Energy at home · Quantitative
Energy in food
A packet says “229 kcal” and also “958 kJ”. Two completely different numbers for the same crisps. Is one of them wrong?
Start here
Two numbers, one packet.
Every food label in the country carries both. A 50 g bag of crisps: 229 kcal, 958 kJ. Neither number is a mistake and neither is a rounding of the other.
Commit to why there are two.
They are the same amount of energy in two different units, like 6 feet and 1.83 metres. One kilocalorie is 4.184 kilojoules, and 229 × 4.184 gives 958 — the figure on the packet. Round it to 4.18 for your own working. The joule is the scientific unit; the calorie survives on labels because people are used to it. Nothing about the crisps changes.
Food is a chemical store, and like any store it holds a measurable number of joules. This lesson measures it — with an instrument that gets an answer close to the label and not identical to it, which is the honest result and worth understanding.
The calorimeter · burn it and watch the water
Measure the store, do not look it up.
A weighed sample of food burned under a boiling tube holding 20 g of water. The energy released warms the water, and the temperature rise tells you how much.
Commit first. Which of these do you expect to hold the most energy per gram?
Water temperature
Rise
Sample left
| Run | Food | Mass | Rise | Energy per gram |
|---|
Every value you record is well below the packet figure, and every one is low for the same reasons — which is the difference between a systematic error and a scatter.
Key fact
Food holds a chemical store, measured in joules. Energy in a portion = energy per gram × mass. One kilocalorie is 4.18 kilojoules — the same energy, a different unit.
Five lines, every time · CFIFA
Energy in a portion = energy per gram × mass
energy in the portion, E, is measured in kilojoules (kJ)
energy per gram, e, is measured in kilojoules per gram (kJ/g)
mass of the portion, m, is measured in grams (g)
The triangle
Cover the one you want
Energy sits alone at the top. Cover it and the other two are side by side — multiply.
Energy per gram sits underneath with total energy above. Cover it and you get E over m — divide.
Mass sits underneath with total energy above. Cover it and you get E over e — divide.
Two things side by side means multiply. One thing over another means divide.
Worked example
A crisp releases 22.0 kJ for every gram. What does a 30 g portion hold?
Step 0 of 5
Convert
22.0 kJ/g stays 22.0 kJ/g · 30 g stays 30 g
The energy density is per gram and the portion is in grams, so there is nothing to convert.
Formula
E = e × m
Cover E on the triangle: e sits beside m, so you multiply.
Insert
E = 22.0 kJ/g × 30 g
The grams on the bottom of kJ/g cancel the grams of the portion.
Fine-tune
22.0 × 30 = 660
Kilojoules per gram times grams gives kilojoules.
Answer
E = 660 kJ
Six hundred and sixty kilojoules, about 158 kcal on a food label.
Worked example
A cereal releases 15.0 kJ for every gram. What does a 0.045 kg portion hold?
Step 0 of 5
Convert
0.045 kg × 1000 = 45 g
The energy density is per gram, so the mass has to be in grams before it can multiply.
Formula
E = e × m
Cover E on the triangle: e sits beside m, so you multiply.
Insert
E = 15.0 kJ/g × 45 g
The converted mass goes in. The 0.045 never does.
Fine-tune
15.0 × 45 = 675
Kilojoules per gram times grams gives kilojoules.
Answer
E = 675 kJ
Insert 0.045 instead of 45 and the answer comes out 0.675 kJ — a thousand times too small.
Think again
“You burn off the calories at the gym, and then they are gone.”
Nothing is destroyed at the gym. The chemical store in the food empties, a small part of it fills a kinetic store while you are actually moving, and almost all of it ends up as a thermal store in you and the room — which is why a gym is warm and why you sweat. Weigh the room's air and you would find the energy has not left the building.
You met this belief when a rolling ball stopped, and again when a car braked, and again when a battery went flat. Every time, the temptation is to say the energy was consumed, and every time the honest answer is a thermal store somewhere unglamorous. “Burned off” is a fair everyday phrase for “moved out of my body's store” and a bad description of what happened to the joules.
One more thing the calorimeter cannot tell you: burning food in air and respiring it are not the same process, even though the energy released is nearly identical. Your body does it in dozens of small controlled steps at 37 °C, not in one flame — and it cannot get at all of it, which is why the number on the label is what a body can actually use rather than what a fire could release.
“A calorie on a food label is the same calorie physicists use.”
It is a thousand of them. The physicist's calorie warms one gram of water by one degree; the label's Calorie — properly a kilocalorie — warms a kilogram. A chocolate bar at 250 kcal is 250 000 of the small ones, or about 1050 kJ. The kilojoule figure beside it on the label exists precisely so that nobody has to know which calorie is meant.
Key fact
Energy in food is measured in kilojoules; the kcal a label prints is 4.18 kJ. A portion holds energy per gram × mass, and that chemical store is filled by eating and emptied by everything the body does, awake or asleep.
Mastery ladder
Not started yet.
Rungs 3 and 4 you mark yourself.
Rung 1 · Recall
Cheddar holds 17 kJ per gram. How much energy is in a 30 g portion?
Rung 2 · The one that catches people
A label reads 229 kcal and 958 kJ for the same bag. Which statement is correct?
Rung 3 · Explain
Your calorimeter gives 8.2 kJ per gram for a cheese puff. The packet says 21.6 kJ per gram. Explain three reasons your value is lower, and say whether repeating the measurement would fix it.
Rung 4 · Take it somewhere new
Two 100 g snacks have the same energy figure, but one is mostly fat and the other mostly carbohydrate. Explain how that is possible, and say what the energy figure alone does not tell you about a food.
Key note
Food is a chemical store measured in joules. Fat holds about twice as much per gram as protein or carbohydrate. 1 kcal = 4.18 kJ, same energy. And nothing is destroyed by exercise — it moves into a thermal store.
Going further
Your school calorimeter will read low — usually only 30 to 42 per cent of the label figure — and every source of that error is worth naming, because they are all in the same direction. Energy escapes from the flame into the room instead of the water. The glass of the tube absorbs some. The sample often stops burning before it is fully consumed. None of these could ever make the reading too high. That one-sidedness is what tells you it is systematic error rather than random scatter, and it is why the professional version is a sealed steel bomb calorimeter, pressurised with pure oxygen and immersed in a weighed water bath — the same idea with every escape route closed. Repeating a measurement helps with scatter. It does nothing at all about a leak.
Before this lesson
Connects to
At GCSE this becomes
- Specific heat capacity and the energy transferred when a fuel or food is burned, calorimetry as a required practical, and the difference between the energy a food contains and the energy a body can actually get out of it.
Where to next
- Next: Power ratings in watts
- Previous: Simple machines
Energy transfers
Ask Mr Badmus AI
Not sure why your value is lower than the packet?
Teacher demonstration only. Eye protection for everyone. Burning food spits, and the boiling tube gets hot enough to burn — a hot tube looks exactly like a cold one, so put it on a heatproof mat and leave it there. Never taste any of the samples, before or after.
Lesson content © MrBadmusAI.