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}