Maxwell–Boltzmann distribution

related topics
{math, energy, light}
{math, number, function}
{rate, high, increase}

The Maxwell–Boltzmann distribution describes particle speeds in gases, where the particles do not constantly interact with each other but move freely between short collisions. It describes the probability of a particle's speed (the magnitude of its velocity vector) being near a given value as a function of the temperature of the system, the mass of the particle, and that speed value. This probability distribution is named after James Clerk Maxwell and Ludwig Boltzmann.

The Maxwell–Boltzmann distribution is usually thought of as the distribution for molecular speeds, but it can also refer to the distribution for velocities, momenta, and magnitude of the momenta of the molecules, each of which will have a different probability distribution function, all of which are related. Unless otherwise stated, this article will use "Maxwell–Boltzmann distribution" to refer to the distribution of speed. This distribution can be thought of as the magnitude of a 3-dimensional vector whose components are independent and normally distributed with mean 0 and standard deviation a. If Xi are distributed as X \sim N(0, a^2), then

is distributed as a Maxwell–Boltzmann distribution with parameter a. Apart from the scale parameter a, the distribution is identical to the chi distribution with 3 degrees of freedom.

Contents

Physical applications of the Maxwell–Boltzmann distribution

The Maxwell–Boltzmann distribution applies to ideal gases close to thermodynamic equilibrium, negligible quantum effects, and non-relativistic speeds. It forms the basis of the kinetic theory of gases, which explains many fundamental gas properties, including pressure and diffusion.

Full article ▸

related documents
Huygens–Fresnel principle
Olbers' paradox
Weight
Resonance
2 Pallas
Weak interaction
Rayleigh scattering
Elementary particle
Gauss's law
Hydrogen atom
Proton decay
Optics
Ganymede (moon)
Optical isolator
Terrestrial planet
Attenuation
Gluon
Gravitational constant
Brownian motion
Axial tilt
Quantum gravity
Cyclotron
Near-Earth asteroid
Star formation
Gamma-ray astronomy
Gravitational singularity
Capacitance
Optical aberration
Compton scattering
Exciton