How Is the Average Energy Calculated in Statistical Mechanics?

[Kara386]

Homework Statement

If the energy of a system depends on $E = \alpha |x|$ where $\alpha$ is positive, what is the average energy of the system?

Homework Equations

The Attempt at a Solution

I've been given no information at all about the system beyond the energy. This is within a statistical mechanics course so I assume it involves some sort of distribution function, but as to which one I have no idea. Alternatively it may be related to equipartition theorem because that's what the previous question was about, although that only deals with quadratic contributions to energy I think.

Apparently the answer is $kT$. I'd really appreciate some pointers on how to get there! :)

 

[TSny]

This is within a statistical mechanics course so I assume it involves some sort of distribution function, but as to which one I have no idea.
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Apparently the answer is $kT$.

Since the answer involves $T$, which distribution function do you think is most appropriate?