Engines and efficiency — Pick the correct statement comparing Otto and diesel engines and how efficiency varies with compression ratio.

Introduction:
Air-standard cycle analysis compares ideal Otto (constant-volume heat addition) and diesel (constant-pressure heat addition) cycles. Understanding efficiency trends with compression ratio and cut-off ratio helps in engine design and performance estimation.

Given Data / Assumptions:

• Ideal air-standard cycles for comparison.
• Same compression ratio r for both cycles when compared.
• Cut-off ratio for diesel cycle greater than 1.

Concept / Approach:
For the ideal Otto cycle, efficiency η_Otto = 1 − r^(1−γ). For the ideal diesel cycle, η_Diesel = 1 − [1/(r^(γ−1))] * [(ρ^γ − 1)/(γ(ρ − 1))], where ρ is the cut-off ratio. With the same r and ρ > 1, the diesel cycle has additional losses during constant-pressure heat addition, yielding lower efficiency than the Otto cycle.

Step-by-Step Solution:
Fix r for both cycles.Note diesel’s constant-pressure heat addition reduces efficiency relative to constant-volume.Conclude: at equal r, η_Otto > η_Diesel.

Verification / Alternative check:
Numerical examples with γ ≈ 1.4 and moderate ρ confirm the inequality. In practice, diesels use higher r to achieve higher real efficiencies, not because the cycle is intrinsically superior at equal r.

Why Other Options Are Wrong:

• (a) and (d) invert practical and theoretical facts; diesels run higher compression ratios than spark-ignition Otto engines.
• (c) is false; η_Otto increases with r.
• (e) ignores distinct heat-addition modes.

Common Pitfalls:
Comparing real engines without controlling for compression ratio; forgetting effect of cut-off ratio in diesel cycle.

Final Answer:
For the same compression ratio, an Otto engine has higher efficiency than a diesel engine