$2\mathrm{.}57$ WP A gas undergoes a cycle in a piston$-$cylinder assembly

consisting of the following three processes:

Process $1-2$: Constant pressure, $p=\frac{1\mathrm{.}4}{b}ar,V_1=0\mathrm{.}028m^3,W_{12}=$

$10\mathrm{.}5$ kJ

Process $2-3$: Compression with $pV=$ constant, $U_3=U_2$

Process $3-1$: Constant volume, $U_1-U_3=-26\mathrm{.}4kJ$

There are no significant changes in kinetic or potential energy.

a$.$ Sketch the cycle on a $p-V$ diagram.

b$.$ Calculate the net work for the cycle, in kJ$.$

c$.$ Calculate the heat transfer for process $1-2,$ in kJ$.$