Energy density is the amount of energy stored in a given system or region of space per unit volume. Colloquially it may also be used for energy per unit mass, though the accurate term for this is specific energy. Often only the useful or extractable energy is measured, which is to say that inaccessible energy (such as rest mass energy) is ignored. 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 the pressures described in the next paragraph.
|In SI base units||kg·m−1s−2|
|U = E/V|
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 the potential to perform work on the surroundings by converting enthalpy to work until equilibrium is reached.
Introduction to energy densityEdit
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 animals to derive energy from food, and by automobiles to derive energy from gasoline. Liquid hydrocarbons (fuels such as gasoline, diesel and kerozene) are today the most dense way known to economically store and transport chemical energy at a very 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 the energy from batteries.
Types of energy contentEdit
There are several different types of energy content. One is the theoretical total amount of thermodynamic work that can be derived from a system, with a given temperature and pressure for the surroundings. This is called exergy. Another is the theoretical amount of work that can be derived from reactants that are initially 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..
Energy density in energy storage and in fuelEdit
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.
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 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.
- 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.
Table of energy contentEdit
This article or section appears to contradict itself.April 2019)(
Unless otherwise stated, the values in the following table are supposed to be lower heating values. The following unit conversions may be helpful when considering the data in the table: 3.6 MJ = 1 kWh ≈ 1.34 HPh.
|Storage type||Specific energy
|Uses and comments|
|Antimatter||89,875,517,874||Depends on the density of the antimatter's form||24,965,421,631,578||Depends on the density of the antimatter's form|
|Deuterium (in Fusion reactor)
|Plutonium-239||83,610,000 (thermal energy)
31,000,000 (electrical energy)
|Depends on crystallographic phase||23,222,915,000 (thermal energy)
8,700,000,000 (electrical energy)
|Depends on crystallographic phase|
|Uranium (in breeder)||80,620,000||1,539,842,000||Electric power plants (Nuclear fission)|
|Thorium (in breeder)||79,420,000||929,214,000||Experimental (Nuclear fission)|
|Hydrogen, liquid||141.86 (HHV)
|Rocket engines, Fuel Cells, H2 Storage/Transport.|
Energy figures apply after reheating to 60°F
|Hydrogen, at 690 bar and 60°F||141.86 (HHV)
|Fuel Cells, Natural Gas Heating Supplement|
|Hydrogen, gas, 1 atm, 60°F||141.86 (HHV)
|Methane (1.013 bar, 15 °C)||55.6||0.0378||15,444.5||10.5|
|LNG (NG at −160 °C)||53.6||22.2||14,888.9||6,166.7|
|CNG (NG compressed to 250 bar/~3,600 psi)||53.6||9||14,888.9||2,500.0|
|Crude oil (according to the definition of tonne of oil equivalent)||41.868||37||11,630||10,278|
|Residential heating oil||46.2||37.3||12,833.3||10,361.1|
|Jet fuel||43||35||Aircraft engines|
|Gasohol E10 (10% ethanol 90% gasoline by volume)||43.54||33.18||12,094.5||9,216.7|
|Biodiesel oil (vegetable oil)||42.20||33||11,722.2||9,166.7|
|Clean Diesel fuel|
|DMF (2,5-dimethylfuran)[clarification needed]||42||37.8||11,666.7||10,500.0|
|Body fat metabolism||38||35||10,555.6||9,722.2||Efficiency 22%|
|Gasohol E85 (85% ethanol 15% gasoline by volume)||33.1||25.65||9,194.5||7,125.0|
|Coal, anthracite||26–33||34–43||7,222.2–9,166.7||9,444.5–11,944.5||Efficiency of conversion to electricity ~36%|
|PET plastic||23.5 (impure)||6,527.8|
|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|
|PVC plastic (improper combustion toxic)[clarification needed]||18.0||25.2||5,000.0||7,000.0|
|Sugars, carbohydrates, and protein metabolism||17||26.2 (dextrose)||4,722.2||7,277.8||Efficiency 22%|
|Dry cow dung and camel dung||15.5||4,305.6|
|Coal, lignite||10–20||2,777.8–5,555.6|
|Sodium (burned to wet sodium hydroxide)||13.3||12.8||3,694.5||3,555.6|
|Sulfur (burned to sulfur dioxide)||9.23||19.11||2,563.9||5,308.3|
|Sodium (burned to dry sodium oxide)||9.1||8.8||2,527.8||2,444.5|
|Battery, lithium-air rechargeable||9.0||2,500.0|
|Iron (burned to iron(III) oxide)||5.2||40.68||1,444.5||11,300.0|
|Teflon plastic (combustion toxic, but flame retardant)||5.1||11.2||1,416.7||3,111.1|
|Iron (burned to iron(II) oxide)||4.9||38.2||1,361.1||10,611.1|
|Liquid nitrogen[clarification needed]||0.77||0.62||213.9||172.2|
|Compressed air at 300 bar (potential energy)||0.5||0.2||138.9||55.6|
|Latent heat of fusion of ice (thermal)||0.335||0.335||93.1||93.1|
|Water at 100 m dam height (potential energy)||0.001||0.001||0.278||0.278||Practical efficiency 85–90%|
|Lithium metal battery||1.8||4.32||Portable electronic devices|
|Lithium-ion battery||0.36–0.875||0.9–2.63||Automotive motors, portable electronic devices, RC vehicles|
|Flywheel||0.36–0.5||5.3||Power plants, Gyrobusses|
|Alkaline battery||0.48||1.3||Portable electronic devices, flashlights|
|Nickel-metal hydride battery||0.41||0.504–1.46||Portable electronic devices, flashlights|
|Lead-acid battery||0.17||0.56||Automotive engine ignition|
|Supercapacitor (EDLC)||0.01–0.036||0.05–0.06||Electronic circuits|
|Electrolytic capacitor||0.00001–0.0002||0.00001–0.001||Electronic circuits|
|Storage type||Energy density by mass (MJ/kg)||Energy density by volume (MJ/L)||Specific energy (Wh/kg)||Energy density (Wh/L)||Uses and comments|
Table on energy content of batteries:
|Storage device||Energy content
(diameter × height in mm)
|Typical volume in L||Energy density
by volume (MJ/L)
by mass (MJ/kg)
|Alkaline AA battery||9,360||Electrochemical||24||14.2 × 50||0,0022||0,45||0,39|
|Alkaline C battery||34,416||Electrochemical||65||26 × 46||0,0036||0,956||0,53|
|NiMH AA battery||9,072||Electrochemical||26||14.2 × 50||0,0027||0,346||0,35|
|NiMH C battery||19,440||Electrochemical||82||26 × 46||0,0038||0,512||0,24|
|Lithium-ion 18650 battery||28,800–46,800||Electrochemical||44–49||18 × 65||0,0037||0,778-1,27||0,59-1,06|
Nuclear energy sourcesEdit
The greatest energy source by far is mass 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 (2018), 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, though the full potential of this source can only be realised through breeder reactors, which are, apart from the BN-600 reactor, 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.
Thermal power of nuclear fission reactorsEdit
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 fieldsEdit
where E is the electric field and B is the magnetic field. 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 normal (linear and nondispersive) substances, the energy density (in SI units) is
In the case of absence of magnetic fields, by exploting Fröhlich's relationships it is also possible to extend these equations to anisotropy and nonlinearity dielectrics, as well as to calculate the correlated Helmholtz free energy and entropy densities.
- "The Two Classes of SI Units and the SI Prefixes". NIST Guide to the SI. Retrieved 2012-01-25.
- "Fossil and Alternative Fuels - Energy Content (2008)". Engineering ToolBox. Retrieved 2018-10-08.
- "Green Power Lacks the Energy Density to Run Our Civilization, LENR Might Provide It." LENR & Cold Fusion News. N.p., 24 July 2014. Web.
- Jeong, Goojin, et al. "Nanotechnology enabled rechargeable Li–SO 2 batteries: another approach towards post-lithium-ion battery systems." Energy & Environmental Science 8.11 (2015): 3173-3180.
- "Panasonic Develops New Higher-Capacity 18650 Li-Ion Cells." Green Car Congress. N.p., 25 Dec. 2009. Web.
- Stura, Enrico, and Claudio Nicolini. "New nanomaterials for light weight lithium batteries." Analytica chimica acta 568.1 (2006): 57-64.
- "Energy Density of Coal - Hypertextbook." The Energy Density of Coal. N.p., 2003. Web.
- "Heat Values of Various Fuels - World Nuclear Association." World Nuclear Association. N.p., Sept. 2016. Web.
- "Overview of Storage Development DOE Hydrogen Program." Office of Energy Efficiency & Renewable Energy. N.p., May 2000. Web.
- Wong, Kaufui Vincent and Dia, Sarah, “Nanotechnology in Batteries.” ASME J. Energy Resour. Technol. 2016.
- Ionescu-Zanetti, C.; et., al. (2005). "Nanogap capacitors: Sensitivity to sample permittivity changes". 99 (2). Bibcode:2006JAP....99b4305I. doi:10.1063/1.2161818.
- Naoi, K.; et., al. (2013). "New generation "nanohybrid supercapacitor"". Accounts of Chemical Research. doi:10.1021/ar200308h.
- Hubler, A.; Osuagwu, O. (2010). "Digital quantum batteries: Energy and information storage in nanovacuum tube arrays". Complexity. 15 (5). doi:10.1002/cplx.20306.
- 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). doi:10.1109/TDEI.2013.6571470.
- J. D. Huba. "NRL Plasma Formulary (revised 2016)" (PDF). Naval Research Laboratory. p. 44. Retrieved 2017-05-16.
- "Characteristics of Tritium" (PDF). springer.com. Retrieved 2018-09-17.
- "Computing the energy density of nuclear fuel". whatisnuclear.com. Retrieved 2014-04-17.
- College of the Desert, “Module 1, Hydrogen Properties”, Revision 0, December 2001 Hydrogen Properties. Retrieved 2014-06-08.
- Greenwood, Norman N.; Earnshaw, Alan (1997), Chemistry of the Elements (2nd ed) (page 164)
- "Boron: A Better Energy Carrier than Hydrogen? (28 February 2009)". Eagle.ca. Retrieved 2010-05-07.
- Envestra Limited. Natural Gas Archived 2008-10-10 at the Wayback Machine. Retrieved 2008-10-05.
- IOR Energy. List of common conversion factors (Engineering conversion factors). Retrieved 2008-10-05.
- Paul A. Kittle, Ph.D. "ALTERNATE DAILY COVER MATERIALS AND SUBTITLE D - THE SELECTION TECHNIQUE" (PDF). Retrieved 2012-01-25.
- "537.PDF" (PDF). June 1993. Retrieved 2012-01-25.
- "Energy Density of Aviation Fuel". Hypertextbook.com. Retrieved 2010-05-07.
- "Handbook of Products" (PDF). Air BP. pp. 11–13. Archived from the original (PDF) on 2011-06-08.
- 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
- 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.
- "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.
- 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. Retrieved 13 April 2018.
- 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%
- Fisher, Juliya (2003). "Energy Density of Coal". The Physics Factbook. Retrieved 2006-08-25.
- Silicon as an intermediary between renewable energy and hydrogen
- "Elite_bloc.indd" (PDF). Archived from the original (PDF) on 2011-07-15. Retrieved 2010-05-07.
- "Biomass Energy Foundation: Fuel Densities". Woodgas.com. Archived from the original on 2010-01-10. Retrieved 2010-05-07.
- "Bord na Mona, Peat for Energy" (PDF). Bnm.ie. Archived from the original (PDF) on 2007-11-19. Retrieved 2012-01-25.
- Justin Lemire-Elmor (April 13, 2004). "The Energy Cost of Electric and Human-Powered Bicycle" (PDF). Retrieved 2012-01-25.
- "energy buffers". Home.hccnet.nl. Retrieved 2010-05-07.
- 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
- Mitchell, Robert R.; Betar M. Gallant; Carl V. Thompson; Yang Shao-Horn (2011). "All-carbon-nanofiber electrodes for high-energy rechargeable Li–O2 batteries". Energy & Environmental Science. 4: 2952–2958. doi:10.1039/C1EE01496J.
- David E. Dirkse. energy buffers. "household waste 8..11 MJ/kg"
- 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. doi:10.1109/ICMREE.2011.5930549. Retrieved 13 April 2018.
- "Technical bulletin on Zinc-air batteries". Duracell. Archived from the original on 2009-01-27. Retrieved 2009-04-21.
- 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.
- "Hydroelectric Power Generation". www.mpoweruk.com. Woodbank Communications Ltd. Retrieved 13 April 2018.
- "2.1 Power, discharge, head relationship | 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.
- "Overview of lithium ion batteries" (PDF). Panasonic. Jan 2007. Archived (PDF) from the original on November 7, 2011.
- "Panasonic NCR18650B" (PDF). Archived from the original (PDF) on 2015-07-22.
- "Test of Duracell Ultra Power AA". lygte-info.dk. Retrieved 2019-02-16.
- "Energizer EN91 AA alkaline battery datasheet" (PDF). Retrieved 2016-01-10.
- "Test of GP ReCyko+ AA 2700mAh (Green)". lygte-info.dk. Retrieved 2019-02-16.
- "Maxwell supercapacitor comparison" (PDF). Retrieved 2016-01-10.
- "Nesscap ESHSP series supercapacitor datasheet" (PDF). Retrieved 2016-01-10.
- "Cooper PowerStor XL60 series supercapacitor datasheet" (PDF). Retrieved 2016-01-10.
- "Kemet S301 series supercapacitor datasheet" (PDF). Archived from the original (PDF) on 2016-03-04. Retrieved 2016-01-10.
- "Nichicon JJD series supercapatcitor datasheet" (PDF). Retrieved 2016-01-10.
- "skelcap High Energy Ultracapacitor" (PDF). Skeleton Technologies. Retrieved 13 October 2015.
- "Vishay STE series tantalum capacitors datasheet" (PDF). Retrieved 2016-01-10.
- "nichicon TVX aluminum electrolytic capacitors datasheet" (PDF). Retrieved 2016-01-10.
- "nichicon LGU aluminum electrolytic capacitors datasheet" (PDF). Retrieved 2016-01-10.
- "Battery Energy Tables".
- "18650 Battery capacities".
- "Supply of Uranium". world-nuclear.org. 2014-10-08. Retrieved 2015-06-13.
- "Facts from Cohen". Formal.stanford.edu. 2007-01-26. Retrieved 2010-05-07.
- "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.
- 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.
- 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
- ^ "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 Density of Aviation Fuel – The Physics Factbook". hypertextbook.com. Retrieved 4 November 2018.
- "Energy and Energy Types – Springer" (PDF). Retrieved 4 November 2018.