$(18$ points total$)$ We have an air filled piston cylinder device with these initial conditions:

$P[1]=100[$bar$],[1]=1000[C],V[1]=1[$Liter$],$ and an Expansion Ratio $=10$

$(Vma\frac{x}{V}$min$).$ The State $1$ conditions are similar to an engine after constant volume heat

addition. Assume air acts like an ideal gas. The piston cylinder device expands in the

three different scenarios below. Finish this problem in this order: a$)$ i$,$ ii$,$ iii, b$)$ i$,$ ii$,$ iii, c$)$

i$,$ ii$,$ iii, bar graph. essentially for each of the three scenarios do i$,$ ii$,$ iii before moving

onto the next scenario, then finally finish with the bar graph.

a$)$ Isobarically

b$)$ Isothermally

c$)$ Polytropically Constant