Uncovering the Mystery of Calorie Constants

In summary, the conversation discusses an experiment to determine the constants for the number of calories per gram in carbs, protein, and fat. The results were compared to the values listed on food labels, and a matrix was used to calculate the values. The calculated values differ from the expected values, but this can be attributed to a slight change in the given numbers.
  • #1
barryj
856
51
When calculating calories of a food..
It is sort of well known that carbs have 4 cal/gram, protein has 4 cal/gram and fat has 9 cal/gram. I wanted to do an experiment to determine these constants 4,4,and 9

I looked at soup, peanut butter, and a protein mix to get the values from the labels per serving and the data is...

soup carb 13, prot 2, fat 2, calories 80 (78)
p butter carb 8, prot 7, fat 15, calories 190 (195)
mix carb 18, prot 2, fat 4, calories 110 (116)

Note: numbers in ( ) are calculated from the 4,4,9 values. These numbers are reasonably close to what was listed on the label

so I set up a matrix where a= cal/gram for carb, b = cal/gram for prot, and c = cal/gram for fat
The matrix is..

13a + 2b + 2c = 80
8a +7b +15c = 190
18a + 2b + 4c = 110

Solving I got a = 3.65, b = 10.391 really?, and c = 5.85 ?really.

My calculated values are not even close to what I expected, around 4,4,9

Does anybody know why this is?? I am really puzzled.
 
Mathematics news on Phys.org
  • #2
barryj said:
so I set up a matrix where a= cal/gram for carb, b = cal/gram for prot, and c = cal/gram for fat
The matrix is..

13a + 2b + 2c = 80
8a +7b +15c = 190
18a + 2b + 4c = 110

Solving I got a = 3.65, b = 10.391 really?, and c = 5.85 ?really.

My calculated values are not even close to what I expected, around 4,4,9
In your matrix calculation, if you use the numbers you showed in parentheses (78, 195, 116), it comes out exactly as you would expect. This shouldn't be a surprise, as you used the values 4, 4, and 9 for the cal/g for carbs, protein, and fats. The seemingly relatively small change from (80, 190, 110) to (78, 195, 116) makes a fairly significant change in the solution, most notably on the value of your b variable (cal/g for protein).
Geometrically, you are working with three planes in space, and determining the point they have in common. By changing all three equations, even relatively slightly, you are changing the intersection point.
 

FAQ: Uncovering the Mystery of Calorie Constants

What are calorie constants?

Calorie constants are numerical values used to calculate the amount of energy in a given food or beverage. They represent the amount of energy required to raise the temperature of 1 gram of water by 1 degree Celsius.

How are calorie constants determined?

Calorie constants are determined through a process called bomb calorimetry, which involves burning a sample of food in a sealed container and measuring the heat released. This heat is then converted to a calorie value using the calorie constant.

Why is it important to uncover the mystery of calorie constants?

Understanding calorie constants is important for accurately determining the energy content of foods and beverages. This information is crucial for individuals trying to maintain a healthy diet and for food manufacturers to accurately label their products.

Do calorie constants vary for different types of food?

Yes, calorie constants can vary depending on the type of food or beverage. For example, the calorie constant for carbohydrates is 4 calories per gram, while the calorie constant for fat is 9 calories per gram.

Can calorie constants change over time?

While calorie constants are generally considered to be constant, there is some evidence that they may vary slightly depending on factors such as the ripeness of fruits and vegetables. However, these variations are minimal and do not significantly impact the overall calculation of calories in a food or beverage.

Hot Threads

Recent Insights

Back
Top