A piston$-$cylinder device initially contains steam at $2$bar, $200$C$,$ and $0\mathrm{.}5$m$3.$ At this state, a linear spring $($F $$ x$)$ is attached to the piston but exerts no force on it$.$ Heat is now slowly transferred to the steam causing the pressure and volume to rise to $5$bar and $0\mathrm{.}6$m$3,$ respectively. Show the process on a P$-$V diagram and determine the final temperature, the work done by the steam, and the total heat transferred.