Ratio of Specific Heats (γ) from DOF (γ = Cp/Cv = 1 + 2/f)
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γ = Cp/Cv = 1 + 2/f
What each symbol means
| Symbol | What it stands for |
|---|---|
| f | Degrees of freedom per molecule |
| Cp | Molar specific heat at constant pressure (J mol⁻¹ K⁻¹) |
| Cv | Molar specific heat at constant volume (J mol⁻¹ K⁻¹) |
| γ | Ratio of specific heats Cp/Cv (dimensionless) |
When to use this
Valid for ideal gases. Derivation: Cv = (f/2)R, Cp = Cv + R = (f/2+1)R = (f+2)R/2. So γ = Cp/Cv = (f+2)/f = 1+2/f. Monatomic f=3: γ=5/3≈1.67. Diatomic rigid f=5: γ=7/5=1.40. Diatomic vib f=7: γ=9/7≈1.29. γ always >1 and decreases as f increases.