In a laboratory experiment, two engineering students are asked to determine the caloric value of a commercial brand of diet cocoa. They are provided with a bomb calorimeter, which had to be calibrated by measuring the heat liberated by a substance with a known heat of combustion. They elect to use benzoic acid, which has a known heat of combustion of 6.318 kcal/g. The test consists of igniting a tablet of the test material inside the bomb and measuring the temperature rise of the surrounding water.
The energy equivalent (EQ) of a bomb calorimeter is defined to be the product of the mass of the system multiplied by its specific heat. Then, the relation between the heat liberated by a test sample and the measured temperature change of the water is Q = EQ(Tfinal -Tinitial).
a. If the change in temperature of the water was 2.905°C when a 1.1523 g tablet of benzoic acid is tested, determine the energy equivalent of the calorimeter.
b. Then, a 1.0825-g tablet of diet cocoa is tested and produces a temperature change of 1.699°C. Using the results of part a, determine the caloric energy content of the cocoa in kilocalories per gram.