Computational Problem $(40$ pts$)$

Water with an initial density of $=3\mathrm{.}42k\frac{g}{m^3}$ is

contained in a piston$-$cylinder assembly shown. The mass

of the circular piston is $80$ kg its area is $0\mathrm{.}00795m^2.$ The

atmospheric pressure of the surroundings is $\frac{1}{b}ar=100$

kPa $.$ The initial and final positions of the piston are shown

on the diagram. From the initial condition, the piston is

raised until it hits the stops. Then heat is transferred until

the pressure in the cylinder is $300$ kPa $.$ Friction between

the piston and the cylinder walls is negligible. $($Use $g=$

$9\mathrm{.}81\frac{m}{s^2})$

a$)$ Find the following for the initial state $($If the phase description is a saturated mixture,

also find the quality$)$:

$T_1(C),v_1(\frac{m^3}{kg}),$ Phase description $,u_1(\frac{kJ}{kg}),P_1(kPa)$

b$)$ When the piston first hits the stops, find the following $($If the phase description is a

saturated mixture, also find the quality$)$:

$T_2(C),v_2(\frac{m^3}{kg}),$ Phase description $,u_2(\frac{kJ}{kg}),P_2(kPa)$

c$)$ How much work was done on the water as the piston was raised from its initial

position to when it first hits the stops?

d$)$ For the final state where $P=300$kPa, find the following $($If the phase description is a

saturated mixture, also find the quality$)$:

$T_3(C),v_3(\frac{m^3}{kg}),$ Phase description $,u_3(\frac{kJ}{kg})$

e$)$ How much heat was transferred to the water from the time the piston first hit the

stops until the pressure reached $300$ kPa $?$

f$)$ Sketch the entire process $($state $1$ state $2$ state $3)$ on a $T-v$ diagram

Please explain how each individual piece was determined