Maxwell-Boltzmanm Distribution of Velocities
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Instructions
Initialization of velocities for N particles:
- Generate Random Numbers: Generate 3N random numbers from a normal distribution with zero mean and
unit variance.
- Generate Velocities: Multiply these random numbers by sqrt(kT/m) to
obtain
the x, y, and z components of velocities for the N particles, where k is
Boltzmann's constant, m is the mass of the particles, and T is the
desired temperature.
- Plot F(vi).
- Plot F(v).
- F(Vi)dvi = fraction of particles with velocity
component vi between vi and vi +
dvi.
- F(v)dv = fraction of particles with speed between v and v + dv.
- P(v)dv = 4
[m/(2kT)]3/2v2e(-mv2/2kT)dv
- P(vx)dvx = [m/(2kT)]1/2e(-mvx2/2kT)dvx