Answer
The calorie content of 100 grams of cookie is 471 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 = (2.00~kg)(4186~J/kg~C^{\circ})(36.0~^{\circ}C-15.0~^{\circ}C) + (0.615~kg+0.524~kg)(900~J/kg~C^{\circ})(36.0~^{\circ}C-15.0~^{\circ}C) $
$Q = 197,339.1~J$
This amount of energy is the energy released by the 10 grams of cookie. We can convert the energy to units of calories.
$Q = (197,339.1~J)(\frac{1~cal}{4.186~J})$
$Q = 47,100~cal = 47.1~kcal$
We can find the calorie content per gram of the cookie.
$\frac{47.1~kcal}{10~g} = 4.71~kcal/g$
We can find the calorie content of 100 grams of cookie.
$(4.71~kcal/g)(100~g) = 471~kcal$
The calorie content of 100 grams of cookie is 471 kcal.
