Dual (mixed) combustion cycle efficiency: Does the thermal efficiency of a dual combustion (limited pressure) cycle depend upon the cut-off ratio?

Introduction / Context:
The dual (mixed) cycle models modern compression-ignition engines more realistically than either the pure Otto or Diesel cycles by splitting heat addition into two parts: constant-volume followed by constant-pressure. Its efficiency depends on several non-dimensional ratios that define the state points of the ideal cycle.

Given Data / Assumptions:

• Air-standard assumptions with constant specific heats.
• Heat addition divided between constant-volume and constant-pressure processes.
• Compression ratio r, pressure ratio during constant-volume addition, and cut-off ratio ρ define the cycle.

Concept / Approach:
In the dual cycle, the cut-off ratio ρ = V3/V2 (volume after constant-pressure addition to volume at the end of constant-volume addition) directly affects the temperature at the end of heat addition and thus the work output and efficiency. For fixed compression ratio and the proportion of heat added at constant volume, increasing ρ generally lowers efficiency, similar to the Diesel trend where larger cut-off extends heat addition to lower average temperatures during expansion.

Step-by-Step Solution:

Verification / Alternative check:
Textbook efficiency expressions for the dual cycle explicitly include ρ along with r and the pressure rise ratio, confirming dependence.

Why Other Options Are Wrong:

• Does not depend / independent: Contradicts the parametric form of η_dual.
• Depends only on compression ratio: Incomplete; other ratios influence efficiency.

Common Pitfalls:
Confusing dual with Otto (no cut-off) or Diesel (single constant-pressure addition); ignoring how splitting heat addition changes mean effective temperature.

Final Answer:
depends