Otto cycle efficiency – dependence on specific heats Does the air-standard efficiency of the Otto (constant-volume heat addition) cycle depend on the specific heats of the working substance?

Introduction / Context:
Air-standard cycle analysis expresses thermal efficiency in terms of compression ratio and the ratio of specific heats (gamma). Understanding this dependence informs material choices and mixture effects in spark-ignition engine modeling.

Given Data / Assumptions:

• Air-standard assumptions, constant properties for simplicity.
• Compression ratio r fixed by engine geometry.
• Gamma = cp / cv.

Concept / Approach:

The ideal Otto-cycle efficiency is η = 1 − 1 / r^(γ−1). Thus efficiency depends on r and γ. Because γ = cp / cv derives from specific heats, any change in cp or cv (and thus γ) alters η. Real gases have temperature-dependent heat capacities, making γ vary with temperature; the dependence persists even in more refined models.

Step-by-Step Solution:

Verification / Alternative check:

Comparing dry air (γ ≈ 1.4) to products-rich mixtures (γ lower) at the same r shows reduced ideal efficiency when γ decreases.

Why Other Options Are Wrong:

“No” or temperature-only claims contradict the standard efficiency formula; compression ratio and γ govern the ideal result.

Common Pitfalls:

Assuming efficiency depends only on r; γ changes with composition and temperature, subtly shifting η even at fixed r.

Final Answer:

Yes