Problem $3.$ A piston$-$cylinder device with a set of stops on the top contains $10$ kg of $H_{2}O.$ Initially, the

piston rests on the stops as shown in the figure. The initial pressure is $1\mathrm{.}5$

bar and the $H_{2}O$ initially occupies a volume of $1m^3.$ Heat is supplied to

$H_{2}O$ and its pressure increases. Once the pressure reaches $10$ bar the

piston begins to move up$.$ The pressure remains constant thereafter. The

process is continued until the final volume is $2\mathrm{.}48m^3.$

$($a$)$ Determine the initial specific volume and the initial quality $(x).$

$($b$)$ Determine the initial specific internal energy.

$($c$)$ Determine the final specific internal energy.

$($d$)$ Determine the change in temperature.

$($e$)$ Determine the amount of work done during the process in kJ $.$

$($f$)$ Apply first law and calculate the amount of heat transfer in kJ $.$

$($g$)$ Sketch the process on a p$-$v diagram. Be sure to include the saturation

lines.