What does the Maxwell-Boltzmann distribution illustrate?

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The Maxwell-Boltzmann distribution is used to describe the fact that at a given temperature the individual atoms of an ideal gas are not all moving at the same velocity and thus have different kinetic energies. 

Take a balloon of helium for instance. It is filled with billions of helium atoms, all of which are moving at different velocities. As kinetic energy is proportional to velocity squared and mass, it is clear that a rise in velocity will increase the kinetic energy value. Mass does not play a significant role as helium atoms all have roughly the same mass (isotopes account for small differences). 

The Maxwell-Boltzmann distribution plots kinetic energy on the x-axis and number of particles of the y-axis. A curve is plotted showing the number of atoms that possess a specified kinetic energy. 

It is important to note that we can create a distribution for different temperatures and that this can help us understand how the distribution of particle kinetic energy changes as the temperature is altered. In the case of raising the temperature we would find that the curve flattens out and shifts along the x-axis. This is in accordance with the fact that as temperature rises, so too does the mean kinetic energy.

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