Open$-$Ended Problem $(25$ points$)$

One $kg$ of liquid water was heated in a piston$-$cylinder system to $110C$ at $0\mathrm{.}1$MPa. The system was then allowed to proceed to equilibrium adiabatically at $0\mathrm{.}10$MPa.

$6\mathrm{.}1$ What is the final temperature at equilibrium? $(8$ points$)$

$6\mathrm{.}2$ Find the fraction of water in the vapor and liquid phases at equilibrium. $(17$ points$)$