The speed distribution functions will allow us to know the fraction of molecules with speeds between two given values.

We are going to use 3 distribution functions:

  • For the velocity components $g(v_x),g(v_y)$ and $g(v_z)$.
  • For the velocity vector $\phi(\vec{v})$
  • For the velocity module $G(v)$.

Distribution functions of the velocity components $g(v_x),g(v_y)$ and $g(v_z)$

The distribution function $g(v_x)$ allows to know the fraction of molecules with velocities between $v_x$ and $v_x+dv_x$.

\begin{equation} dN_{v_{x}}/N=g(v_x)dv_x \end{equation}

Analogous equations can be written for the distribution functions in the y,z direction

\begin{equation} dN_{v_{y}}/N=g(v_y)dv_y \end{equation}

\begin{equation} dN_{v_{z}}/N=g(v_z)dv_z \end{equation}