A piston$-$cylinder device initially contains $0\mathrm{.}095m3$ of nitrogen gas at $110$ kPa and $115$ C $.$ The nitrogen is now expanded polytropically to a state of $95$ kPa and $96$ C $.$ Determine the polytropic index, work done, heat transfer and change in internal energy during this process. Take $R=296\mathrm{.}8\frac{J}{k}gK$ and $c_v=743\frac{J}{k}gK$ for nitrogen.

Please use $4$ signficant digits for all calculations

$n=($note this value may or may not look like the typical values that we used$)$

$W=$ Joules

$U=$ Joules

$Q=$ Joules