$20pts$ A piston$-$cylinder device initially contains steam at $3\mathrm{.}5$ MPa $,$ superheated by $5C.$

Now, steam loses heat to the surroundings and the piston moves down, hitting a set of stops,

at which point the cylinder contains saturated liquid water. The cooling continues until the

cylinder contains water at $200C.$ Determine

$($a$)$ The initial temperature

$($b$)$ The enthalpy change per unit mass of the steam by the time the piston first hits the

stops

$($c$)$ The final pressure and quality $($if it is a mixture$)$

$($d$)$ Draw the $T-v$ diagram for the process.