In a piston$-$cylinder assembly, there is initially $0\mathrm{.}8$ m$^3$ of saturated water vapor at $250$ kPa pressure. In this case, the piston rests on the stopper pins. A pressure of $300$ kPa is required to move the piston upward. Heat is given to the saturated water vapor until its volume doubles.

a$)$ Show the process on a p$-$v diagram.

b$)$ Find the initial and final temperatures.

c$)$ Calculate the work done and total heat transfer during the process.

State your assumptions.