Maxwell–Boltzmann distribution facts for kids

The Maxwell–Boltzmann distribution is a special way to describe how fast tiny particles move. It's named after two scientists, James Clerk Maxwell and Ludwig Boltzmann.

This idea first came from physics, especially when studying how particles move in an ideal gas. Imagine a gas where particles fly around freely in a container. Most of the time, they don't touch each other. But sometimes, they collide and share energy. These particles are usually atoms or molecules. The gas system is assumed to be in a balanced state called thermodynamic equilibrium.

Maxwell first thought of this distribution in 1860. Later, Boltzmann did more research to understand why it works.

What Does This Distribution Tell Us?

A particle speed probability distribution shows which speeds are more likely for particles. It means a particle will have a speed chosen randomly from this distribution. Some speed ranges are more probable than others.

The distribution changes based on the gas's temperature and the particle's mass. Hotter gases mean faster particles. Lighter particles also tend to move faster.

Ideal Gases and Real Gases

The Maxwell–Boltzmann distribution works best for an ideal gas. An ideal gas is a simplified model of a real gas.

Real gases have other things happening, like tiny forces between particles (called van der Waals interactions) or very high speeds that need relativistic physics. These can make their speed distribution different.

However, many gases we find, especially thin (rarefied) gases at normal temperatures, act very much like an ideal gas. For these, the Maxwell speed distribution is a great way to understand them. This idea is a key part of the Kinetic theory of gases. This theory helps explain many basic gas properties, like pressure and how gases spread out.

Images for kids

• 

  This graph shows the probability density function (PDF) of the Maxwell–Boltzmann distribution.

• 

  This graph shows the cumulative distribution function (CDF) of the Maxwell–Boltzmann distribution.

• 

  Simulation of a 2D gas relaxing towards a Maxwell–Boltzmann speed distribution.

• 

  The Maxwell–Boltzmann distribution for the Sun's atmosphere. The particles are protons, and the temperature is 5800 K. The graph shows the most probable, mean, and root mean square velocities.

See also

In Spanish: Distribución de Maxwell-Boltzmann para niños