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Ratio of specific heats
Intermediate
Adiabatic index.
γ = C_p/C_vγ = Cp/Cv: 1.67 for monatomic, 1.4 for diatomic, 1.33 for polyatomic gases. It sets adiabatic curves and sound speed.
Air: γ = 1.4.
γ depends on molecular structure.
In more detail
The ratio of specific heats, γ = C_p/C_v, depends on the number of degrees of freedom of the gas molecules. For monatomic gases γ is about 5/3, and for diatomic gases about 7/5.
Real-world uses
- Sound speed in gases depends on γ.
- Adiabatic processes in engines are described using γ.
- Engineers use the ratio of specific heats to calculate the sound speed in air and the temperature changes in adiabatic compression.
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Frequently asked questions
Why are monatomic gases different?
They have only three translational degrees of freedom, giving a higher γ.
What is γ for air?
About 1.4, since air is mostly diatomic.
What is a typical value of gamma for air?
About 1.4, for a diatomic gas where the molecules have five degrees of freedom.
Related topics in Heat & Thermodynamics
Isochoric process · Cyclic process · Heat capacities C_p and C_v · P–V diagrams · Second law of thermodynamics · Kelvin–Planck statement