In a vessel, the gas is at pressure P. If the mass of all the molecules is halved and their speed is doubled, then the resultant pressure will be

$\text{ As }P=\frac{1}{3}\frac{mN}{V}{v}_{\mathrm{rms}}^2 .....\left(i\right)$

where m is the mass of each molecule, N is the total number of molecules, V is the volume of the gas. When mass of all the molecules is halved and their speed is doubled, then the pressure will be

$$\begin{gathered} P^{\text{'}}=\frac{1}{3}\left(\frac{m}{2}\right)\times \frac{N}{V}\times {\left(2v_{\mathrm{rms}}\right)}^2 \\ =\frac{2}{3}\frac{mN}{V}{v}_{\mathrm{rms}}^2=2P .....\left(u\sin g\right(i\left)\right) \end{gathered}$$