An industrial food company is producing a novel artificial sweetener and needs to calculate the nutritional value of their product. They have a constant-volume calorimeter, with a calibrated inner-shell heat capacity of 520. J/°C and an outer-shell filled with 620. mL distilled water (p = 0.998 g/mL) at an initial temperature of 25.0 °C. They placed 10.51 g of their sweetener in the calorimeter, ignited the sample and observed a final water temperature of 25.4 °C after combustion finished.
Calculate the nutritional value of the artificial sweetener, as the change in internal energy, in kilocalories per 100 gram (kcal/100 g).
Assume that all energy is transferred as heat. Assume that the sample, calorimeter and outer-shell water are at the same temperature and thermally isolated from their surroundings.
You must clearly show all your calculations and reasoning.
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