$2\mathrm{.}23$ AP A gas contained within a piston$-$cylinder assembly undergoes three processes in series:

Process $1-2$: Constant volume from $p_1=\frac{1}{b}ar,V_1=4m^3$ to state $2,$ where $p_2=2$ bar.

Process $2-3$: Compression to $V_3=2m^3,$ during which the pressure$-$volume relationship is $pV=$ constant.

Process $3-4$: Constant pressure to state $4,$ where $V_4=1m^3.$

Sketch the processes in series on $p-V$ coordinates and evaluate the work for each process, in kJ $.$