- #1

ehrenfest

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## Homework Statement

The following is a probability density distribution for an ideal gas:

[tex] p(v_x,v_y,v_z) = (2 \pi \sigma ^2)^{-3/2} \exp\left({\frac{v_x^2 +v_y^2+v_z^2}{2 \sigma^2}}\right) [/tex]

[tex]E = 0.5 m |\vec{v}|^2[/tex]

Find p(E).

## Homework Equations

## The Attempt at a Solution

I want to just plug in what E but that gives the wrong answer and I cannot figure out why.

[tex] p(E) = (2 \pi \sigma ^2)^{-3/2} \exp\left({\frac{E}{m \sigma^2}}\right) [/tex]

Why is that wrong? It makes no sense, but I just plugged in what E was! This is really bothering me.