An ideal gas, $\overline{\mathrm{C}}_{\mathrm{v}}=\frac{5}{2} \mathrm{R}$, is expanded adiabatically against a constant pressure of 1 atm untill it doubles in volume. If the initial temperature and pressure is $298 \mathrm{~K}$ and $5 \mathrm{~atm}$, respectively then the final temperature is _________ $\mathrm{K}$ (nearest integer).

[$\overline{\mathrm{c}}_{\mathrm{v}}$ is the molar heat capacity at constant volume]