Degrees of Freedom (f = 3 (monatomic), 5 (diatomic rigid), 7 (diatomic)

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f = 3 (monatomic), 5 (diatomic rigid), 7 (diatomic vibrating)

What each symbol means

SymbolWhat it stands for
fDegrees of freedom — number of independent quadratic energy terms
CpMolar heat capacity at constant pressure = ((f+2)/2)R
CvMolar heat capacity at constant volume = (f/2)R
γAdiabatic exponent = Cp/Cv = (f+2)/f

When to use this

Monatomic (He, Ne, Ar): f=3 (3 translational, 0 rotational). Diatomic rigid at room T (N₂, O₂, H₂): f=5 (3 trans + 2 rot, vibration frozen). Diatomic vibrating at high T: f=7 (3 trans + 2 rot + 1 vib mode with 2 quadratic terms). Nonlinear polyatomic rigid (H₂O, CO₂ bent): f=6 (3 trans + 3 rot). Linear polyatomic rigid (CO₂ linear): f=5.