`1mol` of an ideal gas at `400K` and `10atm` is allowed to expand, adiabatically, against `2.0atm` external pressure. Find the final temperature of the gas. [Use: `C_(v) = (5)/(2)R]`

Explanation

Assume `P_(2) = P_(ex)` and use `T_(2) = [(C_(v)+((P_(ex))/(P_(1)))R)/(C_(v)+R)]T_(1)`
`rArr T_(2) = [((5)/(2)R+(2)/(10)R)/((5)/(2)R+R)]xx400K`
`= [(2.7R)/(3.5R)] xx400K = 308.6K`