- 2069 Bhadra · 6 marks
Air standard assumptions; diesel cycle; Otto vs diesel
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.
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.
Assumptions of air standard analysis
- The working fluid is a fixed mass of air, circulating in a closed loop, and always behaves as an ideal gas.
- All processes are internally reversible.
- 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.
- 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).
- 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.
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 |
✓ Answer checked by Claude Opus 5.5 (high effort)
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