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.

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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.