A piston with a weight is initially resting between two stops in a cylinder. The piston has a diameter, $d_p,$ of $30$ cm $,$ a thickness, $t_p,$ of $5$ cm $,$ and a mass, $m_p,$ of $173$ kg while the weight has a mass, $m_w,$ of $180$ kg $.$ The upper and lower stops are located at heights, $h_{su}$ and $h_{sl},$ of $80$ and $20$ cm $,$ respectively. The cylinder contains $0\mathrm{.}5$ kg of water at an initial quality, $x_1,$ of $0\mathrm{.}05.$ The atmospheric pressure, $P_0,$ is $101$ kPa $.($Hint: Although a detailed $P-v$ diagram isn't required until part e$),$ you are likely to find a rough $P-v$ sketch very helpful as you work through parts a$)-$d