$($Q$3)$ A piston$-$cylinder device initially contains steam at $\backslash (400^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ and $3\mathrm{.}5$ MPa $.$ Now, steam loses heat to the surroundings and the piston moves down hitting a set of stops at which point the cylinder contains saturated water vapor. The cooling continues until the cylinder contains water at $\backslash (150^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ Determine $($a$)$ the initial temperature, $($b$)$ the enthalpy change per unit mass of the steam by the time the piston first hits the stops, and $($c$)$ the final pressure and the quality $($if mixture$).$ Also, show the process on the $\backslash ($ P$-$v $\backslash )$ diagram with respect to saturation lines.