Air-standard efficiency order at constant maximum pressure and the same heat input: Arrange the cycles by efficiency (highest to lowest).

Introduction / Context:
Efficiency comparisons among Otto, Diesel, and Dual cycles depend on what constraints are held fixed. This item focuses on the case where the maximum pressure is the same and the total heat added is the same for all cycles—an important design-stage comparison for peak-limited machines such as engines and gas generators.

Given Data / Assumptions:

• Air-standard model with constant specific heats.
• Identical maximum pressure p_max for all cycles considered.
• Same total heat input Q_in across cycles.
• Reversible compression/expansion (isentropic legs).

Concept / Approach:
Under fixed p_max and Q_in, the manner of heat addition changes the average temperature at which heat is supplied. Diesel adds heat at constant pressure over a range of volumes and tends to yield a higher mean effective temperature of heat addition than the Otto cycle in this constrained comparison. The Dual cycle splits heat addition between constant volume and constant pressure, and its efficiency typically falls between Diesel and Otto. Hence, the general order is Diesel > Dual > Otto.

Step-by-Step Solution:

Verification / Alternative check:
Standard thermodynamics texts illustrate this ordering with p–V/T–s diagrams and parametric studies; as the cut-off ratio approaches 1, Dual trends toward Otto; as the CV fraction decreases, Dual trends toward Diesel, remaining intermediate.

Why Other Options Are Wrong:

• Otto > Diesel > Dual or Dual-first orders: These contradict the typical ranking for equal p_max and Q_in.

Common Pitfalls:
Carrying over the “same compression ratio” result (Otto > Diesel) to the “same maximum pressure and heat input” case; the constraint change reverses the order.

Final Answer:
Diesel cycle > Dual cycle > Otto cycle