Thermal efficiency comparison at identical peak conditions: For air-standard cycles operating between the same maximum pressure and the same maximum temperature, which cycle is more efficient?

Introduction / Context:
This question probes a classic comparison among ideal air-standard cycles (Otto, Diesel, and Dual) when the upper limits of temperature and pressure are fixed. Understanding which cycle is more efficient under identical peak conditions clarifies how the mode of heat addition (constant volume vs constant pressure) affects thermal efficiency.

Given Data / Assumptions:

• Air-standard assumptions with constant specific heats.
• Same maximum temperature T_max and same maximum pressure p_max for the cycles compared.
• Internally reversible compression and expansion (isentropic legs).

Concept / Approach:
For identical T_max and p_max, the position of state points forces different compression ratios and different amounts of heat addition at various specific volumes. The Diesel cycle, with constant-pressure heat addition, tends to distribute heat at relatively lower average specific volume than the Otto cycle would under the same peak limits, resulting in a higher average temperature of heat addition for Diesel in this constrained comparison. Consequently, for fixed p_max and T_max, η_Diesel > η_Otto, while the Dual cycle efficiency generally lies between them for most parameter choices.

Step-by-Step Solution:

Verification / Alternative check:
Graphical p–V or T–s comparisons with identical peaks show the Diesel rectangle/area achieving a larger net work for the same heat input. Textbook orderings commonly report Diesel > Dual > Otto for fixed maximum pressure and heat input; with both p_max and T_max constrained, Diesel remains more efficient than Otto.

Why Other Options Are Wrong:

• Otto more efficient: True only when compression ratio is fixed (not the case here).
• Dual more efficient than both: Typically lies between Diesel and Otto for comparable constraints.
• Dual less efficient than both: Too strong; depends on parameters and is not generally valid.

Common Pitfalls:
Confusing comparisons at fixed compression ratio with those at fixed peak conditions; assuming conclusions for one constraint automatically carry over to the other.

Final Answer:
Diesel cycle is more efficient than Otto cycle