Answer
The calorie content of 65 grams of candy is 326 kcal
Work Step by Step
The energy $Q$ required to raise the temperature of a substance is:
$Q = mc~\Delta T$
We can find the heat energy gained by the water and the aluminum.
$Q = m_w~c_w~\Delta T + m_a~c_a~\Delta T$
$Q = (1.75~kg)(4186~J/kg~C^{\circ})(53.5~^{\circ}C-15.0~^{\circ}C) + (0.325~kg+0.624~kg)(900~J/kg~C^{\circ})(53.5~^{\circ}C-15.0~^{\circ}C) $
$Q = 314,914.6~J$
This amount of energy is the energy released by the 15 grams of candy. We can convert the energy to units of calories.
$Q = (314,914.6~J)(\frac{1~cal}{4.186~J})$
$Q = 75,230~cal = 75.23~kcal$
We can find the calorie content per gram of the candy.
$\frac{75.23~kcal}{15~g} = 5.015~kcal/g$
We can find the calorie content of 65 grams of candy.
$(5.015~kcal/g)(65~g) = 326~kcal$
The calorie content of 65 grams of candy is 326 kcal.
