$2.(25$ points$)$ A piston$-$cylinder device initially contains refrigerant R$-134$a at $1\mathrm{.}5$ MPa $,$ superheated by $\backslash (5^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ Now, the refrigerant loses heat to the surroundings and the piston moves down hitting a set of stops at which point the cylinder contains saturated $\backslash ($ R $\backslash )-134$a in vapor state only. The cooling continues until the cylinder contains R$-134$a at $\backslash (46^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ Determine $($a$)$ the initial temperature, $($b$)$ the enthalpy change per unit mass of the refrigerant by the time the piston first hits the stops, $($c$)$ the final pressure and the quality $($if mixture$),$ and $($d$)$ show the process on a T$-$v diagram.