Speed distribution

For a system containing a large number of identical non-interacting non-relativistic classical particles in thermodynamic equilibrium, the speed distribution function is a function such that \(f(v) dv\) gives the fraction of particles with speeds in the interval \(dv\) at speed \(v\).

Notation:

1. \(k_\text{B}\) (k_B) is boltzmann_constant.

Notes:

1. Number of particles is big enough that the laws of thermodynamics can be applied.

2. Particles are identical, non-interacting, non-relativistic, and classical.

3. The ensemble of particles is at thermodynamic equilibrium.

Links:

1. Wikipedia.

speed_distribution_function

speed distribution function.

Symbol:

f(v)

Latex:

\(f(v)\)

Dimension:

1/velocity

particle_speed

Particle speed.

Symbol:

v

Latex:

\(v\)

Dimension:

velocity

particle_mass

mass of a particle.

Symbol:

m

Latex:

\(m\)

Dimension:

mass

equilibrium_temperature

Equilibrium temperature of the ensemble.

Symbol:

T

Latex:

\(T\)

Dimension:

temperature

law

f(v) = sqrt(2 / pi) * (m / (k_B * T))^(3/2) * v^2 * exp(-m * v^2 / (2 * k_B * T))

Latex:

\[f(v) = \sqrt{\frac{2}{\pi}} \left(\frac{m}{k_\text{B} T}\right)^{\frac{3}{2}} v^{2} \exp{\left(- \frac{m v^{2}}{2 k_\text{B} T} \right)}\]