Maxwell-Boltzmann distribution

Definition

The Maxwell-Boltzmann distribution describes the distribution of speeds of particles in a gas. It shows that most particles have speeds around an average value, with fewer particles moving much slower or much faster.

5 Must Know Facts For Your Next Test

1. The distribution is derived from the principles of statistical mechanics.
2. It applies to ideal gases where interactions between molecules are negligible.
3. The shape of the Maxwell-Boltzmann curve changes with temperature; higher temperatures lead to a broader and flatter distribution.
4. The area under the curve represents the total number of molecules in the gas.
5. The most probable speed, mean speed, and root-mean-square speed are three key values derived from this distribution.

Review Questions

• What does the Maxwell-Boltzmann distribution describe?
• How does temperature affect the Maxwell-Boltzmann distribution?
• What are the key speeds that can be derived from the Maxwell-Boltzmann distribution?

Related terms

Root-Mean-Square Speed: A measure of the average speed of particles in a gas, calculated as $\sqrt{\left( \frac{3kT}{m} \right)}$, where $k$ is Boltzmann's constant, $T$ is temperature, and $m$ is particle mass.

Most Probable Speed: The speed at which the maximum number of particles in a gas move, given by $\sqrt{\left( \frac{2kT}{m} \right)}$.

Boltzmann's Constant: $k$, a fundamental physical constant relating energy at the particle level with temperature; its value is approximately $1.38 \times 10^{-23}$ J/K.