Answer
The terminal voltage of the three mercury cells in series is higher than the terminal voltage of the 3 dry cells.
Work Step by Step
P=IV, so divide the 2.5 watts of power by the required voltage to find the current passing through the hearing aid.
$$I=\frac{P}{V}=\frac{2.5W}{4.0V}=0.625A$$
Use equation 19-1 to calculate the terminal voltage across the series combinations of three batteries.
$$V_{mercury}=3[\epsilon-Ir]=3[1.35V-(0.625A)(0.030\Omega)=3.99V$$
$$V_{dry}=3[\epsilon-Ir]=3[1.50V-(0.625A)(0.35\Omega)=3.84V$$
The terminal voltage of the three mercury cells in series is closer to 4.0V, and is higher than the terminal voltage of the 3 dry cells. The mercury cells will be a better choice for the hearing aid.
