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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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