The Maxwell–Boltzmann distribution describes how particle speeds are distributed in a classical ideal gas at a given temperature. It applies to non-quantum systems where particles are distinguishable and do not obey the Pauli exclusion principle or Bose–Einstein statistics.
In this framework, most particles in a gas move at moderate speeds, while fewer move very slowly or very quickly. The distribution is shaped by the balance between thermal energy and molecular motion.
Key Features:
- The distribution predicts three key speeds:
- Most probable speed: the speed at which the largest number of particles move.
- Average speed: the mean speed of all particles.
- Root-mean-square speed: related to the average kinetic energy.
- Depends on the temperature and mass of the particles: higher temperatures or lighter particles lead to broader, faster distributions.
Examples:
- Explains gas pressure and temperature in terms of particle collisions and motion.
- Used to model diffusion, effusion, and viscosity in gases.
- Applied in thermodynamics and statistical mechanics for predicting gas behavior.
The Maxwell–Boltzmann distribution is foundational in classical physics and remains a key tool for understanding the kinetic theory of gases and the behavior of non-quantum thermodynamic systems.