Specific Heat Ratio of Air – Typical Value Near Room Conditions For dry air near standard conditions, the specific heat ratio gamma = Cp/Cv is approximately 1.4.

Introduction / Context:
The specific heat ratio gamma affects speed of sound, isentropic relations, nozzle flows, and cycle efficiencies. Knowing its typical value for air is crucial in many thermofluid calculations.

Given Data / Assumptions:

• Dry air modeled as a diatomic ideal gas near room temperature.
• Calorically perfect approximation over a modest temperature range.
• Cp ≈ 1.005 kJ/kg-K, Cv ≈ 0.718 kJ/kg-K.

Concept / Approach:

Gamma is defined as Cp/Cv. For diatomic gases like nitrogen and oxygen (major constituents of air), rotational degrees of freedom lead to Cp and Cv values that yield gamma ≈ 1.4 at ambient conditions. Gamma decreases slightly with temperature as vibrational modes activate.

Step-by-Step Solution:

Verification / Alternative check:

Speed of sound a = sqrt(gamma * R * T) using gamma = 1.4 matches measured acoustic velocities in air near 20°C, supporting the typical value.

Why Other Options Are Wrong:

1 implies monatomic-like ratio at very high temperatures (not typical); 1.8 is unrealistic for air; 23 is nonsensical; 1.2 is more typical of high-temperature effective gamma in some mixtures, not room conditions.

Common Pitfalls:

Using gamma = 1.4 indiscriminately at very high temperatures or with humid air where deviations occur; confusing Cp/Cv with Cv/Cp.

Final Answer:

1.4