P $2\mathrm{.}2(50$ pts$)$

Air is compressed in a piston cylinder device from $100$ kPa and $290$ K to $800$ kPa in a reversible

adiabatic process. Determine the final temperature and the work done during this process assuming

$($a$)$ constant specific heats and $($b$)$ variable specific heats. $($For air use $=1\mathrm{.}4$ and $R=287\frac{J}{k}gK)$