Question $1$

$(12$ points$)$

Given a piston$-$cylinder device with the piston connected to spring such that the volume in the cylinder varies linearly as the pressure changes. Initially, there is $1$ kg of water at $300$ kPa and $293$ K $.$ The whole assembly is heated until the volume in the cylinder becomes $\backslash (0\mathrm{.}1\backslash$mathrm$\{$~m$\}^\{3\}\backslash )$ and the pressure is ten times the initial pressure.

a$)$ Determine the final temperature for the water in the piston$-$cylinder device.

$(4$ points$)$

b$)$ Sketch the process in both $\backslash ($ P$-$v $\backslash )$ and $\backslash ($ T$-$v $\backslash )$ diagrams.

c$)$ Calculate the net work done in the process.