$ \begin{aligned} & \Delta \mathrm{U}=\mathrm{q}+\mathrm{w}(\mathrm{q}=0) \\ & \mathrm{nC}_{\mathrm{V}} \Delta \mathrm{~T}=-\mathrm{P}_{\mathrm{ext}}\left(\mathrm{~V}_2-\mathrm{V}_1\right) \\ & \mathrm{V}_2=2 \mathrm{~V}_1 \\ & \frac{\mathrm{nRT}_2}{\mathrm{P}_2}=\frac{2 \mathrm{nRT}_1}{\mathrm{P}_1} \\ & \mathrm{P}_1=5, \mathrm{~T}_1=298 \\ & \mathrm{P}_2=\frac{5 \mathrm{~T}_2}{2 \times 298} \\ & \mathrm{n} \frac{5}{2} \mathrm{R}\left(\mathrm{~T}_2-\mathrm{T}_1\right)=-1\left(\frac{\mathrm{nRT}_2}{\mathrm{P}_1}-\frac{\mathrm{nRT}_1}{\mathrm{P}_1}\right) \end{aligned} $
Put $\mathrm{T}_1=298$ and $P_2=\frac{5 \mathrm{~T}_2}{2 \times 298}$

Solve and we get $T_2=274.16 \mathrm{~K}$
$ \mathrm{T}_2 \approx 274 \mathrm{~K} $