Energy distribution

For a system containing a large number of identical non-interacting non-relativistic classical particles in thermodynamic equilibrium, the energy distribution function is a function such that \(f(E) dE\) gives the fraction of particles with energies in the interval \(dE\) around energy value \(E\).

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.

energy

energy of the ensemble.

Symbol:

E

Latex:

\(E\)

Dimension:

energy

energy_distribution_function

energy distribution function.

Symbol:

f(E)

Latex:

\(f(E)\)

Dimension:

1/energy

equilibrium_temperature

Equilibrium temperature of the ensemble.

Symbol:

T

Latex:

\(T\)

Dimension:

temperature

law

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

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