College Physics III – Thermodynamics, Electricity, and Magnetism
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.
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The distribution is derived from the principles of statistical mechanics.
It applies to ideal gases where interactions between molecules are negligible.
The shape of the Maxwell-Boltzmann curve changes with temperature; higher temperatures lead to a broader and flatter distribution.
The area under the curve represents the total number of molecules in the gas.
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.