# Maxwell Boltzmann translational energy distribution.

What is the Maxwell Boltzmann translational energy distribution in units of k T

Â© BrainMass Inc. brainmass.com February 24, 2021, 2:34 pm ad1c9bdddfhttps://brainmass.com/physics/boltzmann-distribution/maxwell-boltzmann-translational-energy-distribution-30166

#### Solution Preview

The Maxwell Boltzmann speed distribution, P(v), is given by:

P(v) = 4 pi (m/(2 pi k T))^(3/2) Exp[-m v^2/(2 k T)] v^2

P(v)dv is the probability that a molecule of mass m has a speed between v and v + dv. Let's denote the energy distribution by Q(E). Then Q(E)dE is the probability that a molecule has an energy between E and E + dE. To find Q(E), eliminate v in P(v)dv ...

#### Solution Summary

The formula of the Maxwell Boltzmann translational energy distribution is derived.

$2.19