How do scientists calculate the number of calories in a particular food and the number of calories in a particular exercise?

A calorie is the amount of heat needed to raise the temperature of one gram of water by 1⁰ Celsius. To calculate the number of calories in a certain food, scientists burn the food in a device called bomb-calorimeter. The device uses an electric charge to cause the food to combust, measures the amount of heat produced by the food and expresses that heat in terms of calories.
In point of fact, the amount of energy contained in foods is expressed not in calories but in kilocalories and is always written with a capital C. So, when a nutrition expert says that a particular food item provides 200 calories per 100 grams, s/he is actually referring to kilocalorie which equals to 1000 calories. (Also, 1 kilocalorie = 4184 joules).
The body burns food and gives off heat that represents kilocalorie. To measure the number of such calories consumed during exercise, scientists have built very large calorimeters in which people can live. One type measures the heat given off by the person exercising. Another, called indirect calorimeter, measures the oxygen that is consumed. Oxygen is needed for a substance to burn. An average man who is not very active burns 2,800 calories a day. He can increase the number by about 10 percent by playing squash twice a week and by 15 percent by jogging two hours a week.

The table above gives estimates of the number of calories needed by an average man or woman to perform particular activities for one hour. Men use more calories than women do, because men have more weight to carry around.

Additional reading:
Calorimeter (Wikipedia)

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