Question:
The root mean square speed of molecules of a given mass of a gas at $27^{\circ} \mathrm{C}$ and 1 atmosphere pressure is $200 \mathrm{~ms}^{-1}$. The root mean square speed of molecules of the gas at $127^{\circ} \mathrm{C}$ and 2 atmosphere pressure is $\frac{x}{\sqrt{3}} m s^{-1}$. The value of $x$ will be
Solution:
(400)
$V_{\mathrm{rms}} \sqrt{\frac{3 \mathrm{RT}_{1}}{\mathrm{M}_{0}}}$
$200=\sqrt{\frac{3 R \times 300}{M_{0}}}$
Also, $\frac{x}{\sqrt{3}}=\sqrt{\frac{3 R \times 400}{M_{0}}}$
$(1) \div(2)$
$\frac{200}{x / \sqrt{3}}=\sqrt{\frac{300}{400}}=\sqrt{\frac{3}{4}}$
$\Rightarrow x=400 \mathrm{~m} / \mathrm{s}$
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