6.0 Maxwells's Distribution

In a given mass of gas, the velocities of all molecules are not the same, even when the bulk parameters like temperature, pressure and volume are fixed. Collisions change the direction and the speed of the molecules. However, in a state of equilibrium, the distribution of speeds is constant or fixed. The Maxwell's molecular speed distribution gives the number of molecules between the speeds $C$ and $C+dC$. If $dN$ represents the number of molecules with speeds between $C$ and $C+dC$, then

$$\begin{equation} \begin{aligned} dN = 4\pi N{\left( {\frac{m}{{2\pi kT}}} \right)^{\frac{3}{2}}}{C^2}{e^{ - \frac{{m{C^2}}}{{2kT}}}}dC \\ \\\end{aligned} \end{equation} $$

Here, $k = \frac{R}{{{N_A}}}$ = Boltzmann constant =$ 1.38 \times {10^{ - 23}}{\text{ }}\left( {\frac{J}{K}} \right) $

The graph between against $C$ at a given temperature looks like the one given below.