What are the most probable velocity and the average velocity for a system that follows the Maxwell-Boltzmann distribution?

The Maxwell-Boltzmann distribution is given by

dN/N = (m/2πkbt)1/2x

  • dN/N is the fraction of molecules moving at velocity v to v + dv,
  • m is the mass of the molecule,
  • kb is the Boltzmann constant, and
  • T is the absolute temperature.

Average Velocity is displacement over total time. We calculate the expectation value of v

¯v=∫f(v)vdv

The first typical velocity is the easiest to calculate and termed as the most probable velocity ˜v

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