Question

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

Answer 1

Answer: 400

$V_{rms}=\sqrt{\frac{3R{T}_1}{M_0}}$
$200=\sqrt{\frac{3R\times 300}{M_0}}....\left(1\right)$
Also, $\frac{x}{\sqrt{3}}=\sqrt{\frac{3R\times 400}{M_0}}.....\left(2\right)$
$(1)÷(2)$
$\frac{200}{x/\sqrt{3}}=\sqrt{\frac{300}{400}}=\sqrt{\frac{3}{4}}$
$\Rightarrow x=400m/s$