Aresearcher studying the nutritional value of a new candy places a 6.60 g 6.60 g sample of the candy inside a bomb calorimeter and combusts it in excess oxygen. the observed temperature increase is 2.46 ∘ c. 2.46 ∘c. if the heat capacity of the calorimeter is 33.90 kj ⋅ k − 1 , 33.90 kj⋅k−1, how many nutritional calories are there per gram of the candy?

there are 3.018 kcal= 3018 cal per gram of candy

Explanation:

If the assume that the calorimeter is perfectly insulated, then all the heat released by the combustion is absorbed by the calorimeter.

Also knowing that Q= C * ΔT , where C= heat capacity of the calorimeter , ΔT= temperature change , Q = heat released by the combustion of the candy

replacing values

Q = C * ΔT = 33.90 kJ/°C * 2.46°C = 83.394 kJ

since Q is the heat released when burned all the mass m of the candy, the number of calories per gram of candy will be

q = Q/m =83.394 kJ / 6.60 g = 12.635 kJ/g

q = 12.635 kJ/g * 1 kcal / 4.186 kJ = 3.018 kcal per gram of candy