Power and Efficiency
5. Energy Resources and Energy Density
Learning outcomes
- I can define energy density as the amount of energy stored per unit mass or volume.
- I can compare the energy densities of different fuels and energy storage systems.
- I can explain why energy density is important in transportation and energy production.
- I can evaluate the advantages and disadvantages of various energy resources using energy density data.
- I can analyze how energy density influences technological and environmental decisions.
Energy Resources and Energy Density
Different energy resources store very different amounts of energy. A small mass of one fuel may contain far more usable energy than the same mass of another.
Energy density describes the amount of energy stored or available per unit mass or per unit volume.
Energy density is important because energy resources must often be:
- stored
- transported
- carried by vehicles
- delivered to power stations
- contained safely
- converted into useful energy
A resource with a high energy density can provide a large amount of energy without requiring as much mass or volume.
Energy Density by Mass
Energy density by mass tells us how much energy is available from each unit of mass.
It can be calculated using:
energy density = energy stored / mass
Common units include:
J/kg
kJ/kg
MJ/kg
For fuels, MJ/kg is particularly common.
For example, if 2 kg of a fuel stores 80 MJ:
energy density = 80/2
energy density = 40 MJ/kg
This means each kilogram contains approximately 40 MJ of energy.
Energy Density by Volume
Sometimes volume is more important than mass.
Volumetric energy density can be calculated using:
energy density = energy stored / volume
Possible units include:
J/m³
MJ/m³
MJ/L
kWh/L
This is particularly important when storage space is limited.
For example, fuel tanks in:
- cars
- aircraft
- ships
- spacecraft
have limited volume.
A fuel with high energy per litre can therefore be extremely useful even if another resource has a similar energy density per kilogram.
Gravimetric and Volumetric Energy Density
Two terms are useful when comparing energy-storage systems.
Gravimetric energy density means energy stored per unit mass.
Volumetric energy density means energy stored per unit volume.
These can lead to different conclusions.
A resource may have:
- high energy per kilogram
- but low energy per litre
Hydrogen is an important example. Hydrogen has a very high energy content per kilogram, but hydrogen gas occupies a large volume unless it is compressed or liquefied.
Therefore, both mass and volume must sometimes be considered.
Comparing Energy Resources
Approximate energy densities by mass for some fuels are:
| Energy Resource | Approximate Energy Density |
|---|---|
| Wood | 15–20 MJ/kg |
| Coal | 20–30 MJ/kg |
| Ethanol | 27 MJ/kg |
| Gasoline | 44–46 MJ/kg |
| Diesel | 45–48 MJ/kg |
| Natural gas | 50–55 MJ/kg |
| Hydrogen | about 120 MJ/kg |
Values vary depending on composition and measurement conditions.
The important idea is the comparison, not memorizing every value.
Hydrogen has a very high energy density by mass, while gasoline and diesel also contain large amounts of energy for their mass.
Worked Example: Comparing Fuels
Suppose Fuel A has an energy density of:
20 MJ/kg
and Fuel B has:
45 MJ/kg
For 10 kg of Fuel A:
E = 20 × 10
E = 200 MJ
For 10 kg of Fuel B:
E = 45 × 10
E = 450 MJ
The same mass of Fuel B stores more than twice as much energy.
This can be a major advantage when mass must be minimized.
Finding Energy from Energy Density
The relationship can be rearranged:
energy stored = energy density × mass
For example, gasoline has an approximate energy density of:
46 MJ/kg
If a vehicle carries:
30 kg
of gasoline:
E = 46 × 30
E = 1380 MJ
or:
1.38 GJ
This represents the approximate chemical energy stored in the fuel, not the useful mechanical energy ultimately delivered by the vehicle.
Energy Density and Efficiency
Energy density and efficiency are different concepts.
Energy density tells us how much energy a resource contains per unit mass or volume.
Efficiency tells us how much of that input energy becomes useful output.
A fuel may have a high energy density but be used in a relatively inefficient system.
For example, suppose:
Fuel energy = 1000 MJ
Engine efficiency = 30%
Useful mechanical energy:
useful energy = 0.30 × 1000
useful energy = 300 MJ
The fuel contained 1000 MJ, but only 300 MJ became the intended mechanical output.
Energy Density of Batteries
Batteries store energy chemically and release it electrically.
Battery energy density is often expressed as:
Wh/kg
or:
Wh/L
Recall:
1 Wh = 3600 J
Therefore:
1 kWh = 3.6 MJ
Modern rechargeable batteries store much less energy per kilogram than liquid fuels when comparing the raw stored-energy values.
However, electric motors can convert stored electrical energy into mechanical energy very efficiently.
This means energy density alone does not determine overall vehicle performance.
Worked Example: Battery
A battery has an energy density of:
250 Wh/kg
and has a mass of:
400 kg
Stored energy:
E = 250 × 400
E = 100,000 Wh
Therefore:
E = 100 kWh
Convert to joules:
100 kWh × 3.6 MJ/kWh = 360 MJ
The battery stores approximately:
360 MJ
of energy.
Comparing Battery and Gasoline Energy
Suppose:
Battery system = 250 Wh/kg
Convert this to MJ/kg:
250 Wh/kg × 3600 J/Wh
= 900,000 J/kg
= 0.90 MJ/kg
Gasoline ≈ 46 MJ/kg
By raw stored energy per kilogram, gasoline contains far more energy.
However, this does not mean a gasoline vehicle is automatically more energy efficient.
Electric motors typically convert a greater fraction of their input energy into useful mechanical energy than combustion engines.
Therefore, meaningful comparisons must consider:
energy density + efficiency + system mass + storage requirements + environmental effects
Why Energy Density Matters in Transportation
Transportation systems must carry their energy source with them.
Every kilogram of fuel or battery adds mass.
Greater vehicle mass can require additional energy to:
- accelerate
- climb hills
- support the vehicle
- transport the energy-storage system itself
High energy density is therefore particularly valuable for:
- aircraft
- spacecraft
- long-distance vehicles
- ships
- portable equipment
Aviation and Energy Density
Aircraft provide a clear example of why energy density matters.
An aircraft must lift:
- passengers
- cargo
- engines
- structure
- fuel or energy storage
If the energy-storage system becomes much heavier, additional lift and energy are required.
This makes energy per kilogram extremely important.
Liquid hydrocarbon fuels have historically been useful for aviation partly because they store large amounts of energy for their mass and volume.
Battery-powered aircraft face a major engineering challenge because batteries generally store considerably less energy per kilogram.
Volume Matters Too
Mass is not the only limitation.
Consider two fuels:
Fuel A:
40 MJ/kg
Fuel B:
50 MJ/kg
Fuel B appears better by mass.
But suppose Fuel B requires a very large storage tank.
A vehicle may not have enough physical space.
Engineers therefore consider:
energy per kilogram
and:
energy per litre
A practical energy source must often perform well in both categories.
Hydrogen
Hydrogen demonstrates why the distinction is important.
Hydrogen has a very high energy content by mass.
Approximately:
120 MJ/kg
This is much higher than gasoline.
However, hydrogen gas has a low density under ordinary conditions.
To store useful quantities, hydrogen may need to be:
- compressed to high pressure
- liquefied at extremely low temperature
- stored chemically in another material
These storage methods require additional equipment and energy.
Hydrogen Example
Suppose 5 kg of hydrogen stores approximately:
120 MJ/kg
Total energy:
E = 120 × 5
E = 600 MJ
That is a large amount of energy for only 5 kg of hydrogen.
However, the complete storage system includes:
- pressure tanks or cryogenic tanks
- valves
- insulation
- safety equipment
- fuel delivery systems
Therefore, the energy density of the whole system is lower than that of the hydrogen alone.
This is an important engineering principle:
Always consider the complete system, not just the energy-storage material.
Nuclear Fuel and Energy Density
Nuclear fuels have vastly greater energy density than chemical fuels because nuclear reactions release energy from changes within atomic nuclei rather than ordinary chemical bonds.
A relatively small mass of nuclear fuel can therefore release enormous amounts of energy.
This reduces the quantity of fuel that must be transported to a power station.
Nuclear Energy: Important Trade-Off
Very high energy density does not automatically make an energy resource the best choice.
Nuclear energy also requires consideration of:
- radioactive materials
- radioactive waste
- reactor safety
- construction costs
- decommissioning
- security
- long-term waste management
Therefore:
energy density is only one criterion for evaluating an energy resource.
Fossil Fuels
Fossil fuels include:
- coal
- oil
- natural gas
They have been widely used partly because they:
- contain substantial energy
- can be stored
- can be transported
- provide energy when needed
- have established infrastructure
However, their combustion releases carbon dioxide.
Other environmental concerns can include:
- air pollution
- extraction impacts
- habitat disruption
- spills
- methane leakage
Their energy density must therefore be considered alongside their environmental effects.
Renewable Energy Resources
Some renewable resources do not use a stored fuel in the same way.
Examples include:
- solar
- wind
- hydroelectric
- tidal
- wave energy
For these systems, fuel energy density may not be the most useful comparison.
Instead, engineers may consider:
- power per unit area
- availability
- storage requirements
- capacity factor
- location
- infrastructure
- environmental effects
- cost
Solar Energy
Solar energy does not require fuel to be transported to a solar panel.
This is a major advantage.
However, sunlight is spread over a large area.
Producing large amounts of power may therefore require:
- large areas of solar panels
- suitable locations
- energy storage
- electrical transmission infrastructure
Solar energy illustrates an important point:
low concentration of an energy resource does not necessarily make it unsuitable.
It simply creates different engineering requirements.
Wind Energy
Wind turbines extract kinetic energy from moving air.
There is no fuel tank and therefore no conventional fuel energy density.
Advantages include:
- renewable resource
- no fuel combustion during operation
- no direct carbon dioxide emissions from fuel combustion
Challenges include:
- variable wind
- suitable locations
- energy storage or grid balancing
- land or offshore infrastructure
Again, energy-resource decisions require more than one measurement.
Hydroelectric Energy
Hydroelectric systems store energy as gravitational potential energy in elevated water.
Recall:
ΔEₚ = mgΔh
The amount of stored energy depends on:
- mass of water
- gravitational field strength
- height difference
A reservoir may therefore require an enormous volume of water to store large amounts of energy.
However, hydroelectric systems can provide substantial power and can be highly useful for grid-scale energy storage and electricity production where geography allows.
Pumped Hydroelectric Storage
Pumped-storage systems use excess electrical energy to pump water uphill.
The energy transformation is approximately:
electrical → mechanical → gravitational potential
When electricity is needed:
gravitational potential → kinetic → mechanical → electrical
This system may require a very large volume of water, but it can store enormous total quantities of energy.
This shows that low energy density does not necessarily mean low total energy storage.
Large-scale systems can compensate by using large masses or volumes.
Energy Density and Portable Technology
Energy density is also important in:
- smartphones
- laptops
- cameras
- drones
- medical devices
- power tools
- wearable electronics
A battery with greater energy per kilogram can provide longer operating time without making the device excessively heavy.
A battery with greater energy per litre can store more energy without making the device excessively large.
For portable devices, engineers often want both:
high gravimetric energy density
and:
high volumetric energy density
Energy Density Versus Power Density
Energy density should not be confused with power density.
Energy density tells us:
how much energy can be stored
Power density tells us:
how quickly energy can be delivered relative to mass or volume
A storage system might hold a large amount of energy but be unable to release it very quickly.
Another might store less energy but deliver extremely high power for a short period.
This distinction matters for:
- vehicles
- power tools
- grid storage
- electronics
- acceleration systems
Worked Comparison
Suppose Battery A stores:
200 Wh/kg
Battery B stores:
300 Wh/kg
A device requires:
60,000 Wh
Battery A mass:
mass = energy / energy density
mass = 60,000/200
mass = 300 kg
Battery B:
mass = 60,000/300
mass = 200 kg
Using Battery B reduces the required battery mass by:
100 kg
This could have a major effect on vehicle performance.
Comparing Fuels Using Required Mass
Suppose a system needs:
900 MJ
of stored chemical energy.
Fuel A:
30 MJ/kg
Required mass:
m = 900/30
m = 30 kg
Fuel B:
45 MJ/kg
Required mass:
m = 900/45
m = 20 kg
Fuel B requires 10 kg less fuel to store the same amount of energy.
Including Efficiency in the Comparison
Suppose a vehicle needs:
300 MJ
of useful mechanical energy.
System A
Fuel energy density:
45 MJ/kg
Efficiency:
30%
Required input energy:
300/0.30 = 1000 MJ
Fuel mass:
1000/45 ≈ 22.2 kg
System B
Energy storage density:
1 MJ/kg
Efficiency:
90%
Required input energy:
300/0.90 ≈ 333 MJ
Storage mass:
333/1 ≈ 333 kg
System B is much more efficient but requires a heavier energy-storage system in this simplified comparison.
This demonstrates why transportation engineering involves trade-offs.
Evaluating Energy Resources
Energy density is important, but it should never be the only factor considered.
A complete comparison might include:
| Factor | Question |
|---|---|
| Energy density | How much energy is available per kg or litre? |
| Efficiency | How much becomes useful output? |
| Power | How quickly can energy be delivered? |
| Renewability | Can the resource be replenished? |
| Emissions | What pollutants or greenhouse gases are produced? |
| Storage | How easily can the energy be stored? |
| Transport | How easily can the resource be moved? |
| Safety | What hazards are involved? |
| Reliability | Can energy be supplied when required? |
| Cost | What are the total economic costs? |
| Infrastructure | What systems are required to use it? |
| Waste | What waste products are produced? |
Transportation Decisions
Consider choosing an energy system for a vehicle.
A designer might ask:
- How far must the vehicle travel?
- How heavy can the energy-storage system be?
- How much space is available?
- How quickly must the vehicle refuel or recharge?
- How much power must be delivered?
- What infrastructure exists?
- What emissions are produced?
- How efficient is the drivetrain?
- How safe is the storage system?
Different vehicles can therefore favor different technologies.
Cars
Cars can potentially use:
- gasoline
- diesel
- batteries
- hydrogen
- biofuels
Liquid fuels offer high energy density and rapid refueling.
Battery systems can offer high drivetrain efficiency and avoid direct exhaust emissions.
Hydrogen can offer high energy per kilogram of fuel but requires specialized storage.
The best comparison depends on the whole system and intended use.
Aircraft
Aircraft place especially strong limits on mass.
This makes gravimetric energy density extremely important.
An energy-storage system that is practical for a stationary building or road vehicle may be much more difficult to use in an aircraft because the aircraft must continually carry the storage mass.
Ships
Ships can carry much greater masses than aircraft.
Therefore, mass energy density may be less restrictive.
However, ships travel long distances and require very large total quantities of energy.
Designers must consider:
- fuel volume
- fuel mass
- safety
- emissions
- cost
- refueling infrastructure
Grid Energy Storage
Stationary energy storage has different priorities.
A grid battery or pumped-storage facility does not have to carry its own energy-storage system while moving.
Therefore, mass may be less important.
Engineers may prioritize:
- cost
- lifespan
- efficiency
- safety
- response time
- total storage capacity
- environmental impact
This demonstrates why the "best" energy technology depends strongly on its application.
Technological Trade-Offs
Imagine two storage technologies.
Technology A
- very high energy density
- expensive
- difficult to recycle
- high power output
Technology B
- lower energy density
- inexpensive
- long lifespan
- easy to recycle
There is no automatically correct choice.
For an aircraft, Technology A's low mass may be extremely important.
For a stationary storage facility, Technology B may be preferable.
Engineering decisions involve balancing competing requirements.
Environmental Trade-Offs
Energy density can indirectly affect environmental impacts.
A higher-energy-density fuel may require:
- less material extraction
- less transport mass
- smaller storage systems
But it might also:
- produce greenhouse gases
- create hazardous waste
- require environmentally damaging extraction
- create safety risks
Therefore, high energy density does not automatically mean environmentally preferable.
Life-Cycle Thinking
A complete environmental comparison considers the entire life cycle of an energy technology.
This may include:
raw materials → manufacturing → transportation → operation → maintenance → disposal/recycling
For example, evaluating a battery might include:
- mineral extraction
- battery manufacturing
- electricity used for charging
- operating lifetime
- recycling
- disposal
Similarly, evaluating gasoline should include:
- oil extraction
- refining
- transportation
- combustion
- emissions
This produces a more meaningful comparison than considering energy density alone.
Energy Density and Sustainability
A sustainable energy system must balance many factors.
These include:
- sufficient energy supply
- acceptable environmental impact
- affordability
- reliability
- resource availability
- safety
- efficiency
- appropriate energy density
Energy density can influence which technologies are practical, but sustainability requires a broader evaluation.
Common Mistakes
Confusing Energy Density with Material Density
Material density is:
density = mass / volume
Energy density describes:
energy / mass
or:
energy / volume
They are different quantities.
Confusing Energy Density with Power
Energy density tells us how much energy is stored.
Power tells us how quickly energy is transferred.
Confusing Energy Density with Efficiency
A system can have:
high energy density + low efficiency
or:
low energy density + high efficiency
These quantities describe different characteristics.
Assuming the Highest Energy Density Is Always Best
Energy density is only one criterion.
Other factors include:
- safety
- emissions
- cost
- renewability
- efficiency
- storage
- infrastructure
Comparing Different Units Directly
Do not directly compare:
MJ/kg
with:
MJ/L
One is energy per mass.
The other is energy per volume.
They answer different questions.
Ignoring the Storage System
The energy-storage material may require:
- tanks
- containers
- cooling
- insulation
- electronics
- structural support
These components add mass and volume.
Ignoring Efficiency
Stored energy is not necessarily equal to useful energy.
If a system is:
30% efficient
only 30% of the stored energy becomes the desired useful output.
Assuming Renewable Means High Energy Density
Renewability and energy density are separate characteristics.
Wind and sunlight are renewable but are not stored fuels like gasoline.
Check Your Understanding
- Define energy density.
- Explain the difference between gravimetric and volumetric energy density.
- State two common units for energy density.
- A fuel contains 100 MJ in 4 kg. Calculate its energy density.
- A fuel has an energy density of 40 MJ/kg. How much energy is stored in 15 kg?
- A system requires 600 MJ. Calculate the mass of a fuel with an energy density of 30 MJ/kg.
- Repeat Question 6 for a fuel with an energy density of 50 MJ/kg.
- Which fuel requires less mass?
- Explain why high energy density is particularly important for aircraft.
- Explain why energy density may be less important for stationary energy storage.
- What is the difference between energy density and power density?
- Explain why hydrogen can have a high gravimetric energy density but present volumetric storage challenges.
- Why must the mass of a hydrogen tank be considered when evaluating the complete system?
- A battery has an energy density of 200 Wh/kg and a mass of 300 kg. Calculate its stored energy in kWh.
- Convert the answer to Question 14 into MJ.
- Explain why gasoline's high energy density does not automatically make a gasoline vehicle more efficient than an electric vehicle.
- What is meant by the efficiency of an energy-conversion system?
- A fuel contains 1000 MJ and is used in a 35%-efficient engine. Calculate the useful mechanical energy.
- Explain why nuclear fuels are described as having extremely high energy density.
- Give two disadvantages that must still be considered when evaluating nuclear energy.
- Explain why solar and wind resources cannot be evaluated simply by comparing fuel energy density.
- Describe how pumped hydroelectric storage stores energy.
- Explain why a low-energy-density storage system can still store a very large total amount of energy.
- Why is volumetric energy density important for vehicles with limited storage space?
- Explain how energy density influences the design of portable electronic devices.
- List five factors other than energy density that should be considered when comparing energy resources.
- Explain how life-cycle analysis can improve comparisons between energy technologies.
- Why might the best energy-storage technology for an aircraft differ from the best technology for an electrical grid?
- Explain how energy density can influence environmental impacts.
- Evaluate the statement: "The energy source with the highest energy density is always the best energy source."
Key Terms
Energy density — Amount of energy stored or available per unit mass or volume.
Gravimetric energy density — Energy stored per unit mass.
Volumetric energy density — Energy stored per unit volume.
Energy resource — Source from which usable energy can be obtained.
Fuel — Substance that can release stored energy through a physical, chemical, or nuclear process.
Energy storage — Retaining energy so that it can be used later.
Battery — Device that stores chemical energy and can transfer it electrically.
Power density — Rate at which energy can be delivered relative to mass or volume.
Efficiency — Fraction of input energy transferred into useful output.
Renewable resource — Energy resource replenished naturally on a human timescale.
Non-renewable resource — Resource consumed faster than natural processes replace it.
Fossil fuel — Carbon-rich fuel such as coal, oil, or natural gas formed from ancient biological material.
Hydrogen — Energy carrier with high energy content per unit mass but challenging volumetric storage requirements.
Nuclear fuel — Material capable of releasing energy through nuclear reactions.
Pumped storage — Energy-storage system that stores gravitational potential energy by moving water to a higher elevation.
Life-cycle analysis — Evaluation of environmental impacts throughout production, use, and disposal.
Energy carrier — Substance or system used to transport or deliver energy from one location or process to another.
Key Takeaways
- Energy density describes how much energy is stored per unit mass or volume.
- Gravimetric energy density measures energy per unit mass.
- Volumetric energy density measures energy per unit volume.
- High energy density allows large amounts of energy to be carried using less mass or space.
- Energy density is particularly important in transportation and portable technology.
- Aircraft are especially sensitive to energy-storage mass.
- Batteries generally have lower gravimetric energy density than liquid hydrocarbon fuels, although electric motors can be highly efficient.
- Hydrogen has very high energy content per kilogram but presents significant storage challenges because of its low density.
- The complete storage system must be considered, not just the fuel or battery material.
- Nuclear fuels have extremely high energy densities compared with chemical fuels.
- High energy density does not automatically make an energy resource safe, clean, economical, or sustainable.
- Renewable resources such as wind and solar require different comparisons because they do not use conventional stored fuels.
- Energy density is different from efficiency.
- Energy density is different from power density.
- Energy density by mass and energy density by volume answer different engineering questions.
- Energy resources should be compared using multiple criteria, including efficiency, cost, emissions, storage, safety, reliability, infrastructure, renewability, and environmental impact.
- Life-cycle analysis provides a broader way to compare energy technologies.
- The best energy resource depends strongly on the intended application.
The central idea is:
energy density = energy stored / mass or volume
But choosing an energy technology requires a much broader question:
How much energy can it provide, how efficiently can we use it, what does it take to store and deliver it, and what are the consequences of doing so?