In a coffee-cup calorimeter, a student mixes \(50.0\text{ mL}\) of \(1.0\text{ M HCl(aq)}\) with \(50.0\text{ mL}\) of \(1.0\text{ M NaOH(aq)}\), both initially at \(22.0\text{ }^\circ\text{C}\), and observes a maximum temperature increase of \(\Delta T_1\).

In a second trial, the student mixes \(50.0\text{ mL}\) of \(1.0\text{ M HCl(aq)}\) with \(100.0\text{ mL}\) of \(1.0\text{ M NaOH(aq)}\), both initially at \(22.0\text{ }^\circ\text{C}\), and observes a maximum temperature increase of \(\Delta T_2\).

Assuming negligible heat exchange with the calorimeter and surroundings, and that the densities and specific heat capacities of all solutions are equal to those of pure water, which of the following correctly compares \(\Delta T_2\) to \(\Delta T_1\) and provides the correct justification?