Air within a piston$-$cylinder assembly, initially at $50$lb$($f$)/($i$)$n$.^(2),510\backslash$deg R$,$ and a volume of $6$ft$^(3),$ is compressed isentropically to a final

volume of $3$ft$^(3).$

Assuming the ideal gas model with k$=1\mathrm{.}4$ for the air, determine the:

$($a$)$ mass, in lb$.$

$($b$)$ final pressure, in lb$($f$)/($i$)$n$.^(2)$

$($c$)$ final temperature, in $\backslash$deg R$.$

$($d$)$ work, in Btu.