$($a$)$ A gas within a piston$-$cylinder assembly undergoes a thermodynamic cycle consisting of three processes:

Process $1-2$: Constant volume $V_1=1m^3,p_1=1$ bar, to $p_2=3$ bar, $U_2-U_1=400kJ.$

Process $2-3$: Constant pressure expansion to $V_3=2m^3.$

Process $3-1$: Adiabatic compression, with $W_{31}=-1120kJ.$

There are no significant changes in kinetic or potential energy. Determine the net work for the cycle, in kJ$,$ and the heat transfers

for Processes $1-2$ and $2-3,$ in kJ$.$ Is this a power cycle or refrigeration cycle? Explain.