Aresearcher studying the nutritional value of a new candy places a 4.90 g sample of the candy inside a bomb calorimeter and combusts it in excess oxygen. the observed temperature increase is 2.15 ∘c. if the heat capacity of the calorimeter is 29.40 kj⋅k−1, how many nutritional calories are there per gram of the candy?

3,083 cal = 3.083 kcal = 3.083 nutritional calories

Explanation:

Heat released = heat capacity * change in temperature

Number of calories = number of Joules * (1 calorie/4.184 J)

Step 1: convert heat capacity to Joules per Kelvin (multiply heat capacity by 1000 J/kJ)

Step 2: determine heat released by multiplying heat capacity by change in temperature (2.15 degrees C is equivalent to 2.15 K)

Step 3: determine calories by multiplying value of Joules by (1 cal/4.184 J)

Step 4: determine calories per gram by dividing value of calories by mass of candy (4.90 grams)

29.40 kJ/K * 1000 J/kJ  = 29,400 J/K

29,400 J/K * 2.15 K = 63,210 J

63,210 J * (1 cal/4.184 J) = 15,107 cal

15,107 calories/4.90 grams = 3,083 calories/gram

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