Question

The root mean square speed of gas molecules is C${}_{rms}$. The root mean square speed in a specific direction will be :

• A. C${}_{rms}$
• B. $\frac{C_{rms}}{3}$
• C. $\frac{C_{rms}}{\sqrt{3}}$
• D. $\sqrt{3}{C}_{rms}$

Answer 1

The correct option is C $\frac{C_{rms}}{\sqrt{3}}$

$C_{rms}=\sqrt{\overline{C^2}}$
$\overline{C^2}=\overline{u^2}+\overline{v^2}+\overline{w^2}$
$u^2=v^2=w^2$
$\therefore \overline{C^2}=3\overline{u^2}$
$\Rightarrow \overline{u^2}=\frac{1}{3}\overline{C^2}$
$\therefore u_{rms}=\sqrt{\overline{u^2}}=\sqrt{\frac{1}{3}\overline{C^2}}=\frac{1}{\sqrt{3}}{C}_{rms}$