Question

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

Answer 1

$V_{\text{rms}}=\sqrt{\frac{3R{T}_1}{M_0}}$

$200=\sqrt{\frac{3R\times 300}{M_0}}\text{...........(1)}$

Also, $\frac{x}{\sqrt{3}}=\sqrt{\frac{3R\times 400}{M_0}}\text{...............(2)}$

Dividing equation$\left(1\right)$ by $\left(2\right)$

$\frac{200}{\frac{x}{\sqrt{3}}}=\sqrt{\frac{300}{400}}=\sqrt{\frac{3}{4}}$

$\Rightarrow x=400$