Final answer:
To calculate the amount of heat released when the 1.0-g sample burns, use the equation q = mcΔT. The heat released is 3100 calories. Divide by 1000 to convert to nutritional Calories and find the energy content in Cal/g, which is 3.1 Cal/g. Multiply the energy content by the mass of the candy bar to find the total caloric content in Calories, which is 232.5 Calories.
Step-by-step explanation:
To calculate the amount of heat released when the 1.0-g sample burns, we need to use the equation q = mcΔT, where q represents the heat transferred, m is the mass of the water, c is the specific heat capacity of water, and ΔT is the change in temperature. In this case, the mass of the water is 1000 g, the specific heat capacity of water is 1 calorie/gram °C, and the change in temperature is 24.3 °C - 21.2 °C = 3.1 °C.
Substituting these values into the equation, we get q = (1000 g)(1 calorie/gram °C)(3.1 °C) = 3100 calories.
To convert the heat in calories to nutritional Calories, we divide by 1000 since 1 nutritional Calorie is equal to 1000 calories. Therefore, the energy content (fuel value) in Cal/g is 3100 calories / 1000 = 3.1 Cal/g.
Finally, to calculate the total caloric content of the candy bar in Calories, we multiply the energy content in Cal/g by the mass of the candy bar. The mass of the candy bar is 75.0 grams, so the total caloric content is 3.1 Cal/g * 75.0 g = 232.5 Calories.