A piston$-$cylinder device with a volume of $0\mathrm{.}50$ m$3$ contains water at $325$ kPa $($State $1).$ Initially, $25\%$ of the mass is liquid and $75\%$ of the mass is vapor. Heat is added to the system until the piston is just touching the stopper $($State $2).$ At this state, all the water exists as saturated vapor. Heating is continued until the pressure inside the piston reaches $500$ kPa $($State $3).$ Based on the given information, answer the following questions:a$.$

What is the mass of water inside the piston?

b$.$

Determine the boundary work from State $1$ to State $3($in kJ$).$

c$.$

Determine the amount of heat from State $1$ to State $3($in kJ$).$

d$.$

What is the final state and temperature of the water?