Maxwell Boltzmann Distribution

The Maxwell Boltzmann distribution can be studied with the help of a graph given below in this article.

The graph shows the number of molecules possessing a certain speed on the Y-axis and their respective speeds on the X-axis. We can see that the maximum speed is only possessed by a very small number of molecules whereas most of the molecules possess a speed called most probable speed.

Let us see the Maxwell-Boltzmann distribution curve for an ideal gas at two different temperatures T₁ and T₂ where T₁>T₂.

It can be seen from the above graph that as the temperature rises, the curve begins to flatten and broaden. Also, the particles that possess the most probable speed reduce but the area under the graph increases which shows that more particles gain energy and are set in motion.

From the kinetic theory of gases, we have learnt that all the particles in air travel at different speeds and the speed of each particle are due to the collisions between the particles present in the air. Thus, we cannot tell the speed of each particle in the gas or air. Instead, we can tell the number of particles or in other words, we can say that the distribution of particles with a particular speed in gas at a certain temperature can be known. James Maxwell and Ludwig Boltzmann showed the distribution of the particles having different speeds in an ideal gas. Let us look further into Maxwell Boltzmann’s distribution.