A gas undergoes a cycle in a piston$-$cylinder assembly consisting of the following three processes:

Process $1-2$: Constant pressure, $p=\frac{1\mathrm{.}4}{b}ar,V_1=0\mathrm{.}028m^3,W_{12}=10\mathrm{.}5kJ$

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

$($b$)$ Calculate the heat transfer for process $1-2,$ in $kJ.$