$(2\mathrm{.}78$ Moran $8^{th}$ edition$)$ A gas within a piston$-$cylinder assembly undergoes a thermodynamic cycle consisting of three processes:

Process $1-2$: Compression with $pV=$ constant, from $p_1=\frac{1}{b}ar,V_1=2m^3$ to $V_2=0\mathrm{.}2m^3,$

$U_2-U_1=100kJ.$

Process $2-3$: Constant volume until $p_3=p_1$

Process $3-1$: Constant pressure and adiabatic process.

There are no significant changes in kinetic or potential energy. Determine:

a$)$ the net work of the cycle, in kJ

b$)$ the heat transfer for process $2-3,$ in kJ

c$)$ is this a power cycle or a refrigeration cycle? Explain.