The Maxwell-Boltzmann distribution is a fundamental concept in statistical physics that describes the distribution of velocities for particles in a gas at a given temperature. It provides insights into the energy distribution and behavior of gas molecules in thermal equilibrium.

According to the Maxwell-Boltzmann distribution, the velocities of gas molecules in a sample follow a specific probability distribution. It states that at a given temperature, the majority of gas molecules have velocities around the average, with fewer molecules having higher or lower velocities.

The distribution curve of the Maxwell-Boltzmann distribution is bell-shaped and symmetric, resembling a Gaussian or normal distribution. The peak of the distribution represents the most probable velocity of the gas molecules, which increases with higher temperatures.

The Maxwell-Boltzmann distribution is influenced by the temperature of the gas. As temperature increases, the distribution curve broadens, indicating a wider range of velocities and a greater number of molecules with higher velocities.

The distribution provides valuable insights into various properties of gases, such as the average kinetic energy, the root mean square velocity, and the most probable velocity. It helps explain phenomena like diffusion, effusion, and the behavior of gases in different conditions.