States of Matter - Result Question 35
####35. The average velocity of an ideal gas molecule at $27^{\circ} C$ is $0.3 m / s$. The average velocity at $927^{\circ} C$ will be $(1986,1 M)$
(a) $0.6 m / s$
(b) $0.3 m / s$
(c) $0.9 m / s$
(d) $3.0 m / s$
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Solution:
- Expression for average velocity is $u _{av}=\sqrt{\frac{8 R T}{\pi M}}$
For the same gas but at different temperature
$$ \begin{aligned} \frac{u _{avg}\left(T _1\right)}{u _{avg}\left(T _2\right)} & =\sqrt{\frac{T _1}{T _2}}=\sqrt{\frac{300}{1200}}=\frac{1}{2} \ \Rightarrow \quad u _{av}\left(927^{\circ} C\right) & =2 \times u _{av}\left(27^{\circ} C\right)=0.6 ms^{-1} \end{aligned} $$
