Nitrogen $(N_2)$ at $\frac{1}{b}ar,300K$ enters a compressor operating at steady state and is compressed adiabatically to an exit state of $13\mathrm{.}0$ bar, $670$ K $.$ The $N_2$ is modeled as an ideal gas and kinetic and potential energy effects are negligible.

Determine the work input, in kJ per kg of $N_2$ flowing, the rate of entropy production, in $k\frac{J}{K}$ per kg of $N_2$ flowing, and the isentropic compressor efficiency.