Problem $6(10$ points$)$

Consider a power cycle executed by a gas in a piston$-$cylinder assembly, which follows the $P-V$ relationship shown in the figure below. For process $1-2,U_2-U_1=15kJ.$ For process $3-1,Q_{31}=10$ kJ $.$ Assuming there are no changes in kinetic or potential energy, calculate the following:

a$)$ The work for each process, in kJ $($comment on the signs$).$

b$)$ The heat transfer for processes $1-2$ and $2-3,$ each in kJ $($comment on the signs$).$

c$)$ The thermal efficiency of the power cycle.