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
Curriculum Equation Key قوانين الرقم الهيدروجيني والاتزان الأيوني - pH & Acid-Base Equilibrium FormulasFast Exam Solution
pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴
Word Equation & Conditions: الرقم الهيدروجيني = -لوغاريتم تركيز أيون الهيدروجين | pH + pOH = 14
Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.
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
Section 1 of 9Definition
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.
Section 2 of 9Typical values
| Fuel | Energy density / MJ L−1 |
|---|---|
| Coal | 38 |
| Liquid hydrogen | 9 |
| Methane (natural gas) | 0.3 |
| Diesel | 39 |
| Biodiesel | 33 |
| Vegetable oil | 30 |
| Wood | 3 |
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.
Section 3 of 9Using 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.
Section 4 of 9Choosing 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.
Section 5 of 9Source 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.
Section 6 of 9Related 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)
Section 7 of 9More 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)
Section 8 of 9Key terms
| Term | Meaning |
|---|---|
| Fuel | A substance that can be burned to release energy for use |
| Energy density | Energy released per unit volume of a fuel, in J m−3 |
| Specific energy | Energy released per unit mass of a fuel, in J kg−1 |
| Power density | Power delivered per unit mass or volume |
| Fission | Splitting of a heavy nucleus releasing energy |
| Efficiency | Useful energy out divided by total energy in |
Section 9 of 9Exam technique
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.
Marked practiceQuizzes for this lesson
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