There is a mixing device which produces sub$-$cooled liquid nitrogen at a pressure of $200$ kPa as shown in Figure $3.$ Sub$-$cooled liquid nitrogen at $70$ K enters the mixing chamber from the first feeding line. The nitrogen at the pressure of $1$ MPa and temperature of $300$ K is first expanded to a pressure of $200$ kPa by passing through a throttling valve and then is sent to a mixing chamber from the second feeding line. There is a heat leakage from the environment at $300$ K temperature to the mixing chamber due to high temperature difference between the chamber and the environment although it is insulated. The amount of heat transfer rate due to leakage and mass flow rate of the produced saturated liquid nitrogen are given as $0\mathrm{.}06$ kW and $\backslash (0\mathrm{.}08\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$s$\}\backslash ),$ respectively. Calculate $($a$)$ the mass flow rate of nitrogen at state $1,($b$)$ the net entropy change of the system, and $($c$)$ the entropy generation through this process.