Air-standard efficiencies – comparing Otto, Diesel, and Dual cycles For the same compression ratio, where does the thermal efficiency of the Dual-combustion (mixed) cycle lie relative to the Otto and Diesel cycles?

Introduction / Context:
Otto, Diesel, and Dual cycles differ by how heat is added: constant volume (Otto), constant pressure (Diesel), and a split of both (Dual). For a fixed compression ratio, their ideal thermal efficiencies rank predictably, informing engine design trade-offs and performance expectations.

Given Data / Assumptions:

• Air-standard assumptions (ideal gas with constant properties).
• Same compression ratio across the compared cycles.
• No losses other than those intrinsic to the idealized models.

Concept / Approach:

At a given compression ratio, Otto has the highest efficiency because all heat is added at the smallest volume (highest temperature rise for a given heat input). Diesel has the lowest because heat addition continues while the piston moves, leading to larger mean volumes during heat addition. The Dual cycle splits heat addition; its efficiency therefore lies between those of Otto and Diesel. Hence: Otto > Dual > Diesel for the same compression ratio.

Step-by-Step Solution:

Verification / Alternative check:

Textbook efficiency formulas confirm this ordering; numerical examples with typical cut-off ratios show Dual efficiencies strictly between Otto and Diesel at the same r.

Why Other Options Are Wrong:

Any claim placing Dual below Diesel or above Otto contradicts the heat-addition geometry and standard results.

Common Pitfalls:

Confusing compression ratio with cut-off ratio; changing the cut-off can shift Diesel/Dual efficiencies but not above Otto at the same compression ratio.

Final Answer:

greater than Diesel cycle and less than Otto cycle