$(35$ points$)$ A PVT cell containing pure water $(H_{2}O)$ shows two equilibrium phases of vapor and liquid at $336\mathrm{.}75C.$ Answer the questions below by using Appendix A$.$III of Sandler, "steam table."

a$.(5$ points$)$ What is the pressure $($MPa$)$ of the PVT cell?

b$.(10$ points$)$ The visual window of the PVT cell shows $70c{m}^3$ of vapor and $3c{m}^3$ of liquid at $336\mathrm{.}75C.$ What is the mass of water $($a total of liquid water and vapor water$)$ in the PVT cell?

c$.(20$ points$)$ Since the water in the PVT cell shows two equilibrium phases at the temperature $($and the corresponding pressure you answered in part a$),$ it has no thermodynamic freedom $)=(0.$ When an additional heat is given to the system while keeping the temperature at $336\mathrm{.}75C$ and the pressure $($that you answered in part a$),$ the volume increases from $73c{m}^3$ to $80c{m}^3.$ Note that the system is closed; hence, the total mass of water remains the same as Part $b.$ What is the mass of liquid water, and what is the mass of vapor water?