$2\mathrm{.}25$ Air contained within a piston$-$cylinder assembly undergoes three processes in series:

Process $1-2$: Compression during which the pressure$-$volume relationship is $pV=$ constant from $p_1=10lb\frac{f}{i}n.{?}^2,V_1=4f{t}^3$ to $p_2=50lb\frac{f}{i}{n}^2$

Process $2-3$: Constant volume from state $2$ to state $3$ where $p=10lb\frac{f}{i}n.{?}^2$

Process $3-1$: Constant pressure expansion to the initial state.

Sketch the processes in series on $p-V$ coordinates. Evaluate $($a$)$ the volume at state $2,$ in $f{t}^3,$ and $($b$)$ the work for each process, in Btu.