Energy density explained

Energy density
Unit:J/m3
Otherunits:J/L, W⋅h/L
Basequantities:m−1⋅kg⋅s−2
Derivations:U = E/V
Dimension:wikidata

In physics, 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. It is sometimes confused with stored energy per unit mass, which is called specific energy or .

There are different types of energy stored, corresponding to a particular type of reaction. In order of the typical magnitude of the energy stored, examples of reactions are: nuclear, chemical (including electrochemical), electrical, pressure, material deformation or in electromagnetic fields. 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 from the combustion of 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). Burning local biomass fuels supplies household energy needs (cooking fires, oil lamps, etc.) worldwide. Electrochemical reactions are used by devices such as laptop computers and mobile phones to release energy from batteries.

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. 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.

In cosmological and other contexts in general relativity, the energy densities considered relate to the elements of the stress-energy tensor and therefore do include the rest mass energy as well as energy densities associated with pressure.

Chemical energy

When discussing the chemical energy contained, there are different types which can be quantified depending on the intended purpose. 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, 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:

A convenient table of HHV and LHV of some fuels can be found in the references.[1]

In energy storage and fuels

For energy storage, the energy density relates the stored energy to the volume of the storage equipment, 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 of a fuel per unit mass is called its specific energy.

The adjacent figure 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. The heating values of the fuel describe their specific energies more comprehensively.

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.

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, much more storage volume is necessary. Alternative options are discussed for energy storage to increase energy density and decrease charging time, such as supercapacitors.[2] [3] [4] [5]

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.

Efficiency

In general an engine 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.

Nuclear energy

The greatest energy source by far is matter itself, according to the mass-energy equivalence. This energy is described by E = mc2, where c is the speed of light. In terms of density, m = ρV, where ρ is the mass per unit volume, V is the volume of the mass itself. This energy can be released 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%).

The most effective ways of accessing this energy, aside from antimatter, are fusion and fission. Fusion is the process by which the sun produces energy which will be available for billions of years (in the form of sunlight and heat). However as of 2024, sustained fusion power production continues to be elusive. Power from fission in nuclear power plants (using uranium and thorium) will be available for at least many decades or even centuries because of the plentiful supply of the elements on earth,[6] 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.[7]

Fission reactors

Nuclear fuels typically have volumetric energy densities at least tens of thousands of times higher than chemical fuels. A 1 inch tall uranium fuel pellet is equivalent to about 1 ton of coal, 120 gallons of crude oil, or 17,000 cubic feet of natural gas.[8] In light-water reactors, 1 kg of natural uranium – following a corresponding enrichment and used for power generation– is equivalent to the energy content of nearly 10,000 kg of mineral oil or 14,000 kg of coal.[9] Comparatively, coal, gas, and petroleum are the current primary energy sources in the U.S.[10] but have a much lower energy density.

The density of thermal energy contained in the core of a light-water reactor (pressurized water reactor (PWR) or boiling water reactor (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 that requires a continuous water flow at high velocity at all times in order to remove heat from the core, even after an emergency shutdown of the reactor.

The incapacity to cool the cores of three BWRs at Fukushima after the 2011 tsunami and the resulting loss of external electrical power and cold source caused 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.

Antimatter annihilation

Because antimatter-matter interactions result in complete conversion from the rest mass to radiant energy, the energy density of this reaction depends on the density of the matter and antimatter used. A neutron star would approximate the most dense system capable of matter-antimatter annihilation. 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. Even in the case of relatively small black holes (smaller than astronomical objects) the power output would be tremendous.

Electric and magnetic fields

See main article: Radiant energy density.

Electric and magnetic fields can store energy and its density relates to the strength of the fields within a given volume. This (volumetric) energy density is given by

u=

\varepsilon
2

E2+

1
2\mu

B2

where is the electric field, is the magnetic field, and and are the permittivity and permeability of the surroundings respectively. The solution will be (in SI units) in joules per cubic metre.

In ideal (linear and nondispersive) substances, the energy density (in SI units) is

u=

1
2

(E ⋅ D+H ⋅ B)

where is the electric displacement field and 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.[11]

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.

Pulsed sources

When a pulsed laser impacts a surface, the radiant exposure, i.e. the energy deposited per unit of surface, may also be called energy density or fluence.[12]

Table 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.

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 is vapor, this is generally greater than the lower heat of combustion, whereas if the produced 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).[13]

Specific energy
(MJ/kg)! data-sort-type="number"
Energy density
(MJ/L)		data-sort-type="number" Specific energy
(W⋅h/kg)		data-sort-type="number" Energy density
(W⋅h/L)		Comment
Hydrogen, liquiddata-sort-value="119.93" 141.86 (HHV)
119.93 (LHV)		data-sort-value="8.491" 10.044 (HHV)
8.491 (LHV)		data-sort-value="33,313.9" 39,405.639,405.6 (HHV)
33,313.9 (LHV)		data-sort-value="2,358.6" 2,790.0 (HHV)
2,358.6 (LHV)		Energy figures apply after reheating to 25 °C.[14] See note above about use in fuel cells.
Hydrogen, gas (681 atm, 69 MPa, 25 °C)data-sort-value="119.93" 141.86 (HHV)
119.93 (LHV)		data-sort-value="4.500" 5.323 (HHV)
4.500 (LHV)		data-sort-value="33,313.9" 39,405.639,405.6 (HHV)
33,313.9 (LHV)		data-sort-value="1,250.0" 1,478.6 (HHV)
1,250.0 (LHV)		Date from same reference as for liquid hydrogen.High-pressure tanks weigh much more than the hydrogen they can hold. The hydrogen may be around 5.7% of the total mass,[15] giving just 6.8 MJ per kg total mass for the LHV.

See note above about use in fuel cells.

Hydrogen, gas (25 °C)data-sort-value="119.93" 141.86 (HHV)
119.93 (LHV)		data-sort-value="0.01005" 0.01188 (HHV)
0.01005 (LHV)		data-sort-value="33,313.9" 39,405.639,405.6 (HHV)
33,313.9 (LHV)		data-sort-value="2.8" 3.3 (HHV)
2.8 (LHV)
Diborane78.288.421,722.2data-sort-value="24600" 24,600[16]
Beryllium67.6125.118,777.834,750.0
Lithium borohydride65.243.418,111.112,055.6
Boron58.9137.816,361.138,277.8[17]
Methane (101.3 kPa, 15 °C)55.6data-sort-value="0.0378" 0.037815,444.510.5
LNG (NG at −160 °C)data-sort-value="53.6" 53.6data-sort-value="22.2" 22.214,888.96,166.7
CNG (NG compressed to 247 atm, 25 MPa ≈)data-sort-value="53.6" 53.6data-sort-value="9" 914,888.92,500.0
Natural gasdata-sort-value="53.6" 53.6[18] data-sort-value="0.0364" 0.036414,888.910.1
LPG propane49.6data-sort-value="25.3" 25.313,777.87,027.8[19]
LPG butane49.1data-sort-value="27.7" 27.713,638.97,694.5
Gasoline (petrol)46.4data-sort-value="34.2" 34.212,888.99,500.0
Polypropylene plasticdata-sort-value="46.4" 46.441.712,888.911,583.3
Polyethylene plasticdata-sort-value="46.3" 46.3[20] 42.612,861.111,833.3
Residential heating oil46.2data-sort-value="37.3" 37.312,833.310,361.1
Diesel fuel45.6data-sort-value="38.6" 38.612,666.710,722.2
100LL Avgasdata-sort-value="44.0" 44.0[21] 31.5912,222.28,775.0
Jet fuel (e.g. kerosene)data-sort-value="42.8" 43[22] [23] 3511,944.49,722.2Aircraft engine
Gasohol E10 (10% ethanol 90% gasoline by volume)43.54data-sort-value="33.18" 33.1812,094.59,216.7
Lithium43.123.011,972.26,388.9
Biodiesel oil (vegetable oil)42.20data-sort-value="33" 3311,722.29,166.7
DMF (2,5-dimethylfuran)data-sort-value="42" 42[24] 37.811,666.710,500.0
Paraffin wax42[25] data-sort-value="37.8" 37.8data-sort-value="11700" 11,700data-sort-value="10500" 10,500
Crude oil (tonne of oil equivalent)41.868data-sort-value="37" 3711,63010,278
Polystyrene plasticdata-sort-value="41.4" 41.443.511,500.012,083.3
Body fat38data-sort-value="35" 3510,555.69,722.2Metabolism in human body (22% efficiency[26])
Butanol36.629.210,166.78,111.1
Gasohol E85 (85% ethanol 15% gasoline by volume)33.1data-sort-value="25.65" 25.659,194.57,125.0
Graphite32.772.99,083.320,250.0
Coal, anthracitedata-sort-value="26" 26–33data-sort-value="34" 34–43data-sort-value="7222.2" 7,222.2–9,166.7data-sort-value="9444.5" 9,444.5–11,944.5Figures represent perfect combustion not counting oxidizer, but efficiency of conversion to electricity is ≈36%
Silicon32.675.9data-sort-value="9056" 9,056data-sort-value="21080" 21,080See Table 1 [27]
Aluminium31.083.88,611.123,277.8
Ethanol30248,333.36,666.7
DMEdata-sort-value="28.4" 31.7 (HHV)
28.4 (LHV)		data-sort-value="19.03" 21.24 (HHV)
19.03 (LHV)		data-sort-value="7,888.9" 8,805.68,805.6 (HHV)
7,888.9 (LHV)		data-sort-value="5,286.1" 5,900.0 (HHV)
5,286.1 (LHV)		[28] [29]
Polyester plasticdata-sort-value="26.0" 26.035.67,222.29,888.9
Magnesium24.743.06,861.111,944.5
Phosphorus (white)data-sort-value="24.30" 24.30data-sort-value="44.30" 44.30data-sort-value="6750" 6,750data-sort-value="12310" 12,310[30]
Coal, bituminousdata-sort-value="24" 24–35data-sort-value="26" 26–49data-sort-value="6666.7" 6,666.7–9,722.2data-sort-value="7222.2" 7,222.2–13,611.1
PET plastic (impure)data-sort-value="23.5" 23.5[31] data-sort-value="32.4" < ~32.46,527.8data-sort-value="9000" < ~9000
Methanol19.715.65,472.24,333.3
data-sort-value="19.74" 19.74data-sort-value="88.93" 88.93data-sort-value="5480" 5,480data-sort-value="24700" 24,700burned to titanium dioxide
Hydrazine19.519.35,416.75,361.1burned to nitrogen and water
Liquid ammonia18.611.55,166.73,194.5burned to nitrogen and water
Potassium18.616.55,1604,600burned to dry potassium oxide
PVC plastic (improper combustion toxic)data-sort-value="18.0" 18.025.25,000.07,000.0
Wood18.05,000.0[32]
Peat briquette17.74,916.7[33]
Sugars, carbohydrates, and protein17data-sort-value="26.2" 26.2 (dextrose)4,722.27,277.8Metabolism in human body (22% efficiency[34])
Calcium15.924.64,416.76,833.3
Glucose15.5523.94,319.56,638.9
Dry cow dung and camel dungdata-sort-value="15.5" 15.5[35] 4,305.6
Coal, lignitedata-sort-value="10" 10–202,777.8–5,555.6
Sodium13.312.83,694.53,555.6burned to wet sodium hydroxide
Peat12.83,555.6
Nitromethane11.312.853,138.93,570
Manganese9.4668.22,63018,900burned to manganese dioxide
Sulfur9.2319.112,563.95,308.3burned to sulfur dioxide[36]
Sodium9.18.82,527.82,444.5burned to dry sodium oxide
Household wastedata-sort-value="8.0" 8.0[37] 2,222.2
Iron7.457.72052.916004.1burned to iron(III) oxide[38]

Notes and References

  1. Web site: Fossil and Alternative Fuels - Energy Content (2008).. Engineering ToolBox . 2018-10-08.
  2. Ionescu-Zanetti. C.. et.. al.. 120910476. Nanogap capacitors: Sensitivity to sample permittivity changes. Journal of Applied Physics. 2005. 99. 2. 024305–024305–5. 10.1063/1.2161818. 2006JAP....99b4305I.
  3. Naoi. K.. et.. al.. New generation "nanohybrid supercapacitor".. Accounts of Chemical Research. 46. 5. 1075–1083. 2013. 10.1021/ar200308h. 22433167.
  4. Hubler. A.. Osuagwu. O.. 6994736. Digital quantum batteries: Energy and information storage in nanovacuum tube arrays. Complexity. 2010. 15. 5. NA. 10.1002/cplx.20306. free.
  5. Lyon. D.. et.. al.. Gap size dependence of the dielectric strength in nano vacuum gaps. IEEE Transactions on Dielectrics and Electrical Insulation. 2013. 2. 4. 1467–1471. 10.1109/TDEI.2013.6571470. 709782.
  6. Web site: 2014-10-08 . Supply of Uranium . dead . https://web.archive.org/web/20151017065906/http://www.world-nuclear.org/info/Nuclear-Fuel-Cycle/Uranium-Resources/Supply-of-Uranium/ . 2015-10-17 . 2015-06-13 . world-nuclear.org.
  7. Web site: 2007-01-26 . Facts from Cohen . dead . https://web.archive.org/web/20070410165316/http://www-formal.stanford.edu/jmc/progress/cohen.html . 2007-04-10 . 2010-05-07 . Formal.stanford.edu.
  8. Web site: Venditti . Bruno . Content . Sponsored . 2021-08-27 . The Power of a Uranium Pellet . 2024-08-11 . Elements by Visual Capitalist.
  9. Web site: 2019-05-22 . Fuel comparison . 2024-08-11 . ENS.
  10. Web site: 2009-06-26 . U.S. Energy Information Administration (EIA) - Annual Energy Review . https://web.archive.org/web/20100506022627/http://www.eia.doe.gov/emeu/aer/pecss_diagram.html . 2010-05-06 . 2010-05-07 . Eia.doe.gov.
  11. Parravicini . J. . 2018 . Thermodynamic potentials in anisotropic and nonlinear dielectrics . Physica B . 541 . 54–60 . 2018PhyB..541...54P . 10.1016/j.physb.2018.04.029 . 125817506.
  12. Web site: Terminology . Regenerative Laser Therapy . en.
  13. [CRC Handbook of Chemistry and Physics]
  14. College of the Desert, “Module 1, Hydrogen Properties”, Revision 0, December 2001 Hydrogen Properties. Retrieved 2014-06-08.
  15. Web site: Toyota FCV Mirai launches in LA; initial TFCS specs; $57,500 or $499 lease; leaning on Prius analogy . Mike Millikin. Green Car Congress. 2014-11-18. 2014-11-23.
  16. Greenwood, Norman N.; Earnshaw, Alan (1997), Chemistry of the Elements (2nd ed) (page 164)
  17. Web site: Boron: A Better Energy Carrier than Hydrogen? (28 February 2009). 2010-05-07. Eagle.ca.
  18. Envestra Limited. Natural Gas . Retrieved 2008-10-05.
  19. IOR Energy. List of common conversion factors (Engineering conversion factors). Retrieved 2008-10-05.
  20. Web site: Alternate daily cover materials and subtitle D – The selection technique . Paul A. Kittle, Ph.D. . 2012-01-25 . https://web.archive.org/web/20080527234629/http://www.aquafoam.com/papers/selection.pdf . 2008-05-27 . dead .
  21. Web site: 537.pdf . June 1993 . 2012-01-25 . 2011-09-29 . https://web.archive.org/web/20110929062314/http://www-static.shell.com/static/aus/downloads/aviation/avgas_100ll_pds.pdf . dead .
  22. Web site: Energy density of aviation fuel. Evelyn. Gofman. 2003. The Physics Factbook. Elert. Glenn. 2019-07-28.
  23. Web site: Handbook of Products . Air BP . dead . https://web.archive.org/web/20110608075828/http://www.bp.com/liveassets/bp_internet/aviation/air_bp/STAGING/local_assets/downloads_pdfs/a/air_bp_products_handbook_04004_1.pdf . 2011-06-08 . 11–13 .
  24. Román-Leshkov. Yuriy. Barrett. Christopher J.. Liu. Zhen Y.. Dumesic. James A.. Production of dimethylfuran for liquid fuels from biomass-derived carbohydrates. Nature. 21 June 2007. 447. 7147. 982–985. 10.1038/nature05923. 17581580. 2007Natur.447..982R. 4366510.
  25. Wiener. Harry. January 1947. Structural Determination of Paraffin Boiling Points. Journal of the American Chemical Society. 69. 1. 17–20. 10.1021/ja01193a005. 20291038. 0002-7863.
  26. Web site: The Energy Cost of Electric and Human-Powered Bicycles. Justin Lemire-Elmore. 2004-04-13. 5. 2009-02-26. properly trained athlete will have efficiencies of 22 to 26%.
  27. Web site: Silicon as an intermediary between renewable energy and hydrogen . Deutsche Bank Research . 16 November 2016. 5. https://web.archive.org/web/20081116161500/https://www.dbresearch.com/PROD/DBR_INTERNET_EN-PROD/PROD0000000000079095.pdf . 2008-11-16 .
  28. Web site: Bossel. Ulf. July 2003. The Physics of the Hydrogen Economy. dead. https://web.archive.org/web/20060319173951/https://www.efcf.com/reports/E05.pdf. 2006-03-19. 2019-04-06. European Fuel Cell News. 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..
  29. Web site: 2013-11-18. Dimethyl Ether (DME). 2019-04-06. European Biofuels Technology Platform. DME density and lower heating value were obtained from the table on the first page.
  30. Book: Green Don . Perry Robert . Perry's chemical engineers' handbook . 2008 . McGraw-Hill . New York . 9780071422949 . 8th.
  31. Web site: Elite_bloc.indd. https://web.archive.org/web/20110715061924/http://www.payne-worldwide.com/documents/cms/Elite_bloc_msds.pdf. dead. 2011-07-15. 2010-05-07.
  32. Web site: Biomass Energy Foundation: Fuel Densities. https://web.archive.org/web/20100110042311/http://www.woodgas.com/fuel_densities.htm. 2010-01-10. 2010-05-07. Woodgas.com.
  33. Web site: Bord na Mona, Peat for Energy. https://web.archive.org/web/20071119083231/http://www.bnm.ie/files/20061124040716_peat_for_energy.pdf. 2007-11-19. 2012-01-25. Bnm.ie.
  34. Web site: The Energy Cost of Electric and Human-Powered Bicycle. Justin Lemire-elmore. April 13, 2004. 2012-01-25.
  35. Web site: energy buffers . Home.hccnet.nl . 2010-05-07.
  36. Anne Wignall and Terry Wales. Chemistry 12 Workbook, page 138 . Pearson Education NZ
  37. David E. Dirkse. energy buffers. "household waste 8..11 MJ/kg"
  38. Book: Lu. Gui-e. Chang. Wen-ping. Jiang. Jin-yong. Du. Shi-guo. 2011 International Conference on Materials for Renewable Energy & Environment . Study on the energy density of gunpowder heat source . 1185–1187. May 2011. 10.1109/ICMREE.2011.5930549. IEEE. 978-1-61284-749-8. 36130191.
  39. Web site: Technical bulletin on Zinc-air batteries. https://web.archive.org/web/20090127030703/http://www.duracell.com/oem/primary/Zinc/zinc_air_tech.asp. 2009-01-27. 2009-04-21. Duracell.
  40. Mitchell. Robert R.. Gallant. Betar M.. Thompson. Carl V.. Shao-Horn. Yang. Yang Shao-Horn. 2011. All-carbon-nanofiber electrodes for high-energy rechargeable Li–O2 batteries. Energy & Environmental Science. 4. 8. 2952–2958. 10.1039/C1EE01496J. 96799565.
  41. Web site: Amprius' silicon nanowire Li-ion batteries power Airbus Zephyr S HAPS solar aircraft . 2022-12-31 . Green Car Congress.
  42. Web site: Test of Duracell Ultra Power AA. lygte-info.dk. 2019-02-16.
  43. Web site: Energizer EN91 AA alkaline battery datasheet. 2016-01-10.
  44. Web site: Test of GP ReCyko+ AA 2700mAh (Green). lygte-info.dk. 2019-02-16.
  45. Web site: Maxwell supercapacitor comparison . 2016-01-10 . 2016-03-04 . https://web.archive.org/web/20160304135107/http://www.maxwell.com/images/documents/Product_Comparison_Matrix_3000489_2.pdf . dead .
  46. Web site: Nesscap ESHSP series supercapacitor datasheet . 2016-01-10 . https://web.archive.org/web/20160329001412/http://www.nesscap.com/common/download.jsp?dir=product&sfn=MSCWSMXHBBOMXOZ.pdf . 2016-03-29 . dead.
  47. Web site: Cooper PowerStor XL60 series supercapacitor datasheet . 2016-01-10 . 2016-04-02 . https://web.archive.org/web/20160402213806/http://www.cooperindustries.com/content/dam/public/bussmann/Electronics/Resources/product-datasheets/bus-elx-ds-10339-xl.pdf . dead .
  48. Web site: Kemet S301 series supercapacitor datasheet . 2016-01-10 . dead . https://web.archive.org/web/20160304092326/http://www.kemet.com/Lists/ProductCatalog/Attachments/504/KEM_S6001_S301.pdf . 2016-03-04.
  49. Web site: Nichicon JJD series supercapatcitor datasheet . 2016-01-10 .
  50. Web site: skelcap High Energy Ultracapacitor . Skeleton Technologies. 13 October 2015. https://web.archive.org/web/20160402220331/http://skeletontech.com/datasheets/skelcap-energy-en.pdf. 2 April 2016. dead.
  51. Web site: 3.0V 3400F Ultracapacitor cell datasheet BCAP3400 P300 K04/05. 2020-01-12. 2020-11-01. https://web.archive.org/web/20201101025040/https://www.maxwell.com/images/documents/3V_3400F_datasheet.pdf. dead.
  52. Web site: Vishay STE series tantalum capacitors datasheet. 2016-01-10.
  53. Web site: nichicon TVX aluminum electrolytic capacitors datasheet. 2016-01-10.
  54. Web site: nichicon LGU aluminum electrolytic capacitors datasheet. 2016-01-10.
  55. Web site: Battery Energy Tables. https://web.archive.org/web/20111204090808/http://www.allaboutbatteries.com/Energy-tables.html. 2011-12-04. dead.
  56. Web site: 18650 Battery capacities.
  57. Calculated from fractional mass loss times c squared.
  58. Calculated from fractional mass loss times c squared. Maximizing specific energy by breeding deuterium. Justin . Ball. Nuclear Fusion. 2019. 59. 10 . 106043. 10.1088/1741-4326/ab394c. 1908.00834 . 2019NucFu..59j6043B . 199405246 .
  59. Web site: Computing the energy density of nuclear fuel . whatisnuclear.com . 2014-04-17.
  60. How Much Energy Can You Store in a Rubber Band?. Wired. 2020-01-21. en. 1059-1028.
  61. Web site: MatWeb - The Online Materials Information Resource. www.matweb.com. 2019-12-15.
  62. Web site: Acetal. PubChem. pubchem.ncbi.nlm.nih.gov. en. 2019-12-12.
  63. Web site: C17200 Alloy Specifications E. Jordan Brookes Company. www.ejbmetals.com. 2019-12-15.
  64. Web site: polycarbonate information and properties. www.polymerprocessing.com. 2019-12-12.
  65. Web site: Young's Modulus - Tensile and Yield Strength for common Materials. www.engineeringtoolbox.com. 2019-12-12.
  66. Web site: Elastic Resilience. Brush Wellman Alloy Products. Technical Tidbits. December 15, 2019.
  67. Web site: ASM Material Data Sheet. asm.matweb.com. 2019-12-15.
  68. Web site: Density of steel. Karen. Sutherland. 2004. Monica. Martin. The Physics Factbook. Elert. Glenn. 2020-06-18.
  69. Web site: Aluminum 6061-T6; 6061-T651. 2021-06-13. www.matweb.com.
  70. Web site: Wood Species - Moisture Content and Weight. www.engineeringtoolbox.com. 2019-12-12.
  71. Web site: AISI 1018 Mild/Low Carbon Steel. 2012-06-28. AZoM.com. en. 2020-01-22.
  72. Web site: ASM Material Data Sheet. asm.matweb.com. 2019-12-12.
  73. Web site: American Eastern White Pine Wood. www.matweb.com. 2019-12-15.
  74. Web site: Mass, Weight, Density or Specific Gravity of Different Metals. www.simetric.co.uk. 2019-12-12.
  75. Web site: Physical properties of glass Saint Gobain Building Glass UK. uk.saint-gobain-building-glass.com. 2019-12-12.
  76. Meroueh . Laureen . Chen . Gang . 2020 . Thermal energy storage radiatively coupled to a supercritical Rankine cycle for electric grid support . Renewable Energy . 145 . 604–621 . 10.1016/j.renene.2019.06.036 . 197448761.
  77. A. Fopah-Lele, J. G. Tamba "A review on the use of as a potential material for low temperature energy storage systems and building applications", Solar Energy Materials and Solar Cells 164 175-84 (2017).
  78. 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.
  79. Web site: Hydroelectric Power Generation. www.mpoweruk.com. Woodbank Communications Ltd. 13 April 2018.
  80. Web site: 2.1 Power, discharge, head relationship River Engineering & Restoration at OSU Oregon State University. rivers.bee.oregonstate.edu. en. 13 April 2018. Let ε = 0.85, signifying an 85% efficiency rating, typical of an older powerplant.. 14 April 2018. https://web.archive.org/web/20180414010317/http://rivers.bee.oregonstate.edu/elevation-discharge-power-relationship. dead.
  81. Thomas C. Allison. (2013). NIST-JANAF Thermochemical Tables - SRD 13 (1.0.2) [dataset]. National Institute of Standards and Technology. https://doi.org/10.18434/T42S31|-|Iron|6.7|52.2|1858.3|14487.2|burned to Iron(II,III) oxide|-| Zinc| 5.3| 38.0| 1,472.2| 10,555.6||-| 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| data-sort-value="8" | 4.7–11.3[38] | data-sort-value="9.4" | 5.9–12.9|| data-sort-value="2600" | 1,600–3,580||-| TNT| 4.184| 6.92| data-sort-value="1162" | 1,162| data-sort-value="1920" | 1,920||-| Barium| 3.99| 14.0| data-sort-value="1110" | 1,110| data-sort-value="3890" | 3,890| burned to barium dioxide|-| ANFO| 3.7|| 1,027.8|||}

    Electrochemical reactions (batteries)

    Specific energy
    (MJ/kg)! data-sort-type="number"
    Energy density
    (MJ/L)    		data-sort-type="number" Specific energy
    (W⋅h/kg)    		data-sort-type="number" Energy density
    (W⋅h/L)    		Comment
    Zinc-air battery1.59[39] 6.02441.71,672.2Controlled electric discharge
    Lithium air battery (rechargeable)9.0[40] 2,500.0Controlled electric discharge
    Sodium sulfur batterydata-sort-value="0.54" 0.54–0.86150–240
    Lithium metal battery1.84.325001,200Controlled electric discharge
    Lithium-ion batterydata-sort-value="0.36" 0.36–0.875data-sort-value="0.9" 0.9–2.63data-sort-value="100.00" 100.00–243.06data-sort-value="250.00" 250.00–730.56Controlled electric discharge
    Lithium-ion battery with silicon nanowire anodes1.5664.32data-sort-value="435" 435[41] data-sort-value="1200" 1,200Controlled electric discharge
    Alkaline batterydata-sort-value="0.5" 0.48[42] data-sort-value="1.3" 1.3[43] Controlled electric discharge
    Nickel-metal hydride battery0.41[44] data-sort-value="0.504" 0.504–1.46Controlled electric discharge
    Lead-acid battery0.170.5647.2156Controlled electric discharge
    Supercapacitor (EDLC)data-sort-value="0.01" 0.01–0.030[45] [46] [47] [48] [49] [50] [51] data-sort-value="0.05" 0.006–0.06data-sort-value="8.75" up to 8.57Controlled electric discharge
    Electrolytic capacitordata-sort-value="0.00001" 0.00001–0.0002[52] data-sort-value="0.00001" 0.00001–0.001[53] [54] Controlled electric discharge

    Common battery formats

    Battery energy capacities
    Storage devicedata-sort-type="number" Energy content
    (Joule)    		Energy content
    (W⋅h)    		Energy typedata-sort-type="number" Typical
    mass (g)    		Typical dimensions
    (diameter × height in mm)    		data-sort-type="number" Typical volume (mL)data-sort-type="number" Energy density
    by volume (MJ/L)    		data-sort-type="number" Energy density
    by mass (MJ/kg)
    Alkaline AA battery[55] data-sort-value="9360" 9,3602.6Electrochemical2414.2 × 507.921.180.39
    Alkaline C batterydata-sort-value="34416" 34,4169.5Electrochemical6526 × 4624.421.410.53
    NiMH AA batterydata-sort-value="9072" 9,0722.5Electrochemical2614.2 × 507.921.150.35
    NiMH C batterydata-sort-value="19440" 19,4405.4Electrochemical8226 × 4624.420.800.24
    Lithium-ion 18650 batterydata-sort-value="28800" 28,800–46,8008–13Electrochemicaldata-sort-value="44" 44–49[56] 18 × 6516.541.74–2.830.59–1.06

    Nuclear reactions

    Specific energy
    (MJ/kg)! data-sort-type="number"
    Energy density
    (MJ/L)    		data-sort-type="number" Specific energy
    (W⋅h/kg)    		data-sort-type="number" Energy density
    (W⋅h/L)    		Comment
    Antimatter89,875,517,874 ≈ 90 PJ/kgDepends on the density of the antimatter's form24,965,421,631,578 ≈ 25 TW⋅h/kgDepends on the density of the antimatter's formAnnihilation, counting both the consumed antimatter mass and ordinary matter mass
    Hydrogen (fusion)data-sort-value="639,780,320"639,780,320[57] but at least 2% of this is lost to neutrinos.Depends on conditionsdata-sort-value="177,716,755,600"177,716,755,600Depends on conditionsReaction 4H→4He
    Deuterium (fusion)
    		data-sort-value="571,182,758" 571,182,758[58] Depends on conditionsdata-sort-value="158,661,876,600" 158,661,876,600Depends on conditionsProposed 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)data-sort-value="337,387,388"337,387,388Depends on conditionsdata-sort-value="93,718,718,800"93,718,718,800Depends on conditionsD + T → 4He + n
    Being developed.
    Lithium-6 deuteride (fusion)data-sort-value="268,848,415"268,848,415Depends on conditionsdata-sort-value="74,680,115,100"74,680,115,100Depends on conditionsLiD → 24He
    Used in weapons.
    Plutonium-23983,610,000data-sort-value="1660494600" 1,300,000,000–1,700,000,000 (Depends on crystallographic phase)23,222,915,000data-sort-value="461248500000" 370,000,000,000–460,000,000,000 (Depends on crystallographic phase)Heat produced in Fission reactor
    Plutonium-23931,000,000data-sort-value="615660000" 490,000,000–620,000,000 (Depends on crystallographic phase)8,700,000,000data-sort-value="171016670000" 140,000,000,000–170,000,000,000 (Depends on crystallographic phase)Electricity produced in Fission reactor
    Uraniumdata-sort-value="80,620,000" 80,620,000data-sort-value="1,539,842,000" 1,539,842,00022,394,000,000Heat produced in breeder reactor
    Thoriumdata-sort-value="79,420,000" 79,420,000[59] data-sort-value="929,214,000" 929,214,00022,061,000,000Heat produced in breeder reactor (Experimental)
    Plutonium-2382,239,00043,277,631621,900,000Radioisotope thermoelectric generator. The heat is only produced at a rate of 0.57 W/g.

    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 band1,651–6,605[60] 2,200–8,9001.35
    Steel, ASTM A228 (yield, 1 mm diameter)1,440–1,77011,200–13,8007.80[61] 2102,170–2,410
    Acetals9087540.831[62] 2.865 (ultimate)
    Nylon-6233–1,870253–2,0301.0842–445–90 (ultimate)
    Copper Beryllium 25-1/2 HT (yield)6845,7208.36[63] 1311,224
    Polycarbonates433–615520–7401.2[64] 2.652–62 (ultimate)
    ABS plastics241–534258–5711.071.4–3.1[65] 40 (ultimate)
    Acrylic1,5303.270 (ultimate)
    Aluminium 7077-T8 (yield)3991,120[66] 2.81[67] 71.0400
    Steel, stainless, 301-H (yield)3012,4108.0[68] 193965
    Aluminium 6061-T6 (yield @ 24 °C)2055532.70[69] 68.9276
    Epoxy resins113–1,8102–326–85 (ultimate)
    Douglas fir Wood158–20096.481–.609[70] 1350 (compression)
    Steel, Mild AISI 101842.43347.87[71] 205370 (440 Ultimate)
    Aluminium (not alloyed)32.587.72.70[72] 69110 (ultimate)
    Pine (American Eastern White, flexural)31.8–32.811.1–11.5.350[73] 8.30–8.56 (flexural)41.4 (flexural)
    Brass28.6–36.5250–3068.4–8.73[74] 102–125250 (ultimate)
    Copper23.12078.93117220 (ultimate)
    Glass5.56–10.013.9–25.02.5[75] 50–9050 (compression)

    Other release mechanisms

    Specific energy
    (MJ/kg)! data-sort-type="number"
    Energy density
    (MJ/L)    		data-sort-type="number" Specific energy
    (W⋅h/kg)    		data-sort-type="number" Energy density
    (W⋅h/L)    		Comment
    Silicon (phase change)data-sort-value="1.79" 1.790data-sort-value="4.5" 4.5data-sort-value="500" 500data-sort-value="1285" 1,285Energy stored through solid to liquid phase change of silicon[76]
    Strontium bromide hydratedata-sort-value="0.814" 0.814 [77] 1.93628Thermal energy of phase change at
    Liquid nitrogendata-sort-value="0.77" 0.77[78] 0.62213.9172.2Maximum reversible work at 77.4 K with 300 K reservoir
    Compressed air at 30MPa0.50.2138.955.6Potential energy
    Latent heat of fusion of ice (thermal)0.3340.33493.193.1
    Flywheeldata-sort-value="0.36" 0.36–0.55.3Kinetic energy
    Water at 100 m dam height0.0009810.0009780.2720.272Figures represent potential energy, but efficiency of conversion to electricity is 85–90%[79] [80]

    See also

    Further reading

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

    External links

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