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Human Fuel

Carbohydrates, proteins, and fats are used as biological fuels. Determining the energy (in calories or joules) from these varies types of compounds is generally just a matter of unit conversions. The relevant relationships are

For carbohydrates and proteins: 17 kJ/g

For fats: 38 kJ/g

For conversion between joules and calories: 4.184 J = 1 cal or 4.184 kJ = 1 Cal

>> Example 1

According to the label, a serving of Reduced Fat Triscuit^TM crackers has 3 g fat, 22 g carbohydrate, and 3 g protein. How many Calories are in a serving?

Solution:

The calories due to fat are

3 g fat

38 kJ 1 g

1 Cal 4.184 kJ

=

27.25 Cal

22 g carbohydrates

17 kJ 1 g

1 Cal 4.184 kJ

=

89.39 Cal

3 g protein

17 kJ 1 g

1 Cal 4.184 kJ

=

12.19 Cal

The sum is 27.25 Cal + 89.39 Cal + 12.19 Cal = 128.83 Cal

Note that the number of significant figures for fat and protein is 1, and that for carbohydrates is 2. Both multiplication and addition are involved in the calculation, so to keep track, the digits that are significant are underlined in the preceding problem. So with correct significant figures the answer is 1.3 10² Calories. The package reports 120 Calories. Recalling that the last significant digit is uncertain, the two answers actually do agree.

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