One tablespoon of peanut butter has a mass of 16 g . It is combusted in a calorimeter whose heat capacity is 110 kJ/∘C . The temperature of the calorimeter rises from 22.1 ∘C to 25.4 ∘C.
Part A
Find the food caloric content of peanut butter.
Express your answer using two significant figures.
I assume that when you say food calories you want kcal/g.
q for 15 g peanut butter = Ccal x delta T
q = 110 kJ/C x (25.4 - 22.1) = 363 kJ for 15 g p butter or
363 kJ/15 g = 24.2 kJ/g
24.2 kJ x (1,000 J/kJ) x (1 cal/4.184 J) x (1 kcal/1,000cal) = ? food cal
Why did the peanut butter go to the gym?
To burn off those extra calories! Speaking of calories, let's get to the math.
To find the food caloric content of peanut butter, we can use the equation:
Q = m * C * ΔT
Where:
Q = heat energy transferred to the calorimeter (in Joules)
m = mass of peanut butter (in grams)
C = heat capacity of the calorimeter (in J/∘C)
ΔT = change in temperature (in ∘C)
First, let's convert the mass of the peanut butter to kilograms:
m = 16 g = 0.016 kg
Now, let's calculate the energy transferred to the calorimeter:
Q = 0.016 kg * 110 kJ/∘C * (25.4 ∘C - 22.1 ∘C)
Calculating this gives us:
Q = 0.016 kg * 110,000 J/∘C * (3.3 ∘C) = 5,412 J
Finally, let's convert the energy transferred to calories:
1 calorie = 4.184 J
So, the food caloric content of peanut butter is:
5,412 J * (1 calorie / 4.184 J) = 1,295 calories
Therefore, the food caloric content of peanut butter is approximately 1,300 calories (rounded to two significant figures).
To find the food caloric content of peanut butter, we can use the formula:
Heat released = heat capacity × temperature change
First, let's calculate the heat released:
Heat released = 110 kJ/∘C × (25.4 ∘C - 22.1 ∘C)
Heat released = 110 kJ/∘C × 3.3 ∘C
Heat released = 363 kJ
Next, we need to convert the heat released to food calories. There are 1,000 calories in 1 kilocalorie (kcal), and 1 kilocalorie (kcal) is equal to 1,000 joules (J).
So, 1 kilocalorie (kcal) is equal to 1,000 × 4.184 J.
To convert 1 kilojoule (kJ) to food calories (kcal):
1 kJ = 1,000 J
Dividing both sides by 4.184:
1 kJ ÷ 4.184 = 1,000 J ÷ 4.184
Simplifying, we get:
0.239 kcal = 1 J
Now, we can calculate the food caloric content of peanut butter by converting the heat released from kilojoules (kJ) to food calories (kcal):
Food Caloric Content = Heat released in kJ × Conversion factor
Food Caloric Content = 363 kJ × 0.239 kcal/kJ
Food Caloric Content ≈ 87 kcal
Therefore, the food caloric content of peanut butter is approximately 87 kcal.
To find the food caloric content of peanut butter, we need to use the information given and some equations related to heat capacity and calorimetry.
First, let's calculate the change in temperature of the calorimeter.
ΔT = T2 - T1
ΔT = 25.4 °C - 22.1 °C
ΔT = 3.3 °C
Next, we can use the equation for heat absorbed or released by a substance:
q = m * C * ΔT
where q is the heat absorbed or released, m is the mass of the substance, C is the heat capacity, and ΔT is the change in temperature.
In this case, we are interested in the amount of heat released by the peanut butter. The heat absorbed by the calorimeter is equal and opposite to the heat released by the peanut butter.
Substituting the given values into the equation:
q (peanut butter) = -q (calorimeter)
m (peanut butter) * C (peanut butter) * ΔT (peanut butter) = -m (calorimeter) * C (calorimeter) * ΔT (calorimeter)
We are given that the mass of the peanut butter is 16 g and the calorimeter's heat capacity is 110 kJ/°C. The change in temperature for the calorimeter is 3.3 °C.
Let's calculate the heat release by peanut butter:
q (peanut butter) = -16 g * C (peanut butter) * ΔT (peanut butter) / (m (calorimeter) * C (calorimeter))
Now, we need to convert grams to kilograms and kJ to calories for the final answer:
1 kcal = 4.18 kJ
q (peanut butter in calories) = q (peanut butter in kJ) * 4.18
By substituting the given values and solving the equation, we can find the food caloric content of peanut butter in calories.