IB Physics HLTopic 1 — Motion, Forces & EnergyPaper 1 & 2Work, Energy & Power~8 min read
Energy Density
Fill a car with petrol and a wood-burning stove with logs, and both are storing chemical energy — but litre for litre, the petrol holds vastly more. That’s the idea of energy density: how much energy you can squeeze out of a given volume of fuel. It’s why cars run on liquid fuel rather than firewood, and why choosing a fuel is always a trade-off between how much energy it packs, how safe it is, and how cleanly it burns.
📘 What you need to know
A fuel is anything that can be burned to release heat, which can then do useful work
Energy density is the amount of energy stored per unit volume of a fuel
It’s measured in J m−3 (or often MJ L−1 for convenience)
Different fuels have very different energy densities — coal and diesel pack far more than wood
Useful conversion: 1 litre (L) = 0.001 m3
Fuels are chosen on energy density, safety, and the pollutants they release when burned
What energy density means
Energy density tells you how much energy is packed into each unit of volume of a fuel. The more energy per litre, the less fuel you need to carry to do the same job:
Energy density
Energy density = energy released ÷ volume of fuel
The SI unit is joules per cubic metre (J m−3), though fuel data is often quoted in megajoules per litre (MJ L−1) because the numbers are friendlier. A high energy density means a small volume delivers a lot of energy — exactly what you want for something like a car or an aircraft that has to carry its own fuel.
Don’t confuse energy density (energy per volume) with specific energy (energy per mass). This topic is about volume — how much energy fits in each litre or cubic metre. It matters when space is tight, like a fuel tank. When weight is the concern, engineers care more about energy per kilogram instead.
Comparing fuels
Here are the approximate energy densities of some common fuels. Notice the enormous spread — diesel and coal store more than ten times as much energy per litre as wood, and over a hundred times as much as natural gas:
Fuel
Energy density / MJ L−1
Diesel
39
Coal
38
Biodiesel
33
Vegetable oil
30
Liquid hydrogen
9
Wood
3
Methane (natural gas)
0.3
Energy density of common fuels (MJ L−1). Diesel and coal pack the most energy per litre; wood and natural gas far less. This is why we can get much more energy from a litre of coal than a litre of wood.
Converting between units
Data sheets mix megajoules per litre and joules per cubic metre, so you need to switch between them. The key fact is that a litre is a thousandth of a cubic metre:
Diesel has an energy density of 39 MJ L−1. How much energy is stored in a 50 L tank of diesel?
Step 1 — energy = energy density × volume
E = energy density × volume
Step 2 — substituteE = 39 × 50E = 1950 MJ (≈ 2.0 × 10⁹ J)Nearly two billion joules in one tank — that’s why liquid fuels are so convenient for transport.
WE 2
Coal has an energy density of 38 MJ L−1. Express this in joules per cubic metre (J m−3).
Step 1 — convert MJ to J
38 MJ = 38 × 10⁶ J
Step 2 — convert “per litre” to “per m³” (×1000)= 38 × 10⁶ × 1000 J m⁻³= 3.8 × 10¹⁰ J m⁻³Since 1 m³ holds 1000 L, the “per m³” figure is 1000 times bigger than the “per litre” one.
WE 3
Using the table, what volume of wood (3 MJ L−1) and of diesel (39 MJ L−1) would each be needed to supply 300 MJ of energy?
Step 1 — volume = energy ÷ energy density
V = E ÷ energy density
Step 2 — woodV = 300 ÷ 3 = 100 LStep 3 — dieselV = 300 ÷ 39 = 7.7 LWood: 100 L Diesel: 7.7 LYou’d need about 13 times the volume of wood as diesel for the same energy — the low energy density really shows.
🛠️ Working with energy density
Energy from a volume: multiply energy density by the volume of fuel.
Volume for an energy: divide the energy needed by the energy density.
Match your units: keep MJ with litres, or J with cubic metres — don’t mix.
To convert MJ L−1 to J m−3, multiply by 106 (MJ→J) and by 1000 (per L → per m3).
Compare fairly: when choosing a fuel, weigh energy density against safety and pollution too.
💡 Top tips
Per volume, not per mass. Energy density here is energy per unit volume — don’t confuse it with energy per kilogram.
Mind the 1000. Going from “per litre” to “per m3” multiplies by 1000, since 1 m3 = 1000 L.
It’s a trade-off. The best fuel isn’t always the densest — safety and pollutants matter too (hydrogen is clean but low-density and tricky to store).
Keep units together. MJ with L, or J with m3 — convert before combining.
Quick recap: Energy density is the energy stored per unit volume of a fuel, measured in J m−3 (or MJ L−1). Fuels vary widely — diesel and coal are high, wood and natural gas low. Use 1 L = 0.001 m3 to convert, and remember that fuel choice balances energy density against safety and pollution.
⚠ Common mistakes
Confusing energy per volume with energy per mass (specific energy)
Forgetting the ×1000 when converting between per-litre and per-cubic-metre
Mixing units — using MJ with m3, or J with litres, without converting
Assuming the highest energy density is always the best fuel, ignoring safety and pollution
Dividing when you should multiply — energy = density × volume, not density ÷ volume
And that completes the whole “Work, Energy & Power” section — from conservation of energy and Sankey diagrams, through work, the three energy stores and their conservation, to power, efficiency and now energy density. You’ve got the full picture of how energy is stored, transferred, wasted and measured. Brilliant work getting through it — the next section builds directly on these foundations.
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