Problem $2.$ For a gas contained in a closed system consider two processes, A and B$,$ between the

same end states, $1$ and $2,$ where p$1=1$bar, V$1=1$ m $3,$ U$1=400$ kJ and p$2=10$ bar, V$2=0\mathrm{.}1$ m $3,$

U$2=450$ kJ$.$ Process A: Constant volume process from state $1$ to a pressure of $10$ bar, followed

by a constant pressure process to state $2.$ Process B: Process from state $1$ to state $2$ during which

the pressure$-$volume relationship is pV $=$ constant. For each process A and B$,($a$)$ sketch the

process on a p$-$V diagram, $($b$)$ evaluate the work, in kJ$,$ and $($c$)$ apply first law and evaluate the

heat transfer, in kJ