark ignition (petrol) engines | Compression ignition (diesel) engines | | Heat addition | At constant volume (2-3) | At constant pressure (2-3) | | Heat rejection | Constant volume | Constant volume | | Compression ratio | Low (6-10), limited by knock | High (14-22) | | Efficiency formula | 1 − 1/r^(γ−1) | 1 − (1/r^(γ−1)) (r_c^γ − 1)/(γ(r_c − 1)) | | Efficiency, same r | Higher | Lower (bracket term > 1) | | Efficiency, same maximum pressure | Lower | Higher | | Fuel in cylinder | Air-fuel mixture compressed | Only air compressed; fuel injected | ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. In an air standard analysis, how is the working fluid treated? A. A mixture of air and combustion products flowing through an open system B. A real gas whose specific heats vary strongly with temperature C. A fixed mass of air in a closed loop behaving as an ideal gas D. A fresh air-fuel mixture drawn in every cycle with changing composition Answer: C. The air standard cycle assumes a fixed mass of air circulating in a closed loop and behaving as an ideal gas. (Key point: Working fluid assumption) 2. What replaces combustion and exhaust in the air standard cycle? A. Adiabatic mixing of fresh and burnt gases B. An internal chemical reaction of the fuel with air C. Work addition by the piston during exhaust D. Heat addition from an external source and heat rejection to the surroundings Answer: D. Combustion is modelled as heat addition from an external source and exhaust as heat rejection that restores the initial state. (Key point: Replacement of combustion) 3. In the ideal diesel cycle, which process is heat addition? A. Constant-volume process 2-3 B. Constant-pressure process 2-3 C. Isentropic process 1-2 D. Isentropic process 3-4 Answer: B. In the diesel cycle heat is added at constant pressure (2-3) and rejected at constant volume (4-1). (Key point: Diesel heat addition) 4. For the same compression ratio, how do Otto and Diesel efficiencies compare? A. Diesel is higher because it burns fuel at constant pressure B. Otto is lower because it has a lower compression ratio C. Otto is higher because the diesel bracket term is greater than 1 D. They are equal since both use air as working fluid Answer: C. The diesel efficiency has the extra bracket term (r_c^γ - 1)/(γ(r_c - 1)) which is greater than 1, so diesel is lower at the same r. (Key point: Otto vs Diesel at same r) ## 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 - [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 - [Ideal diesel cycle: diagrams and efficiency](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Adiesel-cycle-efficiency-derivation) — Fundamental of Thermodynamics & Heat Transfer, chapter 6 - [Ideal diesel cycle working principle](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Adiesel-cycle-working-principle) — 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 - [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 ## Related in other subjects - [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 - [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 - [Fuel-air cycle and actual cycle losses](https://www.bctengineer.com/question.md?key=semester_6%2Finternal_combustion_engines%3Afuel-air-cycle-assumptions-losses) — Internal Combustion Engines, chapter 1