Most Probable Speed

v_{p} = \frac{2 k _{B} T}{m} = \frac{2 R T}{M}

Speed at which Maxwell-Boltzmann distribution peaks.

Variables

v_p

Most probable speed

Peak of Maxwell distribution

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

Set df/dv = 0 for Maxwell-Boltzmann distribution f(v) ∝ v²e^(-mv²/2kT). v_p < v_mean < v_rms.

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