Question

The root mean square speed of molecules of a given mass of a gas at $27^\circ C$ and $1$ atmosphere pressure is $200ms^{- 1}.$ The root mean square speed of molecules of the gas at $127^\circ C$ and $2$ atmosphere pressure is $\frac{x}{\sqrt{3}}ms^{- 1}.$ The value of $x$ will be _________.

Answer 1

$V_{rms}=\sqrt{\frac{3 RT_{1}}{M_{0}}}$
$200=\sqrt{\frac{3 R \times 300}{M_{0}}}....\left(1\right)$
Also, $\frac{x}{\sqrt{3}}=\sqrt{\frac{3 R \times 400}{M_{0}}}.....\left(2\right)$
$\left(\right.1\left.\right)\div\left(\right.2\left.\right)$
$\frac{200}{x / \sqrt{3}}=\sqrt{\frac{300}{400}}=\sqrt{\frac{3}{4}}$
$\Rightarrow x=400m/s$