$4.[10$ Pts$]$ A polytropic compressor $\backslash (\backslash$left$($P

u$^\{$n$\}=\backslash$right$.\backslash )$ Constant$)$ compresses air $($ideal gas$)$ at $100$ kPa and $300$ K to $1$ MPa $.$

Compressor work

$($a$)$ What are the specific heat and specific entropy change if $\backslash ($ n$=1\mathrm{.}2\backslash )?[4$ Pts$]$

$($b$)$ What are the specific heat and specific entropy change if this is isentropic$?[3$ Pts$]$

$($c$)$ Draw these two processes in a $\backslash ($ P$-$v $\backslash )$ diagram. Which consumes less work? $[3$ Pts$]$