A closed system completes a cycle consisting of three processes. During the first process, which is adiabatic, $50$ kJ of work is done on the system. During the second phase change, no work is done, while $200$ kJ of heat is transferred to the system. During the third phase change, the system returns to its initial state by doing $90$ kJ of work.$($a$)$ Calculate the heat transfer during the third phase change,$(6)$ Calculate the net work of the cycle.