A sample of an ideal gas is contained in a cylinder fitted with a movable piston at an initial absolute temperature \(T_1\) and pressure \(P_1\). The gas is heated such that its absolute temperature increases by \(50\%\) while the external pressure on the piston is adjusted to \(3.0\) times its initial value. Which of the following represents the ratio of the final molar volume of the gas to its initial molar volume, \(\dfrac{V_{m,\text{final}}}{V_{m,\text{initial}}}\)?