Question $1(10$ pts$)$ : Nitrogen $($ideal gas$)$ expands isentropically in a piston cylinder device from a temperature $227C$ while its volume triples. Nitrogen has constant specific heats and $k=1\mathrm{.}4$ and $C_v=0\mathrm{.}718k\frac{J}{k}g*K.$

Tasks: $($a$)$ Determine the final temperature of the nitrogen $(5$ pts$)$

$($b$)$ Determine the work done by per kg nitrogen against the piston $(5$ pts$)$