In thermal equilibrium, the particle velocity distribution follows the Maxwell-Boltzmann distribution, a statistical law determined by temperature and particle mass, describing the distribution of particle numbers at different velocities in an ideal gas.
Macroscopically, the system is in a stable, uniformly heated state; however, at the microscopic level, particles are constantly undergoing random thermal motion. Although the velocity of each individual particle changes constantly, the overall velocity distribution of a large number of particles exhibits a highly ordered statistical law.
The Influence of Temperature: As temperature increases, the distribution curve widens towards the high-speed region, and the average kinetic energy of the particles increases; conversely, it narrows and concentrates in the low-speed region.
The Influence of Mass: Larger particles (such as oxygen molecules) have a more concentrated velocity distribution in the low-speed region, while lighter particles (such as hydrogen molecules) are more likely to reach high speeds.
Microscopic Mechanism: Detailed Equilibrium and Dynamic Stability
The stability of the velocity distribution in thermal equilibrium stems from the principle of detailed equilibrium:
The probability that each particle gains a certain velocity through a collision is equal to the probability that it loses that velocity through a collision; Macroscopically, there is no directional flow of velocity or energy, and the system reaches dynamic equilibrium.
This also means that although the velocities of individual particles constantly change, the overall distribution remains constant, like a river-the water flows forward continuously, but the shape of the river surface remains unchanged.
Experimental Verification and Application
The Miller-Kush experiment (1955) successfully verified Maxwell's law of velocity distribution by measuring the deposition thickness of bismuth vapor molecules at different locations using high-vacuum technology.
This distribution is widely used in gas dynamics, chemical reaction rate theory, plasma physics, and astrophysics, serving as a bridge connecting microscopic motion and macroscopic phenomena.
