A $2\mathrm{.}00-$mol sample of a diatomic ideal gas expands slowly and adiabatically from a pressure of $5\mathrm{.}02$ atm and a volume of $12\mathrm{.}6$ L to a final volume of $31\mathrm{.}0$ L$.$

$($a$)$ What is the final pressure of the gas?

$($b$)$ What are the initial and final temperatures?

$($c$)$ Find Q for the gas during this process.

$($d$)$ Find $$Eint for the gas during this process.

$($e$)$ Find W for the gas during this process.