$3.[10$ Pts$]$ Diatomic $\backslash (\backslash$mathrm$\{$N$\}\_\{2\}\backslash )$ gas at $500$ K and $1$ MPa is flowing into a spring$-$loaded cylinder. The proportionality constant between the spring pressure and the control volume is $\backslash (100,000\backslash$mathrm$\{$~Pa$\}/\backslash$mathrm$\{$m$\}^\{3\}\backslash ).$ When the spring pressure matches the incoming nitrogen pressure, the flow stops and the cylinder closes. Assume the spring force and the control volume at the beginning of the process start from zero. Use ideal gas law for this question.

$($a$)$ How much specific entropy does this process generate per unit mass of nitrogen in the cylinder? $[8$ Pts$]$

$($b$)$ Is this a reversible process? $[2$ Pts$]$