Cycle comparison – dual (limited pressure) vs. Diesel cycle For the same compression ratio, the air-standard efficiency of the dual-combustion (limited-pressure) cycle is __________ that of the Diesel cycle.

Introduction / Context:
The dual (limited-pressure) cycle splits heat addition between constant volume and constant pressure phases. Comparing it with the Diesel cycle (heat addition at constant pressure) for the same compression ratio reveals how the mode of heat addition affects air-standard efficiency.

Given Data / Assumptions:

• Air-standard assumptions (ideal gas with constant specific heats, internally reversible compression/expansion).
• Same compression ratio for the cycles compared.
• Qualitative comparison over typical parameter ranges.

Concept / Approach:
For a given compression ratio, an Otto-like portion of constant-volume heat addition raises peak temperature more effectively per unit heat than constant-pressure addition. The dual cycle includes a constant-volume stage, so its efficiency lies between Otto (highest at given r) and Diesel (lower at given r). Thus, η_Otto > η_Dual > η_Diesel for the same compression ratio.

Step-by-Step Solution:
Recognize Diesel adds heat at constant pressure, resulting in more entropy generation for the same temperature rise.Dual cycle adds part of the heat at constant volume, improving thermal efficiency relative to Diesel.Therefore, at the same compression ratio, the dual cycle is more efficient than the Diesel cycle.

Verification / Alternative check:
Analytical expressions for η in terms of r, cutoff ratio, and pressure ratio confirm the ordering η_Otto > η_Dual > η_Diesel over practical parameter ranges.

Why Other Options Are Wrong:

• Equal to / less than contradicts standard air-standard comparisons.
• “Indeterminate” ignores typical monotonic relations for standard parameter ranges.
• “Same as Otto” is false; Otto remains the upper bound at the same r.

Common Pitfalls:
Comparing at unequal parameters (e.g., same maximum pressure instead of same compression ratio) can change conclusions; always note the specified basis.

Final Answer:
greater than