What is the typical value of gamma (γ), the ratio of Cp to Cv, for dry air?

What is the typical value of gamma (γ), the ratio of Cp to Cv, for dry air?

• A. 1.4
• B. 1.0
• C. 1.67
• D. 2.0

Answer: (A)

Gamma (γ) is the ratio Cp to Cv for an ideal gas, and it tells how pressure changes with temperature during adiabatic processes. For dry air, which is mainly nitrogen and oxygen and is diatomic at room temperature, the energy that can be stored in molecules comes from translational and rotational motion (vibrational modes aren’t excited yet). In this regime Cp is Cv plus the gas constant, and the classic result for a diatomic gas gives γ ≈ 7/5 = 1.4. Numerically, Cp is about 1.005 kJ/kg·K and Cv about 0.718 kJ/kg·K, yielding γ ≈ 1.4. This is the typical value used for dry air at room temperature. If the gas were monatomic, γ would be about 1.67, and if humidity or higher temperatures excite more modes, γ would shift away from 1.4, but for dry air near room temperature 1.4 is standard.

Gamma (γ) is the ratio Cp to Cv for an ideal gas, and it tells how pressure changes with temperature during adiabatic processes. For dry air, which is mainly nitrogen and oxygen and is diatomic at room temperature, the energy that can be stored in molecules comes from translational and rotational motion (vibrational modes aren’t excited yet). In this regime Cp is Cv plus the gas constant, and the classic result for a diatomic gas gives γ ≈ 7/5 = 1.4. Numerically, Cp is about 1.005 kJ/kg·K and Cv about 0.718 kJ/kg·K, yielding γ ≈ 1.4. This is the typical value used for dry air at room temperature. If the gas were monatomic, γ would be about 1.67, and if humidity or higher temperatures excite more modes, γ would shift away from 1.4, but for dry air near room temperature 1.4 is standard.