Initially a gas of diatomic molecules is contained in a cylinder of volume V_1 at a pressure P_1 and temperature 250 K. Assuming that 25% of the…

Initially a gas of diatomic molecules is contained in a cylinder of volume $\displaystyle \mathrm{V}_1$ at a pressure $\displaystyle \mathrm{P}_1$ and temperature $\displaystyle 250$ K. Assuming that $\displaystyle 25$% of the molecules get dissociated causing a change in number of moles. The pressure of the resulting gas at temperature $\displaystyle 2000$ K, when contained in a volume $\displaystyle 2 \mathrm{~V}_1$ is given by $\displaystyle \mathrm{P}_2$. The ratio $\displaystyle P_2 / P_1$ is \_\_\_\_.