Cycles: Carnot, Otto, Diesel, Dual & Rankine
Air-standard cycles, efficiencies and why real engines deviate — plus heat exchanger basics (LMTD, NTU).
Key formulas
η = 1 − 1/r^(γ−1), γ = cp/cv ≈ 1.4 (air)
Otto efficiency: Only the compression ratio r matters — spark-ignition cycle efficiency.
η = 1 − (1/r^(γ−1)) · (ρ^γ − 1)/(γ(ρ − 1)), ρ = v3/v2
Diesel cut-off ratio: Cut-off ratio ρ > 1 subtracts from Otto-like efficiency at equal r.
η_carnot = 1 − TL/TH
Carnot / Rankine bound: Use it to sanity-check any claimed cycle efficiency; real Rankine plants reach ~35–45%.
ΔTm = (ΔT1 − ΔT2) / ln(ΔT1/ΔT2); Q = U·A·ΔTm
LMTD: Design equation for heat exchangers; ΔT are the terminal temperature differences.
Cheat sheet
- ▸Carnot is the max-efficiency benchmark: η = 1 − TL/TH, achieved by two reversible isotherms + two isentropes — impossible practically.
- ▸Otto (SI engine): heat at constant volume, η = 1 − r^(1−γ). Diesel (CI): heat at constant pressure, η = 1 − (1/r^(γ−1))·(ρ^γ − 1)/(γ(ρ − 1)); higher compression ratio r is allowed because only air is compressed.
- ▸Diesel vs Otto at equal r: Otto is more efficient; but Diesel engines run r = 16–22 vs Otto 6–10, so real Diesels win on efficiency — the classic interview trap.
- ▸Rankine (steam plant): pump, boiler, turbine, condenser. Efficiency improves with higher boiler pressure/temperature, lower condenser pressure, and reheating/regeneration.
- ▸Heat exchangers: LMTD = (ΔT1 − ΔT2)/ln(ΔT1/ΔT2); counter-flow has higher LMTD than parallel-flow for the same end temperatures, so counter-flow is preferred.
- ▸Mean effective pressure (mep) = net work / displacement volume — the cycle's 'size-independent' output used to compare engines.
Otto vs Diesel vs Dual cycle
| Aspect | Otto | Diesel | Dual |
|---|---|---|---|
| Heat addition | Constant volume | Constant pressure | Partly cv, partly cp |
| Engine | Spark ignition (petrol) | Compression ignition (diesel) | Modern CI engines |
| Compression ratio | 6–10 | 16–22 | 12–20 |
| Same-r efficiency | Higher | Lower | Between |
| Practical efficiency | Lower (low r limit) | Higher (high r) | Higher, tunable |
Visual
Rankine cycle (T-s):
T | 3 (boiler exit, superheat)
| / |
| | | turbine (isentropic 3→4)
| 2| 4
| | | pump (1→2)
| 1|_|/____ s
condenser (4→1)Top 4 campus interview questions
MCQ mastery quiz
1. Efficiency of the Otto cycle depends only on…
2. In the Diesel cycle heat is added at constant…
3. The Carnot efficiency between 300 K and 900 K is…
4. For the same terminal temperatures, which flow arrangement gives the higher LMTD?