Estimate the Calorie content of 65 g of candy from the following measurements. A 15-g sample of the candy is placed in a small aluminum container of mass 0.325 kg filled with oxygen. This container is placed in 1.75 kg of water in an aluminum calorimeter cup of mass 0.624 kg at an initial temperature of $15.0 ^\circ \textrm{C}$. The oxygen–candy mixture in the small container (a “bomb calorimeter”) is ignited, and the final temperature of the whole system is $53.5 ^\circ \textrm{C}$.

VIDEO TRANSCRIPT

This is Giancoli Answers with Mr. Dychko. The energy lost by the 15 gram sample of candy put into the calorimeter is going to equal the energy gained by the calorimeter and the water that's in it and the little tiny aluminum bomb that the candy is put inside of. So, the calorimeter is the big container that contains the water and contains the little thing that's called the bomb made of aluminum that the candy is put inside of. So, we have this is the energy gain for each material and they both have the same change in temperature because they initially are all in equilibrium with the same initial temperature and they all end up with the same final temperature. So, it's ΔT subscript c for calorimeter in each of these terms. And factor that out. So, we have a final temperature of 53.5 degrees Celsius minus the initial temperature of 15 degrees Celsius times 0.325 kilograms mass of the small container that the candy is put into times 900 joules per kilogram Celsius degree, specific heat of aluminum, plus 1.75 kilograms, mass of water, times 4,186 joules per kilogram Celsius degree, specific heat of water plus the 0.624 kilograms mass of the calorimeter cup times 900 again because it's made of aluminium. And that's going to be 314,914.6 joules and we times that by 1 kilocalorie for every 4.186 times 10 to 3 joules. And we get 75.23 kilocalories which is 75.23, capital C, Calories which is really confusing but that's the way the unit's work in this subject. So, 1 kilocalorie with a small c here equals 1 capital-C Calorie. So, that's for 15 grams. And so if we want to know the calorie content of a 65 gram sample, we take these 75.23 calories per 15 grams times by 65 grams. And that gives about 333 Calories. And that's the total energy content of a 65 grams sample of the candy.