A sample of an ideal gas expands from an initial state \((P_0, V_0)\) to a final volume \(2V_0\) via two different thermodynamic paths, as shown in the \(P\text{-}V\) diagram. In Process 1, the gas expands isothermally at temperature \(T_0\). In Process 2, the gas expands adiabatically from the same initial state. Which of the following correctly compares the magnitude of the work done by the gas during Process 1 (\(W_1\)) to the work done by the gas during Process 2 (\(W_2\)), and provides the correct physical justification?