$(25$ P$)$ A piston$-$cylinder device contains water initially at $180$C$,$ and $0\mathrm{.}001$ m $3$ at saturated liquid. Saturated liquid then is heated at constant pressure until it reaches $250$ C $.$ Show the process on a T$-$v diagram with respect to saturation lines and determine $($a$)$ the mass of the liquid and $($c$)$ the amount of heat transfer.