One mol of an ideal diatomic gas underwent an adiabatic expansion form `298K, 15.00atm`, and `5.25L` to `2.5atm` against a constant external pressure of `1.00atm`. What is the final temperature of the system?

Explanation

This is an isobaric adiabatic expansion against constant externla pressure, but overall pressure decreases (volume increases, gas expands). Final temperature `T_(2)` is given by `P-V-T` relation as:
`T_(2)=T_(1)((C_(v)+P_(ex)(R )/(P_(1)))/(C_(v)+P_(ex)(R )/(P_(2))))`
For diatomic gas, `C_(v) = (5)/(2) R, T_(1) = 298 K, T_(2) = ?`
`P_(2) = 2.50atm, P_(1) = 15.00atm. P_(ex) = 1.900 atm`
`:. T_(2) = 298 (((5)/(2)R+(R)/(15))/((5)/(2)R+(R)/(2.5))) = 263.7 K`