$6.(15$ points$)$ A free piston$-$cylinder system initially contains $8$ kg of saturated liquid H$2$O at $275$ kPa $.$ This H$2$O in the cylinder is gradually heated until all liquid has been vaporized to saturated vapor.

$(6$a$).(5$p$)$ Please find the volumes of H$2$O in the cylinder at initial state and the final state.

$(6$b$).(5$p$)$ Please calculate the boundary work during this process.

$(6$c$).(5$p$)$ Please determine the heat transfer during this process.