Abstract
Here we consider a volume of an ideal gas comprising molecules in random motion. If D(c i )dc i is the fraction of molecules within the fractional velocity range c i to c i + dc i then the product
You have full access to this open access chapter, Download chapter PDF
Here we consider a volume of an ideal gas comprising molecules in random motion.
If \( D (c_i)\hbox{d}c_{i} \) is the fraction of molecules within the fractional velocity range \( c_{i} {\text{ to }}c_{i} + \hbox{d}c_{i} \) then the product
is the fraction (n) of molecules with velocity \( c = \sqrt {c_{1}^{2} + c_{2}^{2} + c_{3}^{2} } . \)
Thus
This equation can, by expressing it in logarithmic form and differentiating both sides, be recast in the form:
The ‘constant’ is necessary if the equation is to be true for all values of \( c_{i} . \)
The solution to this equation is:
where k is the Boltzmann constant and μ is the molecular weight for the gas. Hence given that the kinetic energy of a molecule is:
we can write
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2011 Springer-Verlag London Limited
About this chapter
Cite this chapter
Sangster, A.J. (2011). Maxwell Distribution. In: Warming to Ecocide. Springer, London. https://doi.org/10.1007/978-0-85729-926-0_11
Download citation
DOI: https://doi.org/10.1007/978-0-85729-926-0_11
Published:
Publisher Name: Springer, London
Print ISBN: 978-0-85729-925-3
Online ISBN: 978-0-85729-926-0
eBook Packages: EngineeringEngineering (R0)