Question

Suppose a container is evacuated to leave just one molecule of a gas in it. Let $v_{av}$ and $v_{rms}$ ​ represent the average speed and rms speed of the gas.

• A. $v_{av}>v_{rms}$
• B. $v_{av}<v_{rms}$
• C. $v_{av}=v_{rms}$
• D. $v_{rms}$ is undefined

Answer 1

The correct option is C $v_{av}=v_{rms}$

We know that,
$v_{av}=\frac{v_1+v_2+v_3+...+v_n}{n}$
$v_{rms}=\sqrt{\frac{v_1^2+v_2^2+v_3^2+...+v_n^2}{n}}$
Let us suppose $v_o$ is the speed of that one molecule.
So, $v_1=v_o$
$n=1$
$\therefore v_{av}=v_o$ ... (1)
and
$v_{rms}=v_o$ ... (2)
From equation (1) and (2), we can see that :
$v_{av}=v_{rms}$