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Theme A — Space, Time and Motion

A.3.10 Energy Density — IB Physics HL Revision Notes & Topical Questions

5 min read 9 parts Lesson 41 of 63 1 quiz

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Lesson summary

A.3.10 Energy Density — IB PHYSICS SL notes: Define energy density, compare fuels and storage systems, and use it to find the energy released from a mass or volume of fuel.Fuel = anything that can be burned to produce heat, which can then run an engine.Energy density = the amount…

  • Specific energy
  • Why it matters
  • Conversion
  • Comparison
  • Per kilogram
  • Order differs

Part 1 of 7Definition

Fuel
Fuel anything that can be burned to produce heat, which can then run an engine.
Energy density
Energy density the amount of energy released per unit volume of a fuel.
  • Volume-based energy density = E/V, in J m−3.
Specific energy
Specific energy the energy released per unit mass, E/m, in J kg−1.
In the IB
  • In the IB both are often called energy density, and the unit shows which one is meant.
Why it matters
  • Why it matters it determines how much fuel must be carried or stored for a given amount of energy.

Part 2 of 7Typical values

FuelEnergy density / MJ L−1
Coal38
Liquid hydrogen9
Methane (natural gas)0.3
Diesel39
Biodiesel33
Vegetable oil30
Wood3
Conversion
  • 1 L = 0.001 m3, so 1 MJ L−1 = 109 J m−3.
Comparison
  • Comparison more energy is obtained from a given volume of coal than from the same volume of wood.
Per kilogram
  • Per kilogram hydrogen about 1.4 × 108 J kg−1, petrol 4.6 × 107, coal 2 to 3 × 107, wood 1.5 × 107 and lithium-ion battery 5 × 105 to 106.
Order differs
  • Order differs hydrogen gas has high energy per kilogram but low energy per cubic metre unless compressed or liquefied.

Part 3 of 7Using energy density

Energy available
  • Energy available energy density × mass (or volume).
Useful energy
  • Useful energy the available energy multiplied by the efficiency.
Fuel needed
  • Fuel needed m = E / .
    • (energy density × efficiency)
Vehicle range
  • Vehicle range battery energy stored divided by the energy used per kilometre.
Unit conversions
  • Unit conversions convert kW h per kilogram or MJ per litre to joules first.
Mass and volume link
  • Mass and volume link a litre of petrol has a mass of about 0.74 kg.

Part 4 of 7Choosing a fuel

Choosing a fuel
Energy density
  • Energy density a high value keeps the mass and volume low for transport.
Safety of use
  • Safety of use it affects the choice of fuel.
Pollutants released
  • Pollutants released emissions on combustion matter.
Cost and availability
  • Cost and availability practical limits on the choice.
Power density
  • Power density the rate at which energy can be delivered.
Rechargeability
  • Rechargeability batteries can be recharged, unlike fuels.
Hydrogen
  • Hydrogen high mass-based density, but it needs heavy high-pressure tanks.
Batteries
  • Batteries lower energy density than liquid fuels but efficient electric drive.
Grid storage
  • Grid storage mass matters far less than cost, lifetime and safety.

Part 5 of 7Source of the energy

1Fossil fuels and food
  • Fossil fuels and food chemical reactions, mostly oxidation, convert electrostatic potential energy to thermal energy.
2Nuclear fission and fusion
  • Nuclear fission and fusion a small decrease in mass is converted according to E = mc2.
3Fission of uranium-235
  • Fission of uranium-235 about 8 × 1013 J kg−1, roughly a million times that of petrol.
4Mass change
  • 1 g converts to about 9 × 1013 J.

Part 6 of 7Related ideas

Power density
  • Power density power per unit mass or volume.
Supercapacitors
  • Supercapacitors high power density but low energy density.
Batteries
  • Batteries high energy density relative to supercapacitors but lower power density.
Fields
  • Fields energy stored per unit volume in a spring, capacitor or electric field can also be expressed as an energy density.
Evaluation
  • Evaluation state the property compared and support the choice with a number.
    • (per kilogram, per litre or per cost)

Part 7 of 7More from the specification

More from the specification
Fuel energy density in combustion motor systems
  • Fuel energy density in combustion motor systems measuring chemical energy release per kilogram provides an engineering means to optimize thermal motor efficiency.
Energy Density and Specific Energy
  • Energy density is the amount of energy stored per unit volume of fuel (J m⁻³),
  • whereas specific energy is the energy stored per unit mass (J kg⁻¹), critical metrics in aerospace and transport.
Energy Transformation Equations
  • Mechanical work done (W = Fd) transfers kinetic energy (KE = ½mv²) into gravitational potential energy (GPE = mgh) or internal thermal energy against frictional resistance.
    What the symbols mean: Ep = gravitational potential energy gained (J) · m = mass (kg) · g = 9.81 N kg−1 · h = change in height (m)
Wasted Energy in Thermal Engines
  • The second law of thermodynamics dictates that no heat engine can convert 100% of input heat into useful mechanical work;
    • a portion is inevitably wasted to a low-temperature sink.
Power Output and Constant Speed
  • When an object moves horizontally at constant speed v against resistive friction forces, the useful mechanical power transferred by the driving force is P = Fv.
Wasted energy
  • Energy transferred to stores that are not useful, usually thermal in the surroundings.
Mechanical energy
  • Sum of kinetic and potential energy.
Sankey diagram
  • Diagram where arrow width shows energy amount.
Energy conservation
  • Mgh = ½Mv2 + ½Iω2.
Resultant force
  • Another name for net force.
Final speed
  • Speed at the end, v
Elastic
  • Returns to original shape when force is removed.
Constant
  • Not changing.
Friction
  • Force parallel to the surface opposing relative motion or its tendency.
Component
  • Part of a vector along one axis.
Position
  • Location relative to a reference point.
Distance
  • Total length of path travelled, a scalar.
Gravitational potential
  • Work done per unit mass in bringing a test mass from infinity to the point.
Kinetic energy
  • K = ½mv2, energy of motion.
W = Fs
What the symbols mean: W = work done = energy transferred (J) · F = force (N) · d, s or x = distance moved in the direction of the force (m)
W
Fs = 25.6 × 20 = 512 J
What the symbols mean: W = work done = energy transferred (J) · F = force (N) · d, s or x = distance moved in the direction of the force (m)

Key terms

TermMeaning
FuelA substance that can be burned to release energy for use
Energy densityEnergy released per unit volume of a fuel, in J m−3
Specific energyEnergy released per unit mass of a fuel, in J kg−1
Power densityPower delivered per unit mass or volume
FissionSplitting of a heavy nucleus releasing energy
EfficiencyUseful energy out divided by total energy in

Avoid these mistakes

1
Confusing energy per unit mass with energy per unit volume — check the unit.
2
Forgetting the efficiency — useful energy = available energy × efficiency.
3
Forgetting to convert litres to cubic metres — 1 L = 0.001 m3.
4
Judging fuels by energy density alone — safety, cost and emissions also matter.
5
Claiming one fuel is better without a number — support with calculations.

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