In a vessel, the gas is at pressure P , if the mass of all the...

The equation of pressure is P=$\frac{1}{3} \frac{m \mathrm{~N}}{v^2}$v_{r m s}^2 where $m=$ mass of each molecules $$\begin{aligned}& N=\text{ number\text{ of }\text{ molecules } }\\ & V=\text{ volume of the gas } \end{aligned}$$According to the question: mass of all molecules is halved an velocity is double then $$\begin{aligned} \mathrm{P}^{\prime}=\frac{1}{3}\left(\frac{m}{2}\right) \times \frac{\mathrm{N}}{\mathrm{V}} \times(& \left(2 \mathrm{~V}_{\mathrm{ras}}\right)^2 \\ & =\frac{2}{3} \frac{m \mathrm{~N}}{\mathrm{~V}} \mathrm{~V}_{\mathrm{ras}}^2 \\ & =2 \mathrm{P} \end{aligned}$$compare with eq (i) $$\begin{aligned}& \mathrm{P}^{\prime}=2 \mathrm{P}\\ & \mathrm{P}^{\prime}=2 \mathrm{P} \end{aligned}$$