A cycle working with $2$ kg of air is assumed to consist of the following ideal gas closed system processes $($change of state$).$process $1-2)75$ kJ heat enters the system while no work is done. process $2-3)120$ kJ work exchange while expanding with no internal energy change. process $3-4)$ Constant volume process.process $4-1)$ The system is compressed back to its initial state without heat transfer.The internal energy change of the gas is $74$ kJ$.$

a$)$ Show the cycle on a P $-$ v diagram.

b$)$ Find the heat exchange during process $(3-4).$

c$)$ Find the net work of the cycle.