Exam Problem:

As shown in Fig. $1,$ a piston$-$cylinder assembly contains water of $2[kg].$ The piston is initially held by the saturated liquid water. The mass of the piston is $1080[kg]$ and its cross$-$section area is $20[c{m}^2].$ The water is heated slowly from the surrounding, and the piston starts moving upward slowly until it touches the stops at $18\mathrm{.}03[m].$ When the piston touches the stops, the heat s$$pply continues until the water becomes saturated vapor. The atmospheric pressure is $1[\frac{?}{\text{b}\text{a}\text{r}}]$ and the accelerate of gravity is $10[\frac{m}{s^2}].$ Neglect the area of the stops, the thickness of the piston, and the kinetic and potential energy changes of the water.

A$)$ Find the pressure and specific internal energy of the water and the height of the piston at the beginning. $(10$ points$)$

B$)$ Find the specific volume, pressure, and specific internal energy of the water and the force provided I by the stops when the heat supply stops. $(8$ points$)$

C$)$ Find the amount of heat supply. $(8$ points$)$

Fig. $1$: Schematic of the piston$-$cylinder system with stops.