States of Matter 1 Question 35
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35. The average velocity of an ideal gas molecule at $27^{\circ} \mathrm{C}$ is $0.3 \mathrm{~m} / \mathrm{s}$. The average velocity at $927^{\circ} \mathrm{C}$ will be $(1986,1 \mathrm{M})$
======= ####35. The average velocity of an ideal gas molecule at $27^{\circ} \mathrm{C}$ is $0.3 \mathrm{~m} / \mathrm{s}$. The average velocity at $927^{\circ} \mathrm{C}$ will be $(1986,1 \mathrm{M})$
3e0f7ab6f6a50373c3f2dbda6ca2533482a77bed (a) $0.6 \mathrm{~m} / \mathrm{s}$
(b) $0.3 \mathrm{~m} / \mathrm{s}$
(c) $0.9 \mathrm{~m} / \mathrm{s}$
(d) $3.0 \mathrm{~m} / \mathrm{s}$
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Solution:
- Expression for average velocity is $u_{\mathrm{av}}=\sqrt{\frac{8 R T}{\pi M}}$
For the same gas but at different temperature
$$ \begin{aligned} \frac{u_{\mathrm{avg}}\left(T_{1}\right)}{u_{\mathrm{avg}}\left(T_{2}\right)} & =\sqrt{\frac{T_{1}}{T_{2}}}=\sqrt{\frac{300}{1200}}=\frac{1}{2} \ \Rightarrow \quad u_{\mathrm{av}}\left(927^{\circ} \mathrm{C}\right) & =2 \times u_{\mathrm{av}}\left(27^{\circ} \mathrm{C}\right)=0.6 \mathrm{~ms}^{-1} \end{aligned} $$
