Thermal Molecular Velocity of Gas Molecules Formulas and Calculator

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Thermal Molecular Velocity of Gas Molecules Formulas and Calculator

Fluid Dynamics Engineering and Design

Gas molecules in a vessel move back and forth in different directions and at different speeds. Their velocity distribution corresponds to a bell curve having its peak at the most probable velocity

Probable Velocity

c_w = [ ( 2 · R · T ) / M ]^1/2

Mean Thermal Velocity

c_mean = [ ( 8 · R · T ) / ( π · M ) ]^1/2

Where:

c_w = Probable Velocity (m/s),
c_mean = Mean Velocity (m/s),
R = General gas constant R = 8.314510 kJ / (kmol K),
T = Thermodynamic temperature [K],
M = Molar mass [kg / kmol]

Molar masses and mean thermal velocities of various gases

Gas	Molar Mass (g/mol)	Mean Velocity (m/s)	Mach Number
H₂	2	1,762	5.3
He	4	1,246	3.7
H₂O	18	587	1.8
N₂	28	471	1.4
Air	29	463	1.4
Ar	40	394	1.2
CO₂	44	376	1.1

Thermal Molecular Velocity of Gas Molecules

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References:

Karl Jousten (Hrsg.), Wutz Handbuch Vakuumtechnik,
Pupp / Hartmann, Vakuumtechnik Carl Hanser Verlag
Schweitzer, Bleuler, Traxler, Active Magnetic Bearings, Hochschulverlag AG an der ETH Zürich
Fremerey, Vacuum 32 (1982) S.
Hobson und Redhead, Can. J. Phys. 36 (1958)
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Dawson, Quadrupol Mass Spectrometry, Elsevier Amsterdam (1976)
Brubaker, 14th National Symposium, Am. Vac. Soc. (1967)
Fachbericht Balzers BG 800003 Das Funktionsprinzip des Quadrupol Massenspektrometers. (1990)