If one mole of the polyatomic gas is having two vibrational modes and $\beta$ is the ratio of molar specific heats for polyatomic gas $\left(\beta =\frac{{\mathrm{C}}_{\mathrm{P}}}{{\mathrm{C}}_{\mathrm{v}}}\right)$ then the value of $\beta$ is :

Figure shows graphs of pressure vs density for an ideal gas at two temperatures $T_1$ and $T_2.$

In the figure, the volume of container $X$ is double of the volume of container $Y$. Both are filled with ideal gas. The temperature of $X$ is $200 \mathrm{K}$ and that of $Y$ is $400 \mathrm{K}$. If the mass of gas in $X$ is $m$, then the mass of gas in $Y$ will be?