The Maxwell-Boltzmann Distribution: Difference between revisions
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:<math> f(v) = \sqrt{\left(\frac{m}{2 \pi kT}\right)^3}\, 4\pi v^2 e^{- \frac{mv^2}{2kT}}, </math> | :<math> f(v) = \sqrt{\left(\frac{m}{2 \pi kT}\right)^3}\, 4\pi v^2 e^{- \frac{mv^2}{2kT}}, </math> | ||
where <math>m</math> is the particle mass and <math>kT</math> is the product of Boltzmann's constant, <math>k<math>, and thermodynamic temperature, given by <math>T<math>. | where <math>m</math> is the particle mass and <math>kT</math> is the product of Boltzmann's constant, <math>k</math>, and thermodynamic temperature, given by <math>T</math>. | ||
The probability that a molecule of a gas has a center-of-mass speed within the range <math>v</math> to <math>v+dv</math> is given by <math>f(v)dv</math>. | |||
===A Computational Model=== | ===A Computational Model=== | ||
Revision as of 14:17, 4 December 2015
Claimed by Sai Srinivas
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A Mathematical Model
The Maxwell–Boltzmann distribution is the function
- [math]\displaystyle{ f(v) = \sqrt{\left(\frac{m}{2 \pi kT}\right)^3}\, 4\pi v^2 e^{- \frac{mv^2}{2kT}}, }[/math]
where [math]\displaystyle{ m }[/math] is the particle mass and [math]\displaystyle{ kT }[/math] is the product of Boltzmann's constant, [math]\displaystyle{ k }[/math], and thermodynamic temperature, given by [math]\displaystyle{ T }[/math].
The probability that a molecule of a gas has a center-of-mass speed within the range [math]\displaystyle{ v }[/math] to [math]\displaystyle{ v+dv }[/math] is given by [math]\displaystyle{ f(v)dv }[/math].
A Computational Model
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