A gas contained within a piston$-$cylinder assembly undergoes two processes, A and B $,$ between the same end states, $1$ and $2,$ where $p_1=\frac{10}{b}ar,V_1=0\mathrm{.}1m^3,U_1=400kJ$

and $p_2=1$ bar, $V_2=1\mathrm{.}0m^3,U_2=200kJ$ :

Process A: Process from $1$ to $2$ during which the pressure$-$ volume relation is $pV=$ constant.

Process B: Constant$-$volume process from state $1$ to a pressure of $2$ bar, followed by a linear pressure$-$volume process to state $2.$

Kinetic and potential energy effects can be ignored. For each of the processes A and B $,($a$)$ sketch the process on $p-V$ coordinates, $($b$)$ evaluate the work, in kJ $,$ and $($c$)$ evaluate the heat transfer, in kJ $.$