Maxwell-boltzman distribution under gallilean transformation

[diganta]

Could anyone tell me what happens to the Maxwell-Boltzmann velocity distribution law under
Galilean transformation!

 

[weejee]

Should be simply v -> v-u, so that particles have net average velocity u.

 

[charng]

The Maxwell-Boltzmann velocity distribution law is a fundamental concept in statistical mechanics, describing the distribution of velocities of particles in a gas at a certain temperature. This distribution is based on the assumption that the particles are in thermal equilibrium and obey the laws of classical mechanics.

Under a Galilean transformation, which is a mathematical transformation used to describe the relationship between different frames of reference, the Maxwell-Boltzmann velocity distribution law remains unchanged. This is because the transformation only affects the coordinate system and not the physical properties of the particles.

In other words, the distribution of velocities of particles in a gas will remain the same regardless of which frame of reference we use to measure them. This is a fundamental principle in classical mechanics, known as the principle of relativity.

However, it is important to note that this only applies to classical systems and does not hold true in the realm of quantum mechanics. In quantum systems, the velocity distribution of particles is described by the Fermi-Dirac or Bose-Einstein distribution, which can be affected by a change in reference frame.

In conclusion, the Maxwell-Boltzmann velocity distribution law remains unchanged under Galilean transformation, highlighting the robustness and applicability of this fundamental concept in statistical mechanics.