TITLE:
New Probability Distributions in Astrophysics: III. The Truncated Maxwell-Boltzmann Distribution
AUTHORS:
Lorenzo Zaninetti
KEYWORDS:
05.20.-y Classical Statistical Mechanics, 05.20.Dd Kinetic Theory
JOURNAL NAME:
International Journal of Astronomy and Astrophysics,
Vol.10 No.3,
August
19,
2020
ABSTRACT: The Maxwell-Boltzmann (MB) distribution for velocities in ideal gases is usually defined between zero and infinity. A double truncated MB distribution is here introduced and the probability density function, the distribution function, the average value, the rth moment about the origin, the root-mean-square speed and the variance are evaluated. Two applications are presented: 1) a numerical relationship between root-mean-square speed and temperature, and 2) a modification of the formula for the Jeans escape flux of molecules from an atmosphere.