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## Homework Statement

Compute the mean energy and mean square energy of a free particle using the Boltzmann distribution.

## Homework Equations

## The Attempt at a Solution

I calculated the mean energy to be 3/2 kT by computing the mean square velocity directly from the Boltmann distribution function and then multiplying it by 1/2 m and then again multiplying by 3 to get the answer in three dimensions.

However, I cannot figure out how to compute the mean square energy as E^2 is proportional v^4 and computing it in one dimension does not allow me to simply multiply by 3 to get the answer in 3 dimensions.