Maxwell speed distribution of a mixture of gases vs. of one gas How is it qualitatively justifiable that, in a mixture of molecules of different kinds in complete equilibrium, each kind of molecule has the same Maxwellian distribution in speed that it would have if the other kinds were not present?
 A: At the base of the Maxwellian velocity distribution, there are three key ingredients:

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*the equipartition theorem, connecting the average value of each component of the velocity with the temperature of the system (it is important to connect the average value of each cartesian component of velocity to the temperature);

*the central limit theorem (CLT), which ensures a gaussian distribution of each component of the velocity of one particle since it may be considered as the sum of a huge number of variations due to the other particles. Notice that CLT holds under very mild assumption on the distribution of velocity variations);

*the statistical independence of each component of the velocity of one particle on any other component of the velocity of the same or other particles. Such a hypothesis is certainly satisfied for a system at equilibrium with a thermostat at temperature $T$ since, under such conditions, there is no constraint on the velocities.

All these three points together are enough to imply the Maxwellian distribution. Consequently, that each kind of molecule has the same Maxwellian distribution in speed that it would have if the other species were not present.
