Energy density

This article is about energy per unit volume. For energy per unit mass or energy density of foods, see specific energy.

Energy density is the amount of energy stored in a given system or region of space per unit volume. Often only the useful or extractable energy is measured, which is to say that chemically inaccessible energy such as rest mass energy is ignored.

Energy density is sometimes useful for comparing fuels. For example, liquid hydrogen fuel has a higher specific energy (energy per unit mass) than gasoline does, but a much lower volumetric energy density.

Energy per unit volume has the same physical units as pressure, and in many circumstances is a synonym: for example, the energy density of a magnetic field may be expressed as (and behaves as) a physical pressure, and the energy required to compress a compressed gas a little more may be determined by multiplying the difference between the gas pressure and the external pressure by the change in volume. In short, pressure is a measure of the enthalpy per unit volume of a system. A pressure gradient has a potential to perform work on the surroundings by converting enthalpy until equilibrium is reached.

Introduction to energy density

Stored energy can take many forms, and there are several types of reactions that release energy. In order of typical magnitude, these are: nuclear, chemical, electrochemical, and electrical.

Chemical reactions are used by animals to derive energy from food, and by automobiles to derive energy from gasoline. Electrochemical reactions are used by most mobile devices such as laptop computers and mobile phones.

Energy densities of common energy storage materials

The following is a list of the energy densities of commonly used or well-known energy storage materials; it doesn't include uncommon or experimental materials. Note that this list does not consider the mass of reactants commonly available such as the oxygen required for combustion.

The following unit conversions may be helpful when considering the data in the table: 1 MJ ≈ 0.28 kWh ≈ 0.37 HPh.

Storage material	Energy type	Specific energy (MJ/kg)	Energy density (MJ/L)	Direct uses
Deuterium–tritium	Nuclear fusion	330 000 000	0.14	Proposed power plants (under development)
Uranium-235	Nuclear fission	83 140 000	1 546 000 000	Electric power plants (nuclear reactors)
Hydrogen (compressed at 70 MPa)	Chemical	123	5.6	Experimental automotive engines
Gasoline (petrol) / Diesel	Chemical	~46	~36	Automotive engines
Propane (including LPG)	Chemical	46.4	26	Cooking, home heating, automotive engines
Fat (animal/vegetable)	Chemical	37		Human/animal nutrition
Coal	Chemical	24		Electric power plants, home heating
Carbohydrates (including sugars)	Chemical	17		Human/animal nutrition
Protein	Chemical	16.8		Human/animal nutrition
Wood	Chemical	16.2		Heating, outdoor cooking
TNT	Chemical	4.6		Explosives
Gunpowder	Chemical	3		Explosives
Lithium battery (non-rechargeable)	Electrochemical	1.8	4.32	Portable electronic devices, flashlights
Lithium-ion battery	Electrochemical	0.72–0.875	0.9–2.63	Laptop computers, mobile devices, some modern electric vehicles
Alkaline battery	Electrochemical	0.67	1.8	Portable electronic devices, flashlights
Nickel-metal hydride battery	Electrochemical	0.288	0.504–1.08	Portable electronic devices, flashlights
Lead-acid battery	Electrochemical	0.17	0.34	Automotive engine ignition
Supercapacitor	Electrical	0.018		Electronic circuits
Electrolytic capacitor	Electrical	0.000036		Electronic circuits

Energy capacities of common storage forms

Storage device	Energy type	Energy content	Typical mass	W × H × D (mm)	Uses
Automotive lead-acid battery	Electrochemical	2.6 MJ	15 kg	230 × 180 × 185	Automotive starter motor and accessories
Alkaline AA battery	Electrochemical	15.4 kJ	23 g	14.5 × 50.5 × 14.5	Portable electronic equipment, flashlights
Lithium-ion battery (Nokia BL-5C)	Electrochemical	12.9 kJ	18.5 g	54.2 × 33.8 × 5.8	Mobile phones

Energy density in energy storage and in fuel

Selected energy densities plot

In energy storage applications the energy density relates the mass of an energy store to the volume of the storage facility, e.g. the fuel tank. The higher the energy density of the fuel, the more energy may be stored or transported for the same amount of volume. The energy density of a fuel per unit mass is called the specific energy of that fuel. In general an engine using that fuel will generate less kinetic energy due to inefficiencies and thermodynamic considerations—hence the specific fuel consumption of an engine will always be greater than its rate of production of the kinetic energy of motion.

The greatest energy source by far consists of mass itself. This energy, E = mc², where m = ρろーV, ρろー is the mass per unit volume, V is the volume of the mass itself and c is the speed of light. This energy, however, can be released only by the processes of nuclear fission (.1%), nuclear fusion (1%), or the annihilation of some or all of the matter in the volume V by matter-antimatter collisions (100%). Nuclear reactions cannot be realized by chemical reactions such as combustion. Although greater matter densities can be achieved, the density of a neutron star would approximate the most dense system capable of matter-antimatter annihilation possible. A black hole, although denser than a neutron star, doesn't have an equivalent anti-particle form.

The highest density sources of energy aside from antimatter are fusion and fission. Fusion includes energy from the sun which will be available for billions of years (in the form of sunlight) but so far (2011), sustained fusion power production continues to be elusive. Fission of uranium and thorium in nuclear power plants will be available for a long time due to the vast supply of the element on earth, though the full potential of this source can only be realised through breeder reactors, which are not yet used commercially. Coal, gas, and petroleum are the current primary energy sources in the U.S. but have a much lower energy density. Burning local biomass fuels supplies household energy needs (cooking fires, oil lamps, etc.) worldwide.

Energy density (how much energy you can carry) does not tell you about energy conversion efficiency (net output per input) or embodied energy (what the energy output costs to provide, as harvesting, refining, distributing, and dealing with pollution all use energy). Like any process occurring on a large scale, intensive energy use impacts the world. For example, climate change, nuclear waste storage, and deforestation may be some of the consequences of supplying our growing energy demands from carbohydrate fuels, nuclear fission, or biomass.

No single energy storage method boasts the best in specific power, specific energy, and energy density. Peukert's Law describes how the amount of useful energy that can be obtained (for a lead-acid cell) depends on how quickly we pull it out. To maximize both specific energy and energy density, one can compute the specific energy density of a substance by multiplying the two values together, where the higher the number, the better the substance is at storing energy efficiently.

Gravimetric and volumetric energy density of some fuels and storage technologies (modified from the Gasoline article):

Note: Some values may not be precise because of isomers or other irregularities. See Heating value for a comprehensive table of specific energies of important fuels.

Note: Also it is important to realise that generally the density values for chemical fuels do not include the weight of oxygen required for combustion. This is typically two oxygen atoms per carbon atom, and one per two hydrogen atoms. The atomic weight of carbon and oxygen are similar, while hydrogen is much lighter than oxygen. Figures are presented this way for those fuels where in practice air would only be drawn in locally to the burner. This explains the apparently lower energy density of materials that already include their own oxidiser (such as gunpowder and TNT), where the mass of the oxidiser in effect adds dead weight, and absorbs some of the energy of combustion to dissociate and liberate oxygen to continue the reaction. This also explains some apparent anomalies, such as the energy density of a sandwich appearing to be higher than that of a stick of dynamite.

Energy densities ignoring external components

This table lists energy densities of systems that require external components, such as oxidisers or a heat sink or source. These figures do not take into account the mass and volume of the required components as they are assumed to be freely available and present in the atmosphere. Such systems cannot be compared with self-contained systems. These values may not be computed at the same reference conditions. Most of them seem to be higher heating value (HHV).

Energy densities of energy media

Storage type	Specific energy (MJ/kg)	Energy density (MJ/L)	Peak recovery efficiency %	Practical recovery efficiency %
Planck energy density	8.99e10	4.633016e104
Hydrogen, liquid	141.86	8.491
Hydrogen, at 690 bar and 15°C	141.86	4.5
Hydrogen, gas	141.86	0.01005
Beryllium	67.6	125.1
Lithium borohydride	65.2	43.4
Boron	58.9	137.8
Methane (1.013 bar, 15°C)	55.6	0.0378
Natural gas	53.6	0.0364
LNG (NG at −160°C)	53.6	22.2
CNG (NG compressed to 250 bar/~3,600 psi)	53.6	9
LPG propane	49.6	25.3
LPG butane	49.1	27.7
Gasoline (petrol)	46.4	34.2
Polypropylene plastic	46.4	41.7
Polyethylene plastic	46.3	42.6
Crude oil (according to the definition of ton of oil equivalent)	46.3	37
Diesel fuel/residential heating oil	46.2	37.3
100LL Avgas	44.0	31.59
Gasohol E10 (10% ethanol 90% gasoline by volume)	43.54	33.18
Lithium	43.1	23.0
Jet A aviation fuel/kerosene	42.8	33
Biodiesel oil (vegetable oil)	42.20	33
DMF (2,5-dimethylfuran)	42	37.8
Polystyrene plastic	41.4	43.5
Body fat metabolism	38	35	22
Butanol	36.6	29.2
Gasohol E85 (85% ethanol 15% gasoline by volume)	33.1	25.65
Graphite	32.7	72.9
Coal, anthracite	32.5	72.4	36
Silicon	32.2	75.1
Aluminum	31.0	83.8
Ethanol	30	24
Polyester plastic	26.0	35.6
Magnesium	24.7	43.0
Coal, bituminous	24	20
PET plastic	23.5 (impure)
Methanol	19.7	15.6
Hydrazine (toxic) combusted to N2+H2O	19.5	19.3
Liquid ammonia (combusted to N2+H2O)	18.6	11.5
PVC plastic (improper combustion toxic)	18.0	25.2
Wood	18.0
Peat briquette	17.7
Sugars, carbohydrates, and protein metabolism	17	26.2(dextrose)	2222
Calcium	15.9	24.6
Glucose	15.55	23.9
Dry cow dung and cameldung	15.5
Coal, lignite	14.0
Sodium (burned to wet sodium hydroxide)	13.3	12.8
Sod peat	12.8
Nitromethane	11.3
Sulfur (burned to sulfur dioxide)	9.23	19.11
Sodium (burned to dry sodium oxide)	9.1	8.8
Battery, lithium-air rechargeable	9.0
Household waste	8.0
Zinc	5.3	38.0
Iron (burned to iron(III) oxide)	5.2	40.68
Teflon plastic (combustion toxic, but flame retardant)	5.1	11.2
Iron (burned to iron(II) oxide)	4.9	38.2
ANFO	3.7
Battery, zinc-air	1.59	6.02
Liquid nitrogen	0.77	0.62
Compressed air at 300 bar (potential energy)	0.5	0.2		>50%
Latent heat of fusion of ice (thermal)	0.335	0.335
Water at 100 m dam height (potential energy)	0.001	0.001		8585-90%
Storage type	Energy density by mass (MJ/kg)	Energy density by volume (MJ/L)	Peak recovery efficiency %	Practical recovery efficiency %

Divide joule metre⁻³ with 10⁹ to get MJ L⁻¹.

Energy density of electric and magnetic fields

Electric and magnetic fields store energy. In a vacuum, the (volumetric) energy density (in SI units) is given by

$U={\frac {\varepsilon _{0}}{2}}\mathbf {E} ^{2}+{\frac {1}{2\mu _{0}}}\mathbf {B} ^{2}$

where E is the electric field and B is the magnetic field. The solution will be in Joules per cubic metre. In the context of magnetohydrodynamics, the physics of conductive fluids, the magnetic energy density behaves like an additional pressure that adds to the gas pressure of a plasma.

In normal (linear) substances, the energy density (in SI units) is

$U={\frac {1}{2}}(\mathbf {E} \cdot \mathbf {D} +\mathbf {H} \cdot \mathbf {B} )$

where D is the electric displacement field and H is the magnetizing field.

See also

• Energy density Extended Reference Table
• Power density and specifically
  • Power-to-weight ratio
• Orders of magnitude (specific energy density)
• Figure of merit
• Energy content of biofuel
• Heat of combustion
• Heating value
• Rechargeable battery
• Specific impulse

External references

Density data

• ^ "Aircraft Fuels." Energy, Technology and the Environment Ed. Attilio Bisio. Vol. 1. New York: John Wiley and Sons, Inc., 1995. 257–259

• "Fuels of the Future for Cars and Trucks" - Dr. James J. Eberhardt - Energy Efficiency and Renewable Energy, U.S. Department of Energy - 2002 Diesel Engine Emissions Reduction (DEER) Workshop San Diego, California - August 25–29, 2002

Energy storage

• energy fundamentals

Books

• The Inflationary Universe: The Quest for a New Theory of Cosmic Origins by Alan H. Guth (1998) ISBN 0-201-32840-2
• Cosmological Inflation and Large-Scale Structure by Andrew R. Liddle, David H. Lyth (2000) ISBN 0-521-57598-2
• Richard Becker, "Electromagnetic Fields and Interactions", Dover Publications Inc., 1964