Why root mean square for temperature?

[Galap]

I was wondering why it is that when the temperature of something is being described, the root mean square speed of its atoms is used and not simply the mean speed. Why is the RMS more meaningful/useful when describing these things than the mean?

Thanks.

 

[ideasrule]

It's simply because the total kinetic energy of the molecules is given by E=n*(1/2)mv^2, where v is the RMS speed. That equation wouldn't work if v were the average speed.

 

[Galap]

It's simply because the total kinetic energy of the molecules is given by E=n*(1/2)mv^2, where v is the RMS speed. That equation wouldn't work if v were the average speed.

I guess the question would be better rephrased as: What physical properties of the atoms make it that v being the RMS work as opposed to the average?