$($b$)$ Air at $\backslash (20^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ and $100$ kPa in an adiabatic cylinder is compressed in a reversible manner until the volume is reduced by $\backslash (50\backslash \%\backslash ).$ Assuming constant specific heats, determine:

$($i$)$ the final temperature of the air;

$(2$ marks$)$

$($ii$)$ the work done per unit mass.

$(3$ marks$)$