In a piston$-$water vapour system, there is initially wet water vapour at a pressure of P$=100$ kPa and a dryness of x$1=0\mathrm{.}1($state$-1).$ When q$=500$ kJ$/$kg heat is applied to the system, the piston rises without friction and starts to contact the spring $($state$-2).$ The heating process is continued until the wet vapour becomes saturated vapour $($state$-3)$ and the pressure increases according to the relation P$($v$)=$a$+$bv and reaches P$3-300$ kPa. Draw the P$-$v graph of the state changes and calculate the given heat and boundary work during the state changes