An ideal gas, \(\overline{C_V} = \frac{5}{2} R\), is expanded adiabatically against a constant pressure of 1 atm until it doubles in volume.
If the initial temperature and pressure are \(298 \, \text{K}\) and \(5 \, \text{atm}\), respectively, then the final temperature is ______ \( \, \text{K} \) (nearest integer).
Given: \(\overline{C_V}\) is the molar heat capacity at constant volume.