Air-Standard Diesel Cycle – Parameters Governing Thermal Efficiency In the ideal (air-standard) Diesel cycle, the thermal efficiency primarily depends on the compression ratio as well as the cut-off ratio (for a given specific heat ratio of the working gas).

Introduction / Context:Diesel engines are modeled by the air-standard Diesel cycle, which differs from the Otto cycle by admitting heat partly at constant pressure. This question checks which parameters control the ideal thermal efficiency, a core topic in thermodynamics and internal combustion engine theory.

Given Data / Assumptions:

• Air-standard assumptions (ideal gas with constant specific heats).
• Reversible compression and expansion (isentropic), heat addition partly at constant pressure, heat rejection at constant volume.
• Definitions: compression ratio r_c = V1/V2; cut-off ratio r_cut = V3/V2 (volume change during constant-pressure heating).

Concept / Approach:

The Diesel cycle efficiency eta_Diesel is a function of r_c, r_cut, and gamma (specific heat ratio). For fixed gamma, increasing r_c raises efficiency, while increasing r_cut (longer constant-pressure addition) lowers efficiency. Absolute temperature or pressure limits do not directly define eta in the air-standard idealization; they are embedded through these ratios.

Step-by-Step Solution:

Verification / Alternative check:

Limiting case r_cut → 1 collapses the Diesel cycle to an Otto-like cycle, recovering the Otto efficiency dependence on compression ratio alone. Numerical plots of eta versus r_c for several r_cut values confirm the trends.

Why Other Options Are Wrong:

Temperature limits and pressure ratio are not independent inputs in the air-standard model; they are consequences of r_c and r_cut. Compression ratio alone (without cut-off) is incomplete. Specific heat ratio influences eta but is not the controlling design parameter like r_c and r_cut.

Common Pitfalls:

Confusing Diesel with Otto (constant-volume heat addition); assuming higher cut-off always improves performance (it usually reduces efficiency by adding heat at higher average temperature of exhaust).

Final Answer:

cut-off ratio and compression ratio