CARBON DIOXIDE $\backslash (\backslash$left$(\backslash$mathrm$\{$CO$\}\_\{2\}\backslash$right$)\backslash )$ and NITROGEN $\backslash (\backslash$left$(\backslash$mathrm$\{$N$\}\_\{2\}\backslash$right$)\backslash )$ initially reside in the apparatus and at the states shown below.

The valve between the tanks is opened. During the mixing process, the piston moves. The final mixture has a temperature of $\backslash (27^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ and a pressure of $1$ bar. The process was adiabatic.

a$)$ Determine the magnitude and direction of work transfer for the process.

b$)$ Determine the entropy production for the process.