Energy density

This article is about energy per unit volume. For energy per unit mass, see Specific energy.

Energy density
SI unit	J/m3
Other units	J/L, W⋅h/L
In SI base units	m−1⋅kg⋅s−2
Derivations from other quantities	U = E/V
Dimension

In physics, energy density is the amount of energy stored in a given system or region of space per unit volume. It is sometimes confused with energy per unit mass which is properly called specific energy or gravimetric energy density.

Often only the useful or extractable energy is measured, which is to say that inaccessible energy (such as rest mass energy) is ignored.<ref>"The Two Classes of SI Units and the SI Prefixes". NIST Guide to the SI. 2009-07-02. Retrieved 2012-01-25.</ref> In cosmological and other general relativistic contexts, however, the energy densities considered are those that correspond to the elements of the stress-energy tensor and therefore do include mass energy as well as energy densities associated with pressure.

Energy per unit volume has the same physical units as pressure and in many situations is synonymous. For example, the energy density of a magnetic field may be expressed as and behaves like a physical pressure. Likewise, the energy required to compress a gas to a certain volume may be determined by multiplying the difference between the gas pressure and the external pressure by the change in volume. A pressure gradient describes the potential to perform work on the surroundings by converting internal energy to work until equilibrium is reached.

Overview

There are different types of energy stored in materials, and it takes a particular type of reaction to release each type of energy. In order of the typical magnitude of the energy released, these types of reactions are: nuclear, chemical, electrochemical, and electrical.

Nuclear reactions take place in stars and nuclear power plants, both of which derive energy from the binding energy of nuclei. Chemical reactions are used by organisms to derive energy from food and by automobiles to derive energy from gasoline. Liquid hydrocarbons (fuels such as gasoline, diesel and kerosene) are today the densest way known to economically store and transport chemical energy at a large scale (1 kg of diesel fuel burns with the oxygen contained in ≈15 kg of air). Electrochemical reactions are used by most mobile devices such as laptop computers and mobile phones to release energy from batteries.

Types of energy content

There are several different types of energy content. One is the theoretical total amount of thermodynamic work that can be derived from a system, at a given temperature and pressure imposed by the surroundings. This is called exergy. Another is the theoretical amount of electrical energy that can be derived from reactants that are at room temperature and atmospheric pressure. This is given by the change in standard Gibbs free energy. But as a source of heat or for use in a heat engine, the relevant quantity is the change in standard enthalpy or the heat of combustion.

There are two kinds of heat of combustion:

• The higher value (HHV), or gross heat of combustion, includes all the heat released as the products cool to room temperature and whatever water vapor is present condenses.
• The lower value (LHV), or net heat of combustion, does not include the heat which could be released by condensing water vapor, and may not include the heat released on cooling all the way down to room temperature.

A convenient table of HHV and LHV of some fuels can be found in the references.<ref name="engineeringtoolbox">"Fossil and Alternative Fuels - Energy Content (2008)". Engineering ToolBox. Retrieved 2018-10-08.</ref>

In energy storage and fuels

Selected energy densities plot<ref name=tzar2 /><ref name=tzar3 /><ref name=tzar4 /><ref name="fisher">Fisher, Julia (2003). Elert, Glenn (ed.). "Energy density of coal". The Physics Factbook. Retrieved 2019-07-28.</ref><ref name=tzar6 /><ref name=tzar7 /><ref name=tzar8 />

In energy storage applications the energy density relates the energy in 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. Given the high energy density of gasoline, the exploration of alternative media to store the energy of powering a car, such as hydrogen or battery, is strongly limited by the energy density of the alternative medium. The same mass of lithium-ion storage, for example, would result in a car with only 2% the range of its gasoline counterpart. If sacrificing the range is undesirable, it becomes necessary to carry that much more fuel.

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.

Energy density differs from energy conversion efficiency (net output per input) or embodied energy (the energy output costs to provide, as harvesting, refining, distributing, and dealing with pollution all use energy). Large scale, intensive energy use impacts and is impacted by climate, waste storage, and environmental consequences.

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 it is pulled out.

Alternative options are discussed for energy storage to increase energy density and decrease charging time.<ref>Ionescu-Zanetti, C.; et., al. (2005). "Nanogap capacitors: Sensitivity to sample permittivity changes". Journal of Applied Physics. 99 (2): 024305–024305–5. Bibcode:2006JAP....99b4305I. doi:10.1063/1.2161818. S2CID 120910476.</ref><ref>Naoi, K.; et., al. (2013). "New generation "nanohybrid supercapacitor"". Accounts of Chemical Research. 46 (5): 1075–1083. doi:10.1021/ar200308h. PMID 22433167.</ref><ref>Hubler, A.; Osuagwu, O. (2010). "Digital quantum batteries: Energy and information storage in nanovacuum tube arrays". Complexity. 15 (5): NA. doi:10.1002/cplx.20306. S2CID 6994736.</ref><ref>Lyon, D.; et., al. (2013). "Gap size dependence of the dielectric strength in nano vacuum gaps". IEEE Transactions on Dielectrics and Electrical Insulation. 2 (4): 1467–1471. doi:10.1109/TDEI.2013.6571470. S2CID 709782.</ref>

The figure above shows the gravimetric and volumetric energy density of some fuels and storage technologies (modified from the Gasoline article).

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.

Generally the density values for chemical fuels do not include the weight of the oxygen required for combustion. The atomic weights of carbon and oxygen are similar, while hydrogen is much lighter. Figures are presented in 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 contain their own oxidizer (such as gunpowder and TNT), where the mass of the oxidizer in effect adds 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.

List of material energy densities

See also: Energy density Extended Reference Table

The following unit conversions may be helpful when considering the data in the tables: 3.6 MJ = 1 kW⋅h ≈ 1.34 hp⋅h. Since 1 J = 10⁻⁶ MJ and 1 m³ = 10³ L, divide joule/m³ by 10⁹ to get MJ/L = GJ/m³. Divide MJ/L by 3.6 to get kW⋅h/L.

In chemical reactions (oxidation)

See also: Energy content of biofuel and Food energy

Unless otherwise stated, the values in the following table are lower heating values for perfect combustion, not counting oxidizer mass or volume. When used to produce electricity in a fuel cell or to do work, it is the Gibbs free energy of reaction (ΔG) that sets the theoretical upper limit. If the produced H₂O is vapor, this is generally greater than the lower heat of combustion, whereas if the produced H
₂O is liquid, it is generally less than the higher heat of combustion. But in the most relevant case of hydrogen, ΔG is 113 MJ/kg if water vapor is produced, and 118 MJ/kg if liquid water is produced, both being less than the lower heat of combustion (120 MJ/kg).<ref>CRC Handbook of Chemistry and Physics, 49th Edition, page D-42.</ref>

Energy released by chemical reactions (oxidation)

Material	Specific energy (MJ/kg)	Energy density (MJ/L)	Specific energy (W⋅h/kg)	Energy density (W⋅h/L)	Comment
Hydrogen, liquid	141.86 (HHV) 119.93 (LHV)	10.044 (HHV) 8.491 (LHV)	39,405.639,405.6 (HHV) 33,313.9 (LHV)	2,790.0 (HHV) 2,358.6 (LHV)	Energy figures apply after reheating to 25 °C.<ref name="H2">College of the Desert, “Module 1, Hydrogen Properties”, Revision 0, December 2001 Hydrogen Properties. Retrieved 2014-06-08.</ref> See note above about use in fuel cells.
Hydrogen, gas (681 atm, 69 MPa, 25 °C)	141.86 (HHV) 119.93 (LHV)	5.323 (HHV) 4.500 (LHV)	39,405.639,405.6 (HHV) 33,313.9 (LHV)	1,478.6 (HHV) 1,250.0 (LHV)	Date from same reference as for liquid hydrogen.<ref name="H2" /> High-pressure tanks weigh much more than the hydrogen they can hold. The hydrogen may be around 5.7% of the total mass,<ref name=GCCspecs>Mike Millikin (2014-11-18). "Toyota FCV Mirai launches in LA; initial TFCS specs; $57,500 or $499 lease; leaning on Prius analogy". Green Car Congress. Retrieved 2014-11-23.</ref> giving just 6.8 MJ per kg total mass for the LHV. See note above about use in fuel cells.
Hydrogen, gas (1 atm or 101.3 kPa, 25 °C)	141.86 (HHV) 119.93 (LHV)	0.01188 (HHV) 0.01005 (LHV)	39,405.639,405.6 (HHV) 33,313.9 (LHV)	3.3 (HHV) 2.8 (LHV)	<ref name="H2" />
Methane (101.3 kPa, 15 °C)	55.6	0.0378	15,444.5	10.5
LNG (NG at −160 °C)	53.6<ref name="ngau" />	22.2	14,888.9	6,166.7
CNG (NG compressed to 247 atm, 25 MPa ≈ 3,600 psi)	53.6<ref name="ngau" />	9	14,888.9	2,500.0
Natural gas	53.6<ref name="ngau">Envestra Limited. Natural Gas Archived 2008-10-10 at the Wayback Machine. Retrieved 2008-10-05.</ref>	0.0364	14,888.9	10.1
LPG propane	49.6	25.3	13,777.8	7,027.8	<ref name="IOR">IOR Energy. List of common conversion factors (Engineering conversion factors). Retrieved 2008-10-05.</ref>
LPG butane	49.1	27.7	13,638.9	7,694.5	<ref name="IOR" />
Gasoline (petrol)	46.4	34.2	12,888.9	9,500.0	<ref name="IOR" />
Polypropylene plastic	46.4<ref name="aquafoam" />	41.7	12,888.9	11,583.3
Polyethylene plastic	46.3<ref name="aquafoam">Paul A. Kittle, Ph.D. "ALTERNATE DAILY COVER MATERIALS AND SUBTITLE D - THE SELECTION TECHNIQUE" (PDF). Archived from the original (PDF) on 2008-05-27. Retrieved 2012-01-25.</ref>	42.6	12,861.1	11,833.3
Residential heating oil	46.2	37.3	12,833.3	10,361.1	<ref name="IOR" />
Diesel fuel	45.6	38.6	12,666.7	10,722.2	<ref name="IOR" />
100LL Avgas	44.0<ref>"537.PDF" (PDF). June 1993. Retrieved 2012-01-25.</ref>	31.59	12,222.2	8,775.0
Jet fuel (e.g. kerosene)	43<ref>Gofman, Evelyn (2003). Elert, Glenn (ed.). "Energy density of aviation fuel". The Physics Factbook. Retrieved 2019-07-28.</ref><ref>"Handbook of Products" (PDF). Air BP. pp. 11–13. Archived from the original (PDF) on 2011-06-08. </ref><ref>Characteristics of Petroleum Products Stored and Dispensed (PDF), Petroleum Products Division - GN, p. 132, archived from the original (PDF) on 16 January 2017, retrieved 15 January 2017</ref>	35	11,944.4	9,722.2	Aircraft engine
Gasohol E10 (10% ethanol 90% gasoline by volume)	43.54	33.18	12,094.5	9,216.7
Lithium	43.1	23.0	11,972.2	6,388.9
Biodiesel oil (vegetable oil)	42.20	33	11,722.2	9,166.7
DMF (2,5-dimethylfuran)	42<ref>Román-Leshkov, Yuriy; Barrett, Christopher J.; Liu, Zhen Y.; Dumesic, James A. (21 June 2007). "Production of dimethylfuran for liquid fuels from biomass-derived carbohydrates". Nature. 447 (7147): 982–985. Bibcode:2007Natur.447..982R. doi:10.1038/nature05923. PMID 17581580. S2CID 4366510.</ref>	37.8	11,666.7	10,500.0
Paraffin wax	42<ref>Wiener, Harry (January 1947). "Structural Determination of Paraffin Boiling Points". Journal of the American Chemical Society. 69 (1): 17–20. doi:10.1021/ja01193a005. ISSN 0002-7863. PMID 20291038.</ref>	37.8	11,700	10,500
Crude oil (tonne of oil equivalent)	41.868	37<ref name="ngau" />	11,630	10,278
Polystyrene plastic	41.4<ref name="aquafoam" />	43.5	11,500.0	12,083.3
Body fat	38	35	10,555.6	9,722.2	Metabolism in human body (22% efficiency<ref name="JLE5">Justin Lemire-Elmore (2004-04-13). "The Energy Cost of Electric and Human-Powered Bicycles" (PDF). p. 5. Retrieved 2009-02-26. properly trained athlete will have efficiencies of 22 to 26%</ref>)
Butanol	36.6	29.2	10,166.7	8,111.1
Gasohol E85 (85% ethanol 15% gasoline by volume)	33.1	25.65	9,194.5	7,125.0
Graphite	32.7	72.9	9,083.3	20,250.0
Coal, anthracite	26–33	34–43	7,222.2–9,166.7	9,444.5–11,944.5	Figures represent perfect combustion not counting oxidizer, but efficiency of conversion to electricity is ≈36%<ref name="fisher" />
Silicon	32.6	75.9	9,056	21,080	See Table 1 <ref>"Silicon as an intermediary between renewable energy and hydrogen" (PDF). Deutsche Bank Research. p. 5. Archived from the original (PDF) on 2008-11-16. Retrieved 16 November 2016.</ref>
Aluminium	31.0	83.8	8,611.1	23,277.8
Ethanol	30	24	8,333.3	6,666.7
DME	31.7 (HHV) 28.4 (LHV)	21.24 (HHV) 19.03 (LHV)	8,805.68,805.6 (HHV) 7,888.9 (LHV)	5,900.0 (HHV) 5,286.1 (LHV)	<ref name="DME1">Bossel, Ulf (July 2003). "The Physics of the Hydrogen Economy" (PDF). European Fuel Cell News. Archived from the original (PDF) on 2006-03-19. Retrieved 2019-04-06. The Higher Heating Values are 22.7, 29.7 or 31.7 MJ/kg for methanol, ethanol and DME, respectively, while gasoline contains about 45 MJ per kg.</ref><ref name="DME2">"Dimethyl Ether (DME)" (PDF). European Biofuels Technology Platform. 2013-11-18. Retrieved 2019-04-06. DME density and lower heating value were obtained from the table on the first page.</ref>
Polyester plastic	26.0<ref name="aquafoam" />	35.6	7,222.2	9,888.9
Magnesium	24.7	43.0	6,861.1	11,944.5
Phosphorus (white)	24.30	44.30	6,750	12,310	<ref>Green Don; Perry Robert (2008). Perry's chemical engineers' handbook (8th ed.). New York: McGraw-Hill. ISBN 9780071422949.</ref>
Coal, bituminous	24–35	26–49	6,666.7–9,722.2	7,222.2–13,611.1	<ref name="fisher" />
PET plastic (impure)	23.5<ref>"Elite_bloc.indd" (PDF). Archived from the original (PDF) on 2011-07-15. Retrieved 2010-05-07.</ref>	< ~32.4	6,527.8	< ~9000
Methanol	19.7	15.6	5,472.2	4,333.3
Titanium	19.74	88.93	5,480	24,700	burned to titanium dioxide
Hydrazine (combusted to N2+H2O)	19.5	19.3	5,416.7	5,361.1
Liquid ammonia (combusted to N2+H2O)	18.6	11.5	5,166.7	3,194.5
Potassium	18.6	16.5	5,160	4,600	burned to dry potassium oxide
PVC plastic (improper combustion toxic)	18.0<ref name="aquafoam" />	25.2	5,000.0	7,000.0
Wood	18.0		5,000.0		<ref>"Biomass Energy Foundation: Fuel Densities". Woodgas.com. Archived from the original on 2010-01-10. Retrieved 2010-05-07.</ref>
Peat briquette	17.7		4,916.7		<ref>"Bord na Mona, Peat for Energy" (PDF). Bnm.ie. Archived from the original (PDF) on 2007-11-19. Retrieved 2012-01-25.</ref>
Sugars, carbohydrates, and protein	17	26.2 (dextrose)	4,722.2	7,277.8	Metabolism in human body (22% efficiency<ref>Justin Lemire-elmore (April 13, 2004). "The Energy Cost of Electric and Human-Powered Bicycle" (PDF). Retrieved 2012-01-25.</ref>)
Calcium	15.9	24.6	4,416.7	6,833.3
Glucose	15.55	23.9	4,319.5	6,638.9
Dry cow dung and camel dung	15.5<ref>"energy buffers". Home.hccnet.nl. Retrieved 2010-05-07.</ref>		4,305.6
Coal, lignite	10–20		2,777.8–5,555.6
Sodium	13.3	12.8	3,694.5	3,555.6	burned to wet sodium hydroxide
Peat	12.8		3,555.6
Nitromethane	11.3	12.85	3,138.9	3,570
Manganese	9.46	68.2	2,630	18,900	burned to manganese dioxide
Sulfur	9.23	19.11	2,563.9	5,308.3	burned to sulfur dioxide<ref name="Wignall">Anne Wignall and Terry Wales. Chemistry 12 Workbook, page 138 Archived 2011-09-13 at the Wayback Machine. Pearson Education NZ ISBN 978-0-582-54974-6</ref>
Sodium	9.1	8.8	2,527.8	2,444.5	burned to dry sodium oxide
Battery, lithium-air rechargeable	9.0<ref>Mitchell, Robert R.; Gallant, Betar M.; Thompson, Carl V.; Shao-Horn, Yang (2011). "All-carbon-nanofiber electrodes for high-energy rechargeable Li–O2 batteries". Energy & Environmental Science. 4 (8): 2952–2958. doi:10.1039/C1EE01496J. S2CID 96799565.</ref>		2,500.0		Controlled electric discharge
Household waste	8.0<ref>David E. Dirkse. energy buffers. "household waste 8..11 MJ/kg"</ref>		2,222.2
Zinc	5.3	38.0	1,472.2	10,555.6
Iron	5.2	40.68	1,444.5	11,300.0	burned to iron(III) oxide
Teflon plastic	5.1	11.2	1,416.7	3,111.1	combustion toxic, but flame retardant
Iron	4.9	38.2	1,361.1	10,611.1	burned to iron(II) oxide
Gunpowder	4.7–11.3<ref>Lu, Gui-e; Chang, Wen-ping; Jiang, Jin-yong; Du, Shi-guo (May 2011). "Study on the energy density of gunpowder heat source". 2011 International Conference on Materials for Renewable Energy & Environment. IEEE. pp. 1185–1187. doi:10.1109/ICMREE.2011.5930549. ISBN 978-1-61284-749-8. S2CID 36130191.</ref>	5.9–12.9		1,600–3,580
TNT	4.184	6.92	1,162	1,920
Barium	3.99	14.0	1,110	3,890	burned to barium dioxide
ANFO	3.7		1,027.8

In nuclear reactions

Energy released by nuclear reactions

Material	Specific energy (MJ/kg)	Energy density (MJ/L)	Specific energy (W⋅h/kg)	Energy density (W⋅h/L)	Comment
Antimatter	89,875,517,874 ≈ 90 PJ/kg	Depends on the density of the antimatter's form	24,965,421,631,578 ≈ 25 TW⋅h/kg	Depends on the density of the antimatter's form	Annihilation, counting both the consumed antimatter mass and ordinary matter mass
Hydrogen (fusion)	639,780,320<ref name="ReferenceA">Calculated from fractional mass loss times c squared.</ref> but at least 2% of this is lost to neutrinos.	Depends on conditions	177,716,755,600	Depends on conditions	Reaction 4H→4He
Deuterium (fusion)	571,182,758<ref>Calculated from fractional mass loss times c squared. Ball, Justin (2019). "Maximizing specific energy by breeding deuterium". Nuclear Fusion. 59 (10): 106043. arXiv:1908.00834. Bibcode:2019NucFu..59j6043B. doi:10.1088/1741-4326/ab394c. S2CID 199405246.</ref>	Depends on conditions	158,661,876,600	Depends on conditions	Proposed fusion scheme for D+D→4He, by combining D+D→T+H, T+D→4He+n, n+H→D and D+D→3He+n, 3He+D→4He+H, n+H→D
Deuterium+tritium (fusion)	337,387,388<ref name="ReferenceA"/>	Depends on conditions	93,718,718,800	Depends on conditions	D + T → 4He + n Being developed.
Lithium-6 deuteride (fusion)	268,848,415<ref name="ReferenceA"/>	Depends on conditions	74,680,115,100	Depends on conditions	6LiD → 24He Used in weapons.
Plutonium-239	83,610,000	1,300,000,000–1,700,000,000 (Depends on crystallographic phase)	23,222,915,000	370,000,000,000–460,000,000,000 (Depends on crystallographic phase)	Heat produced in Fission reactor
Plutonium-239	31,000,000	490,000,000–620,000,000 (Depends on crystallographic phase)	8,700,000,000	140,000,000,000–170,000,000,000 (Depends on crystallographic phase)	Electricity produced in Fission reactor
Uranium	80,620,000<ref name="whatisnuclear" />	1,539,842,000	22,394,000,000		Heat produced in breeder reactor
Thorium	79,420,000<ref name="whatisnuclear">"Computing the energy density of nuclear fuel". whatisnuclear.com. Retrieved 2014-04-17.</ref>	929,214,000	22,061,000,000		Heat produced in breeder reactor (Experimental)
Plutonium-238	2,239,000	43,277,631	621,900,000		Radioisotope thermoelectric generator. The heat is only produced at a rate of 0.57 W/g.

Other release mechanisms

Energy released by electrochemical reactions or other means

Material	Specific energy (MJ/kg)	Energy density (MJ/L)	Specific energy (W⋅h/kg)	Energy density (W⋅h/L)	Comment
Battery, zinc-air	1.59	6.02	441.7	1,672.2	Controlled electric discharge<ref name="duracell-za-tech">"Technical bulletin on Zinc-air batteries". Duracell. Archived from the original on 2009-01-27. Retrieved 2009-04-21.</ref>
Silicon (phase change)	1.790	4.5	500	1,285	Energy stored through solid to liquid phase change of silicon<ref name="Meroueh">Meroueh, Laureen (2020). "Thermal energy storage in Silicon". doi:10.1016/j.renene.2019.06.036. S2CID 197448761. {{cite journal}}: Cite journal requires |journal= (help)</ref>
Strontium bromide hydrate	0.814 <ref name="Fopah-Lele">A. Fopah-Lele, J. G. Tamba "A review on the use of SrBr2·6H2O as a potential material for low temperature energy storage systems and building applications", Solar Energy Materials and Solar Cells 164 175-84 (2017).</ref>	1.93		628	Thermal energy of phase change at 88.6 °C (361.8 K)
Liquid nitrogen	0.77<ref name="Knowlen">C. Knowlen, A.T. Mattick, A.P. Bruckner and A. Hertzberg, "High Efficiency Conversion Systems for Liquid Nitrogen Automobiles", Society of Automotive Engineers Inc, 1988.</ref>	0.62	213.9	172.2	Maximum reversible work at 77.4 K with 300 K reservoir
Sodium sulfur battery	0.54–0.86		150–240
Compressed air at 30 MPa	0.5	0.2	138.9	55.6	Potential energy
Latent heat of fusion of ice (thermal)	0.334	0.334	93.1	93.1
Lithium metal battery	1.8	4.32	500	1,200	Controlled electric discharge
Lithium-ion battery	0.36–0.875<ref group=""><ref>"Overview of lithium ion batteries" (PDF). Panasonic. Jan 2007. Archived (PDF) from the original on November 7, 2011.</ref><ref>"Panasonic NCR18650B" (PDF). Archived from the original (PDF) on 2015-07-22.</ref></ref>	0.9–2.63	100.00–243.06	250.00–730.56	Controlled electric discharge
Lithium-ion battery with silicon nanowire anodes	1.566	4.32	435<ref name=":2">"Amprius' silicon nanowire Li-ion batteries power Airbus Zephyr S HAPS solar aircraft". Green Car Congress. Retrieved 2022-12-31.</ref>	1,200<ref name=":2" />	Controlled electric discharge
Flywheel	0.36–0.5	5.3			Kinetic energy
Alkaline battery	0.48<ref>"Test of Duracell Ultra Power AA". lygte-info.dk. Retrieved 2019-02-16.</ref>	1.3<ref name=":8">"Energizer EN91 AA alkaline battery datasheet" (PDF). Retrieved 2016-01-10.</ref>			Controlled electric discharge
Nickel-metal hydride battery	0.41<ref name="lygte">"Test of GP ReCyko+ AA 2700mAh (Green)". lygte-info.dk. Retrieved 2019-02-16.</ref>	0.504–1.46<ref name="lygte" />			Controlled electric discharge
Lead-acid battery	0.17	0.56	47.2	156	Controlled electric discharge
Supercapacitor (EDLC)	0.01–0.030<ref name="maxwell">"Maxwell supercapacitor comparison" (PDF). Retrieved 2016-01-10.</ref><ref name="ESHSP">"Nesscap ESHSP series supercapacitor datasheet" (PDF). Archived from the original (PDF) on 2016-03-29. Retrieved 2016-01-10.</ref><ref name="XL60">"Cooper PowerStor XL60 series supercapacitor datasheet" (PDF). Retrieved 2016-01-10.</ref><ref name=":3">"Kemet S301 series supercapacitor datasheet" (PDF). Archived from the original (PDF) on 2016-03-04. Retrieved 2016-01-10.</ref><ref name=":4">"Nichicon JJD series supercapatcitor datasheet" (PDF). Retrieved 2016-01-10.</ref><ref name=":5">"skelcap High Energy Ultracapacitor" (PDF). Skeleton Technologies. Archived from the original (PDF) on 2 April 2016. Retrieved 13 October 2015.</ref><ref name="maxwell2">"3.0V 3400F ULTRACAPACITOR CELL DATASHEET BCAP3400 P300 K04/05" (PDF). Retrieved 2020-01-12.</ref>	0.006–0.06<ref name="maxwell" /><ref name="ESHSP" /><ref name="XL60" /><ref name=":3" /><ref name=":4" /><ref name=":5" />	up to 8.57<ref name="maxwell2" />		Controlled electric discharge
Water at 100 m dam height	0.000981	0.000978	0.272	0.272	River Engineering & Restoration at OSU | Oregon State University"]. rivers.bee.oregonstate.edu. Retrieved 13 April 2018. Let ε = 0.85, signifying an 85% efficiency rating, typical of an older powerplant.</ref>
Electrolytic capacitor	0.00001–0.0002<ref name=":7">"Vishay STE series tantalum capacitors datasheet" (PDF). Retrieved 2016-01-10.</ref>	0.00001–0.001<ref name=":7" /><ref>"nichicon TVX aluminum electrolytic capacitors datasheet" (PDF). Retrieved 2016-01-10.</ref><ref>"nichicon LGU aluminum electrolytic capacitors datasheet" (PDF). Retrieved 2016-01-10.</ref>			Controlled electric discharge

In material deformation

The mechanical energy storage capacity, or resilience, of a Hookean material when it is deformed to the point of failure can be computed by calculating tensile strength times the maximum elongation dividing by two. The maximum elongation of a Hookean material can be computed by dividing stiffness of that material by its ultimate tensile strength. The following table lists these values computed using the Young's modulus as measure of stiffness:

Mechanical energy capacities

Material	Energy density by mass (J/kg)	Resilience: Energy density by volume (J/L)	Density (kg/L)	Young's modulus (GPa)	Tensile yield strength (MPa)
Rubber band	1,651–6,605<ref name="Band">"How Much Energy Can You Store in a Rubber Band?". Wired. ISSN 1059-1028. Retrieved 2020-01-21.</ref>	2,200–8,900<ref name="Band" />	1.35<ref name="Band" />
Steel, ASTM A228 (yield, 1 mm diameter)	1,440–1,770	11,200–13,800	7.80<ref name=":2a">"MatWeb - The Online Materials Information Resource". www.matweb.com. Retrieved 2019-12-15.</ref>	210<ref name=":2a" />	2,170–2,410<ref name=":2a" />
Acetals	908	754	0.831<ref>PubChem. "Acetal". pubchem.ncbi.nlm.nih.gov. Retrieved 2019-12-12.</ref>	2.8<ref name=":0" />	65 (ultimate)<ref name=":0" />
Nylon-6	233–1,870	253–2,030	1.084	2–4<ref name=":0" />	45–90 (ultimate)<ref name=":0" />
Copper Beryllium 25-1/2 HT (yield)	684	5,720<ref name=":3a" />	E. Jordan Brookes Company"]. www.ejbmetals.com. Retrieved 2019-12-15.</ref>	131<ref name=":3a" />	1,224<ref name=":3a" />
Polycarbonates	433–615	520–740	1.2<ref>"polycarbonate information and properties". www.polymerprocessing.com. Retrieved 2019-12-12.</ref>	2.6<ref name=":0" />	52–62 (ultimate)<ref name=":0" />
ABS plastics	241–534	258–571	1.07	1.4–3.1<ref name=":0">"Young's Modulus - Tensile and Yield Strength for common Materials". www.engineeringtoolbox.com. Retrieved 2019-12-12.</ref>	40 (ultimate)<ref name=":0" />
Acrylic		1,530		3.2<ref name=":0" />	70 (ultimate)<ref name=":0" />
Aluminium 7077-T8 (yield)	399	1,120<ref name=":3a">Brush Wellman Alloy Products. "Elastic Resilience" (PDF). Technical Tidbits. Retrieved December 15, 2019.</ref>	2.81<ref>"ASM Material Data Sheet". asm.matweb.com. Retrieved 2019-12-15.</ref>	71.0<ref name=":3a" />	400<ref name=":3a" />
Steel, stainless, 301-H (yield)	301	2,410<ref name=":3a" />	8.0<ref>Sutherland, Karen; Martin, Monica (2004). Elert, Glenn (ed.). "Density of steel". The Physics Factbook. Retrieved 2020-06-18.</ref>	193<ref name=":3a" />	965<ref name=":3a" />
Aluminium 6061-T6 (yield @ 24 °C)	205	553	2.70<ref name=":1">"Aluminum 6061-T6; 6061-T651". www.matweb.com. Retrieved 2021-06-13.</ref>	68.9<ref name=":1" />	276<ref name=":1" />
Epoxy resins		113–1,810		2–3<ref name=":0" />	26–85 (ultimate)<ref name=":0" />
Douglas fir Wood	158–200	96	.481–.609<ref>"Wood Species - Moisture Content and Weight". www.engineeringtoolbox.com. Retrieved 2019-12-12.</ref>	13<ref name=":0" />	50 (compression)<ref name=":0" />
Steel, Mild AISI 1018	42.4	334	7.87<ref name="MildSteel">"AISI 1018 Mild/Low Carbon Steel". AZoM.com. 2012-06-28. Retrieved 2020-01-22.</ref>	205<ref name="MildSteel" />	370 (440 Ultimate)<ref name="MildSteel" />
Aluminium (not alloyed)	32.5	87.7	2.70<ref>"ASM Material Data Sheet". asm.matweb.com. Retrieved 2019-12-12.</ref>	69<ref name=":0" />	110 (ultimate)<ref name=":0" />
Pine (American Eastern White, flexural)	31.8–32.8	11.1–11.5	.350<ref name=":1a">"American Eastern White Pine Wood". www.matweb.com. Retrieved 2019-12-15.</ref>	8.30–8.56 (flexural)<ref name=":1a" />	41.4 (flexural)<ref name=":1a" />
Brass	28.6–36.5	250–306	8.4–8.73<ref name="MWD">"Mass, Weight, Density or Specific Gravity of Different Metals". www.simetric.co.uk. Retrieved 2019-12-12.</ref>	102–125<ref name=":0" />	250 (ultimate)<ref name=":0" />
Copper	23.1	207	8.93<ref name="MWD" />	117<ref name=":0" />	220 (ultimate)<ref name=":0" />
Glass	5.56–10.0	13.9–25.0	Saint Gobain Building Glass UK"]. uk.saint-gobain-building-glass.com. Retrieved 2019-12-12.</ref>	50–90<ref name=":0" />	50 (compression)<ref name=":0" />

In batteries

Battery energy capacities

Storage device	Energy content (Joule)	Energy content (W⋅h)	Energy type	Typical mass (g)	Typical dimensions (diameter × height in mm)	Typical volume (mL)	Energy density by volume (MJ/L)	Energy density by mass (MJ/kg)
Alkaline AA battery<ref name=":9">"Battery Energy Tables". Archived from the original on 2011-12-04.</ref>	9,360	2.6	Electrochemical	24	14.2 × 50	7.92	1.18	0.39
Alkaline C battery<ref name=":9" />	34,416	9.5	Electrochemical	65	26 × 46	24.42	1.41	0.53
NiMH AA battery	9,072	2.5	Electrochemical	26	14.2 × 50	7.92	1.15	0.35
NiMH C battery	19,440	5.4	Electrochemical	82	26 × 46	24.42	0.80	0.24
Lithium-ion 18650 battery	28,800–46,800	8–13	Electrochemical	44–49<ref name=":10">"18650 Battery capacities".</ref>	18 × 65	16.54	1.74–2.83	0.59–1.06

Nuclear energy sources

The greatest energy source by far is matter itself. This energy, E = mc², where m = ρV, ρ 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 (0.1%), 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, does not have an equivalent anti-particle form, but would offer the same 100% conversion rate of mass to energy in the form of Hawking radiation. In the case of relatively small black holes (smaller than astronomical objects) the power output would be tremendous.

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 (2021), sustained fusion power production continues to be elusive.

Power from fission of uranium and thorium in nuclear power plants will be available for many decades or even centuries because of the plentiful supply of the elements on earth,<ref>"Supply of Uranium". world-nuclear.org. 2014-10-08. Retrieved 2015-06-13.</ref> though the full potential of this source can only be realized through breeder reactors, which are, apart from the BN-600 reactor, not yet used commercially.<ref name="cohen">"Facts from Cohen". Formal.stanford.edu. 2007-01-26. Archived from the original on 2007-04-10. Retrieved 2010-05-07.</ref> Coal, gas, and petroleum are the current primary energy sources in the U.S.<ref>"U.S. Energy Information Administration (EIA) - Annual Energy Review". Eia.doe.gov. 2009-06-26. Archived from the original on 2010-05-06. Retrieved 2010-05-07.</ref> but have a much lower energy density. Burning local biomass fuels supplies household energy needs (cooking fires, oil lamps, etc.) worldwide.

Thermal power of nuclear fission reactors

The density of thermal energy contained in the core of a light water reactor (PWR or BWR) of typically 1 GWe (1,000 MW electrical corresponding to ≈3,000 MW thermal) is in the range of 10 to 100 MW of thermal energy per cubic meter of cooling water depending on the location considered in the system (the core itself (≈30 m³), the reactor pressure vessel (≈50 m³), or the whole primary circuit (≈300 m³)). This represents a considerable density of energy which requires under all circumstances a continuous water flow at high velocity in order to be able to remove the heat from the core, even after an emergency shutdown of the reactor. The incapacity to cool the cores of three boiling water reactors (BWR) at Fukushima in 2011 after the tsunami and the resulting loss of the external electrical power and of the cold source was the cause of the meltdown of the three cores in only a few hours, even though the three reactors were correctly shut down just after the Tōhoku earthquake. This extremely high power density distinguishes nuclear power plants (NPP's) from any thermal power plants (burning coal, fuel or gas) or any chemical plants and explains the large redundancy required to permanently control the neutron reactivity and to remove the residual heat from the core of NPP's.

Energy density of electric and magnetic fields

Main article: Radiant energy density

Electric and magnetic fields store energy. The (volumetric) energy density is given by

<math> u = \frac{\varepsilon}{2} \mathbf{E}^2 + \frac{1}{2\mu} \mathbf{B}^2 </math>

where E is the electric field, B is the magnetic field, and ε and µ are the permittivity and permeability of the surroundings respectively. The solution will be (in SI units) 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 ideal (linear and nondispersive) substances, the energy density (in SI units) is

<math> u = \frac{1}{2} ( \mathbf{E} \cdot \mathbf{D} + \mathbf{H} \cdot \mathbf{B} ) </math>

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

In the case of absence of magnetic fields, by exploiting Fröhlich's relationships it is also possible to extend these equations to anisotropic and nonlinear dielectrics, as well as to calculate the correlated Helmholtz free energy and entropy densities.<ref>Parravicini, J. (2018). "Thermodynamic potentials in anisotropic and nonlinear dielectrics". Physica B. 541: 54–60. Bibcode:2018PhyB..541...54P. doi:10.1016/j.physb.2018.04.029. S2CID 125817506.</ref>

When a pulsed laser impacts a surface, the radiant exposure, i.e. the energy deposited per unit of surface, may be called energy density or fluence.<ref>"Terminology". Regenerative Laser Therapy.</ref>

See also

• Energy content of biofuel
• Energy density Extended Reference Table
• Figure of merit
• Food energy
• Heat of combustion
• High-energy-density matter
• Power density and specifically
• Power-to-weight ratio
• Rechargeable battery
• Solid-state battery
• Specific energy
• Specific impulse

Further reading

• 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

External links

• ^ "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
• "Heat values of various fuels – World Nuclear Association". www.world-nuclear.org. Retrieved 4 November 2018.
• "Energy and Energy Types – Springer" (PDF). Retrieved 4 November 2018.