Question

The root mean square velocity, $v_{rms}$, the average velocity $v_{av}$ and the most probable velocity, $v_{mp}$ of the molecules of the gas are in the order.

• A. $v_{mp}>v_{av}>v_{rms}$
• B. $v_{rms}>v_{av}>v_{mp}$
• C. $v_{av}>v_{mp}>v_{rms}$
• D. $v_{mp}>v_{rms}>v_{av}$

Answer 1

The correct option is B $v_{rms}>v_{av}>v_{mp}$

$v_{rms}=\sqrt{\frac{3kT}{m}},v_{av}=\sqrt{\frac{8kT}{m\pi }}$ and $v_{mp}=\sqrt{\frac{2kT}{m}}$
$\Rightarrow v_{rms}:v_{av}:v_{mp}=1:0.92:0.816$.
$\therefore v_{rms}>v_{av}>v_{mp}$.