Please include a system diagram, assumptions, and basic equations

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 $0\mathrm{.}05m^3$ saturated liquid

and $0\mathrm{.}05m^3$ saturated vapor $($State $1)$ to a temperature of $200C($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 $160C($State $4)$

$($a$)$ Considering the constant temperature process from State $2$ to State $3$ to be polytropic $P{v}^n=$ constant,

find the value of $n.$

$($b$)$ Calculate the specific work for each process, in $k\frac{J}{k}g.$

$($c$)$ Determine the specific heat transfer for each process, in $k\frac{J}{k}g.$

$($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: $P_{\text{c}\text{r}\text{i}\text{t}\text{i}\text{c}\text{a}\text{l}}=221$ bar and $T_{\text{c}\text{r}\text{i}\text{t}\text{i}\text{c}\text{a}\text{l}}=374C.$