Problem $1$: $(8$ points$)$

A system has a $0\mathrm{.}22$ Kg of fluid undergoes a cycle consists of four process:

Process $1-2$: fluid is expanding isothermally from $P_1=4\mathrm{.}15$ bar to $P_2=\frac{1\mathrm{.}15}{b}ar$ and $v_2=0\mathrm{.}12\frac{m^3}{k}g.$

Process $2-3$: fluid is expanding at constant pressure with $w_{2-3}=0\mathrm{.}525kJ$

Process $3-4$: fluid is cooled at constant volume to pressure $P_4=\frac{0\mathrm{.}62}{b}ar$

Process $4-1$: fluid is compressed according to $P{V}^n=c$ back to the initial condition.

Determine the following:

a$)$ sketch the cycle on a P$-$V diagram $($not relative to the vapor dome$)$

b$)$ the net work of the cycle

Solution: