Problem $1(5$ marks$).$ An insulated piston$-$cylinder device contains $5$ L of saturated liquid water at a pressure of $200$ kPa $.$ Water is stirred by a paddle wheel while a current of $5$ A $,$ from a $120$ V source, flows for $45$ min through a resistor placed in the water. If one$-$half of the liquid is evaporated during this constant pressure process and the paddle$-$wheel work amounts to $400$ kJ $,$ do the following:

Figure P$1$ Schematic for Problem $1$

a$)$ Determine the final Volume of the piston$-$cylinder.

b$)$ Determine the boundary work.

c$)$ Show the process on a $\backslash ($ T$-$v $\backslash )$ diagram with respect to saturation lines.