A cylinder having a piston restrained by a linear spring $($of spring constant $15k\frac{N}{m})$ contains $0\mathrm{.}5$ kg of superheated water vapor at $800C,500$kpa, as shown in the figure below. Heat

is transferred from the water $($cooling process$),$ causing the piston to move down. If the piston cross$-$sectional area is $0\mathrm{.}05m^2,$ and the pressure varies linearly with volume until a

final pressure of $200$ kPa is reached. Find

$1-$ The final temperature and volume

$2-$ The work and heat transfer for the process.

$3-$ Draw the process on a P $-$ v and $T-v$ diagrams