Physics - Heat & Thermo Question with Solution | TestHub

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