Maxwell-Boltzmann Distribution
Watch ideal gas molecules bounce around in a box. The histogram shows their actual speed distribution alongside the theoretical Maxwell-Boltzmann curve. Raise the temperature to see the distribution broaden and shift.
The Maxwell-Boltzmann Distribution
In an ideal gas at thermal equilibrium, molecular speeds follow the Maxwell-Boltzmann distribution. This arises from the statistical mechanics of many particles exchanging energy through collisions. The distribution depends on temperature and molecular mass.
Key Speeds
The most probable speed vmp = sqrt(2kT/m) is the peak of the distribution. The mean speed vavg = sqrt(8kT/(πm)) is slightly higher. The root-mean-square speed vrms = sqrt(3kT/m) is higher still. These three speeds shift rightward with increasing temperature.
Dimensions
In 1D, the speed distribution is a half-Gaussian (since speed = |vx|). In 2D, it follows a Rayleigh distribution. The familiar 3D Maxwell-Boltzmann distribution has its characteristic v² factor from the spherical shell in velocity space.