Solve the following problem:
Q: A gas initially at p1 = 1 bar and occupying a volume of 1 liter is compressed within a piston-cylinder assembly to a final pressure p2 = 4 bar.
(a) If the relationship between pressure and volume during the compression is PV = constant, determine the volume, in liters, at a pressure of 3 bar. Also plot the overall process on a graph of pressure versus volume.
(b) Repeat for a linear pressure-volume relationship between the same end states.