One tablespoon of peanut butter has a mass of 17g . It is combusted in a calorimeter whose heat capacity is 130kJ/∘C . The temperature of the calorimeter rises from 22.5∘C to 25.3∘C.
Find the food caloric content of peanut butter.
To find the food caloric content of peanut butter, we need to calculate the heat released during its combustion in the calorimeter. We can use the formula:
Heat released = mass of substance * specific heat * change in temperature
In this case, the mass of peanut butter is given as 17 g, the specific heat of the calorimeter is given as 130 kJ/∘C, and the change in temperature is 25.3∘C - 22.5∘C = 2.8∘C.
Substituting the values into the formula, we have:
Heat released = 17 g * 130 kJ/∘C * 2.8∘C
Now we need to convert grams to kilograms since the specific heat is given in kJ/∘C. There are 1,000 grams in a kilogram, so the mass becomes 0.017 kg.
Heat released = 0.017 kg * 130 kJ/∘C * 2.8∘C
Now we can calculate the heat released:
Heat released = 0.017 kg * 130 kJ/∘C * 2.8∘C
= 0.636 kJ
So, the heat released during the combustion of one tablespoon of peanut butter in the calorimeter is 0.636 kJ.
Now, let's convert the heat released to food calories. 1 calorie (cal) is equal to 4.184 joules (J), and 1 kilojoule (kJ) is equal to 1,000 joules (J). Therefore:
0.636 kJ * 1,000 J/kJ * 1 cal/4.184 J
= 152.287 cal
So, the food caloric content of one tablespoon of peanut butter is approximately 152.287 calories.