Mean Speed

v_{m e an} = \frac{8 k _{B} T}{π m} = \frac{8 R T}{π M}

Average speed of gas molecules from Maxwell-Boltzmann distribution.

Variables

v_mean

Mean speed

Average molecular speed

m/s

k_B

Boltzmann constant

1.38×10⁻²³

J/K

T

Temperature

Absolute temperature

K

m

Molecular mass

Mass per molecule

kg

R

Gas constant

8.314

J/(mol·K)

M

Molar mass

Mass per mole

kg/mol

Derivation

v_mean = ∫v f(v)dv = √(8kT/πm). Order: v_p < v_mean < v_rms.

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