Problem $2\mathrm{.}24$

Carbon dioxide $(C{O}_2)$ gas in a piston$-$cylinder assembly undergoes three processes in series that begin and end at the same state $($a cycle$).$

Process $1-2$: Expansion from State $1$ where $p_1=\frac{10}{b}ar,V_1=1m^3,$ to State $2$ where $V_2=4m^3.$ During the process, pressure and volume are related by $p{V}^{1\mathrm{.}5}=$ constant.

Process $2-3$: Constant volume heating to State $3$ where $p_3=10$ bar.

Process $3-1$: Constant pressure compression to State $1.$

Sketch the processes on $p-V$ coordinates and evaluate the work for each process, in kJ $.$ What is net work for the cycle, in kJ $?$