An ideal gas follows an equation $P^{2}V=$ constant. The volume and temperature of the gas will be V and T. If the gas expands to double its volume then the final temperature of the gas is

$P^{2}V$ =constant      (1)

             From $PV=nRT\Rightarrow P=\frac{nRT}{V}$

             Substitute in (1) $\Rightarrow \frac{n^2{R}^2{T}^2}{V^2}V=$ constant

             $\frac{T^2}{V}=$ constant

             $\frac{T^2}{V}=\frac{T_2^2}{2V}\Rightarrow T_2^2=2T^2$

                                                $T_2=\sqrt{2}T$