A piston with a weight is initially resting between two stops in a cylinder. The piston has a

diameter, dp$,$ of $30$ cm$,$ a thickness, tp$,$ of $5$ cm$,$ and a mass, mp$,$ of $173$ kg while the weight

has a mass, mw$,$ of $180$ kg$.$ The upper and lower stops are located at heights, hsu and hsl$,$

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$)).$

a$)$ The water is heated until the temperature reaches $250$C$.$ Calculate the pressure, specific

volume, and quality at this state.

b$)$ The weight is removed, and the water is cooled until the piston hits the lower stops.

What is the temperature at this state?

c$)$ Cooling continues until the water reaches a final temperature of $90$C$.$ Find the pressure

and quality at this final state.

d$)$ Calculate the total work of the entire process.

e$)$ Plot the entire process on a P $$v diagram, clearly indicating important intermediate

states, process direction, and all calculated P $,$ v$,$ and T values.