IB Physics SLTopic A.3 — Work, Energy & PowerPaper 1 & 2Energy Density~6 min read
Energy Density
Two fuel tanks the same size can store wildly different amounts of energy. Energy density is what lets you compare fuels fairly, by asking how much energy is packed into each unit of volume.
📘 What you need to know
Energy density is the amount of energy per unit volume of a fuel
Its SI unit is J m⁻³, though MJ L⁻¹ is far more common in everyday use
1 L (litre) = 0.001 m³
A fuel with a higher energy density stores more energy in the same amount of space
Fuel choice depends on more than energy density alone — cost, safety and emissions all matter too
What Does Energy Density Tell You?
Energy density measures how much chemical energy is squeezed into a given volume of fuel. It’s the reason a small tank of diesel can power a car much further than the same-sized tank of, say, compressed hydrogen gas — diesel simply packs more energy into every litre.
Relating energy density to a volume of fuel
Energy stored = Energy density × Volume
Comparing Common Fuels
The chart below shows typical energy density values for a range of everyday fuels. Real figures vary somewhat depending on purity, moisture content and how the fuel is measured, so treat these as representative rather than exact.
Liquid fuels like diesel and petrol typically pack far more energy per litre than gaseous or solid fuels
Notice that liquid fuels tend to have much higher energy densities than gases or solids — which is exactly why liquid hydrogen or compressed natural gas need bulkier tanks than petrol or diesel to store the same amount of energy.
Quick recap: Energy density = energy stored per unit volume. Higher energy density means less volume needed to store the same amount of energy.
WE 1
A car’s fuel tank holds 45 L of petrol, with an energy density of 34 MJ L⁻¹. Calculate the total chemical energy stored in a full tank.
Step 1 — Write the relationship
Energy stored = Energy density × Volume
Step 2 — SubstituteEnergy stored = 34 × 45= 1530 MJ ≈ 1.53 × 10⁹ J
WE 2
A hydrogen-powered scooter needs to store 720 MJ of energy for a delivery route. Liquid hydrogen has an energy density of 9 MJ L⁻¹. Calculate the minimum tank volume needed, and compare it with the volume that would be needed if diesel (38 MJ L⁻¹) were used instead.
Step 1 — Rearrange for volume
Volume = Energy stored ÷ Energy density
Step 2 — Calculate for liquid hydrogenV = 720 ÷ 9 = 80 LStep 3 — Calculate for dieselV = 720 ÷ 38 ≈ 18.9 LDiesel tank ≈ 19 L vs. hydrogen tank = 80 LThe hydrogen tank needs to be over four times larger to store the same amount of energy.
💡 Top tips
Don’t confuse energy density (per volume) with specific energy (per mass) — they’re related but different quantities
Convert litres to m³ by multiplying by 0.001 if you need SI units throughout a calculation
Quoted energy density values are typical figures — real fuels vary with purity, moisture content and how they’re measured
A higher energy density isn’t automatically “better” — safety, emissions and cost all factor into real-world fuel choices
⚠ Common mistakes
Mixing up energy density and specific energy when a question specifies mass rather than volume, or vice versa
Forgetting to convert between litres and cubic metres when working in strict SI units
Assuming energy density values are fixed constants, rather than typical figures that vary by source
Concluding that the fuel with the highest energy density is always the most practical choice
That wraps up Work, Energy & Power — nice work getting through it. Up next, we’ll move on to a new area of the course.
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