The thermodynamic processes are as follows:

1. Isothermal expansion from volume $V$ to $3V$: According to Boyle's law, $P \propto \frac{1}{V}$ at constant temperature. On a $P-V$ diagram, this is represented by a curve (rectangular hyperbola) where pressure decreases as volume increases.
2. Isobaric compression from volume $3V$ to $V$: At constant pressure, the volume decreases. On a $P-V$ diagram, this is represented by a horizontal straight line parallel to the volume axis, moving from right to left. The correct diagram will show a downward curve followed by a horizontal line moving leftwards back to the initial volume.