Question

The $RMS$ velocity of an ideal gas at ${27}^{0}C$ is 0.3 $m/sec$. Its $RMS$ velocity at ${927}^{o}C$ is :

• A. 6 $m/sec$
• B. 0.3 $m/sec$
• C. 0.6 $m/sec$
• D. 3 $m/sec$

Answer 1

The correct option is C 0.6 $m/sec$

$27°C=300K$
$927°C=1200K$

We know, RMS velocity ∝$\sqrt{T}$

So, $\frac{v_1}{v_2}=\sqrt{\left(\frac{T_1}{T_2}\right)}$

$\frac{0.3}{v}=\sqrt{\left(\frac{300}{1200}\right)}$

$⟹v=0.6m/s$

So, the correct option is $C$