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Molecular velocity distribution at large Knudsen numbers

Authors: W. Jitschin; G. Reich;

Molecular velocity distribution at large Knudsen numbers

Abstract

It is commonly assumed that the distribution of molecular velocities follows a Maxwellian distribution also in the range of high and ultrahigh vacuum, i.e., at large Knudsen numbers. This distribution is theoretically derived from statistical analysis of an ensemble of molecules with frequent molecule–molecule collisions. Such a situation prevails at higher pressures, i.e., at small Knudsen numbers. However, at smaller pressures the molecule–wall collisions prevail, and due to the different nature of these collisions, the statistical arguments fail. As a consequence, the molecular velocity distribution cannot be predicted a priori at such pressures. In the present paper the applicability of the Maxwellian distribution in vacuum metrology at large Knudsen numbers, i.e., in the molecular regime is investigated. For this purpose, the pressures generated in primary standards of the static and dynamic expansion type are calculated for an arbitrary velocity distribution after expansion. The pressure generated by static expansion is proportional to the expectation value 〈v2z〉, that generated by dynamic expansion proportional to the ratio of expectation values 〈v2z〉/〈‖vz‖〉 (vz denotes the one-dimensional velocity component). Available experimental calibration data obtained by static and dynamic expansion of common gases are compared to each other and with direct pressure measurements with a liquid column manometer. These data provide a decisive test for the expectation values 〈v2z〉 and 〈‖vz‖〉 in the molecular range. Excellent agreement within the uncertainty of less than 1% between experimental values and values calculated assuming a Maxwellian distribution is found. Thus one may conclude that in common vacuum metrology the Maxwellian distribution can be applied for deriving pressures also in the molecular regime with high accuracy.

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
13
Average
Top 10%
Average
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