To determine the amount of protein there is a technique called the kjeldahl method to measure the amount of nitrogen in the food and convert it to protein content; you can also use UV spectroscopy. Protein has about 4 Calories/gram.
Fat can be measured through a Soxhlet extraction or gas chormatography. Fat has 9 Calories/gram.
Carbohydrates are everything that isn’t fat, alcohol, protein, water or ash; carbs have 4 Calories/gram and alcohol has 7.
The other way is to dehydrate the food and then burn it in a bomb calorimeter and measure the heat that is released. 4,184 J of heat = 1 Calorie. You dehydrate the food first since water has 0 Calories.
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