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Energy in food

Energy and power · level 4, lesson 4 of 6

A question to start

A food label says a bar of chocolate holds 1,000 kJ, or 240 kcal. What do those numbers mean, and how long would that energy keep a person going?

The idea

Food labels give energy in two units:

  • kilojoules, kJ: 1 kJ = 1,000 J;
  • kilocalories, kcal, often written "Calories" with a capital C: 1 kcal = 4.184 kJ.

An adult needs roughly 8,000 to 10,000 kJ of food a day (about 2,000 to 2,400 kcal), more if very active, less for young children.

Spread over a day, that is a power:

\[\frac{8{,}400{,}000 \text{ J}}{86{,}400 \text{ s}} \approx 100 \text{ W}.\]

So a person runs at about 100 W, like an old-fashioned light bulb. And almost all of it ends up as body heat: a room full of people warms up.

A slice of bread A chocolate bar A day's food for an adult
Energy about 330 kJ about 1,000 kJ about 8,400 kJ
In kcal about 80 about 240 about 2,000
In kWh 0.09 0.28 2.3
body heatmovementabout 8,400 kJ a day

On Mars, every kilojoule of food would be grown in greenhouses or flown from Earth. Astronauts doing hard work in spacesuits need more food than people in an office, so planning food is planning energy.

Worked examples

1. kcal to kJ. A 500 kcal meal: \(500 \times 4.184 = 2{,}092\) kJ.

2. kJ to kWh. 8,400 kJ \(= 8.4\) MJ \(= 8.4 \div 3.6 = 2.3\) kWh. A whole day's food holds about as much energy as a 2 kW kettle uses in a little over an hour.

3. Burning off a chocolate bar. Brisk walking uses about 200 W more than resting. To use 1,000 kJ extra: \(1{,}000{,}000 \div 200 = 5{,}000\) s, about an hour and 23 minutes.

Try it

  1. Change 300 kcal into kJ.
  2. A cereal bar has 420 kJ. How many kcal is that?
  3. A teenager eats 10,000 kJ a day. What is their average power in watts?
  4. Why does a crowded room get warm?
Answers
  1. \(300 \times 4.184 = 1{,}255\) kJ.
  2. \(420 \div 4.184 = 100\) kcal.
  3. \(10{,}000{,}000 \div 86{,}400 = 116\) W.
  4. Each person gives out about 100 W of body heat.

Common mistake

Mixing up calories and kilocalories. The "Calories" on a food label are kilocalories. A small calorie (cal) is a thousand times smaller.

Where it leads