Problem $1$: As show in the figure, $0\mathrm{.}27$ kg of water is contained

within a piston$-$cylinder assembly. The piston, with a mass of $52$

kg and area of $0\mathrm{.}013m^2,$ is free to move smoothy in the cylinder.

The local atmospheric pressure and acceleration of gravity are

$102\mathrm{.}8$ kPa and $9\mathrm{.}85\frac{m}{s^2},$ respectively. For the water, if the total

volume is $0\mathrm{.}022m^3,$ determine the pressure, in kPa $,$ and quality.