A closed system undergoes a process $1-2$ in which it absorbs $150 \: \mathrm{kJ}$ of energy as heat and does $90 \: \mathrm{kJ}$ of work. Then it follows another process $2-3$ in which $80 \: \mathrm{kJ}$ of work is done on it while it rejects $60\: \mathrm{ kJ}$ as heat. If it is desired to restore the system to the initial state (state $1$) by an adiabatic path, the work interaction (in $\mathrm{kJ}$) in this process will be
- $80$
- $100$
- $50$
- $70$
