Thermodynamics

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]