Maxwellian velocity distribution formula

This relationship should be familiar to the reader—it is the famous maxwellian velocity distribution formula for a gas at equilibrium. 

FYom this formula it is seen that to calculate /i we need to determine the mean molecular speed ( ci )m- For real systems the average molecular speed is difficult to determine. Assuming that the system is sufficiently close to equilibrium the velocity distribution may be taken to be Maxwellian. For molecules in the absolute Maxwellian state the peculiar velocity equals the microscopic molecular velocity, i.e., Ci = ci, because the macroscopic velocity... 

This result is purely statistical. Replacing the distribution function by particular expressions, depending on the temperature, is the last operation When a dynamical process occurs the equilibrium distribution function (maxwellian) should be modified, and the greater the reaction rate compared to the relaxation rates of both the velocities and the intramolecular states, the greater the modification Thus it is only for low reaction rates that equilibrium distribution functions can be inserted in the formulas above, and that the reaction rate depends on the temperature, but neither on the time nor on the concentrations. 

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