Question

For any distribution of speeds $V_{rms}\ge V_{av}$. Is this statement true or false?

Answer 1

As per Maxwell's speed distribution, various speeds are given by,

$v_{rms}=\sqrt{\frac{3RT}{M}}$

$v_{av}=\sqrt{\frac{8RT}{\pi M}}$

Now, since $3\pi >8$. Hence $3>\frac{8}{\pi }$.

This implies that $v_{rms}\ge v_{av}$ where equality holds at 0K.

Thus the given statement is true.