A $107\mathrm{.}2$ mL sample of $1\mathrm{.}00$ M NaOH is mixed with $53\mathrm{.}6$ mL of $1\mathrm{.}00$ M H$2$SO$4$ in a large Styrofoam coffee cup; the cup is fitted with a lid through which passes a calibrated thermometer. The temperature of each solution before mixing is $22\mathrm{.}05\backslash$deg C$.$ After adding the NaOH solution to the coffee cup and stirring the mixed solutions with the thermometer, the maximum temperature measured is $30\mathrm{.}70\backslash$deg C$.$ Assume that the density of the mixed solutions is $1\mathrm{.}00$ g$/$mL$,$ that the specific heat of the mixed solutions is $4\mathrm{.}18$ J$/($g$\backslash$deg C$),$ and that no heat is lost to the surroundings.