A sample of an ideal gas is initially in state \(i\) with pressure \(P_0\) and volume \(V_0\). The gas expands to a final volume of \(2V_0\) along three different thermodynamic paths shown in the \(PV\) diagram: Path 1 is an isobaric expansion, Path 2 is an isothermal expansion, and Path 3 is an adiabatic expansion. Which of the following statements correctly compares the work done by the gas along these paths and provides the correct physical justification?