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Thermal Molecular Velocity of Gas Molecules Formulas and Calculator
Fluid Dynamics Engineering and Design
Thermal Molecular Velocity of Gas Molecules Formulas and Calculator
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

H_{2} 
2

1,762

5.3

He 
4

1,246

3.7

H_{2}O 
18

587

1.8

N_{2} 
28

471

1.4

Air 
29

463

1.4

Ar 
40

394

1.2

CO_{2} 
44

376

1.1

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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)
 Redhead, Electron Stimulated Desorption, Vacuum 12 (1962)
 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)
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