Root Mean Square Speed

v_{r m s} = \frac{3 k _{B} T}{m} = \frac{3 R T}{M}

RMS speed of gas molecules.

Variables

v_rms

RMS speed

Root mean square velocity

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

From ½m⟨v²⟩ = (3/2)kT: v_rms = √(3kT/m).

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