Water contained inside a closed piston$-$cylinder device undergoes three processes.

Process $1$ to $2$: A constant pressure process from an absolute pressure of $5$ bar with $0\mathrm{.}05$ m$3$ saturated liquid

and $0\mathrm{.}05$ m $3$ saturated vapor $($State $1)$ to a temperature of $200$C $($State $2)$

Process $2$ to $3$: A constant temperature process to saturated vapor $($State $3)$

Process $3$ to $4$: A constant pressure process to a temperature of $160$C $($State $4)$

$($a$)$ Considering the constant temperature process from State $2$ to State $3$ to be polytropic Pv n $=$ constant,

find the value of n$.$

$($b$)$ Calculate the specific work for each process, in kJ$/$kg$.$

$($c$)$ Determine the specific heat transfer for each process, in kJ$/$kg$.$

$($d$)$ Show the three processes on T$-$v diagram relative to the vapor dome and the appropriate lines of constant

pressure for the four states. Label states and identify process directions with arrows.

For water: Pcritical $=221$ bar and Tcritical $=374$C$.$