# Energy density

Energy density
SI unit J/m3
In SI base units kg·m−1s−2
Derivations from
other quantities
U = E/V

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.[1] 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.

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 density

There are many 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 are used by 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. Electrochemical reactions are used by most mobile devices such as laptop computers and mobile phones to release the energy from batteries.

### Energy densities of common energy storage materials

The following is a list of the thermal energy densities (that is to say: the amount of heat energy that can be extracted) of commonly used or well-known energy storage materials; it doesn't include uncommon or experimental materials. Note that this list does not consider the mass of reactants commonly available such as the oxygen required for combustion or the energy efficiency in use. An extended version of this table is found at Energy density#Extended Reference Table.

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

Storage material Energy type Specific energy
(MJ/kg)
Energy density
(MJ/L)
Uses
Deuterium (in Fusion reactor) Nuclear fusion 87,900,000[2] 3,930,000 Experimental
Uranium (in breeder) Nuclear fission 80,620,000[3] 1,539,842,000 Electric power plants
Thorium (in breeder) Nuclear fission 79,420,000[3] 929,214,000 Experimental
Plutonium 238 Nuclear decay 2,239,000 43,277,631 RTGs
Tritium Nuclear decay 583,529 Experimental
Hydrogen (compressed at 700 bar) Chemical 142 9.17 Rocket engines
Methane or Liquefied natural gas(compressed) Chemical 55.5 22.2 Cooking, home heating, electric power plants
Diesel Chemical 48 35.8 Automotive engines, electric power plants
LPG (including Propane / Butane) Chemical 46.4 26 Cooking, home heating, automotive engines, lighter fluid
Gasoline (petrol) Chemical 46.4 34.2 Automotive engines, electric power plants
Jet fuel (Kerosene) Chemical 42.8[4] 37.4 Aircraft engines
Fat (animal/vegetable) Chemical 37 34 Human and animal nutrition
Coal (anthracite or bituminous) Chemical ~30 ~38 Electric power plants, home heating
Methanol Chemical 19.7 15.6 Fuel engines
Carbohydrates (including sugars) Chemical 17 Human and animal nutrition
Protein Chemical 16.8 Human and animal nutrition
Wood Chemical 16.2[5] 13 Home heating, cooking
Gunpowder Chemical 4.7–11.3[6] Explosives, Ammunition
TNT Chemical 4.610 6.92 Explosives
Lithium metal battery (Li-Po, Li-Hv) Electrochemical 1.8 4.32 Portable electronic devices, flashlights, RC vehicles
Lithium-ion battery Electrochemical 0.36–0.875[9] 0.9–2.63 Automotive motors, portable electronic devices, flashlights
Flywheel Mechanical 0.36–0.5 Power plants, Gyrobusses
Alkaline battery Electrochemical 0.5[10] 1.3[10] Portable electronic devices, flashlights
Nickel-metal hydride battery Electrochemical 0.288 0.504–1.08 Portable electronic devices, flashlights
Lead-acid battery Electrochemical 0.17 0.56 Automotive engine ignition
Supercapacitor (EDLC) Electrical (electrostatic) 0.01–0.036[17] 0.05–0.06[18] Electronic circuits
Electrolytic capacitor Electrical (electrostatic) 0.00001–0.0002[19] 0.00001–0.001[22] Electronic circuits

Energy capacities of common storage forms
Storage device Energy content
(Joule)
Energy type Typical mass
(g)
Typical volume
(width × height × depth in mm)
Alkaline AA battery[23] 9360 Electrochemical 24 14.2 × 50
Alkaline C battery[23] 34,416 Electrochemical 65 26 × 46
NiMH AA battery 9072 Electrochemical 26 14.2 × 50
NiMH C battery 19,440 Electrochemical 82 26 × 46
Lithium-ion 18650 battery 28,800–46,800 Electrochemical 44–49[24] 18 × 65
Potato Chip 41,900[25] Chemical 1.89 60 × 40 × 1
Ham and Cheese Sandwich[26] 1,470,000 Chemical 145 100 × 100 × 28

## Energy density in energy storage and in fuel

Selected energy densities plot[27][28][29][30][31][32][33][34]

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.

### Nuclear energy sources

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%),[citation needed] 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 (2016), 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,[35] 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.[36] Coal, gas, and petroleum are the current primary energy sources in the U.S.[37] but have a much lower energy density. Burning local biomass fuels supplies household energy needs (cooking fires, oil lamps, etc.) worldwide.

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.

Alternative options are discussed for energy storage to increase energy density and decrease charging time.[38][39][40][41]

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

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

## Energy density of electric and magnetic fields

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

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

where E is the electric field and B is the magnetic field. The solution will be (in 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

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

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

## Footnotes

1. ^ "The Two Classes of SI Units and the SI Prefixes". NIST Guide to the SI. Retrieved 2012-01-25.
2. ^ J. D. Huba. "NRL Plasma Formulary (revised 2016)" (PDF). Naval Research Laboratory. p. 44. Retrieved 2017-05-16.
3. ^ a b "Computing the energy density of nuclear fuel". whatisnuclear.com. Retrieved 2014-04-17.
4. ^ http://www.exxonmobilaviation.com/AviationGlobal/Files/WorldJetFuelSpec2008.pdf
5. ^ Wilfred Weihe "Electric Fireplace Costs Secrets"
6. ^ 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.
7. ^ "Overview of lithium ion batteries" (PDF). Panasonic. Jan 2007. Archived (PDF) from the original on November 7, 2011.
8. ^ "Panasonic NCR18650B" (PDF). Archived from the original (PDF) on 2015-07-22.
9. ^
10. ^ a b "Energizer EN91 AA alkaline battery datasheet" (PDF). Retrieved 2016-01-10.
11. ^ a b "Maxwell supercapacitor comparison" (PDF). Retrieved 2016-01-10.
12. ^ a b "Nesscap ESHSP series supercapacitor datasheet" (PDF). Retrieved 2016-01-10.
13. ^ a b "Cooper PowerStor XL60 series supercapacitor datasheet" (PDF). Retrieved 2016-01-10.
14. ^ a b "Kemet S301 series supercapacitor datasheet" (PDF). Archived from the original (PDF) on 2016-03-04. Retrieved 2016-01-10.
15. ^ a b "Nichicon JJD series supercapatcitor datasheet" (PDF). Retrieved 2016-01-10.
16. ^ a b "skelcap High Energy Ultracapacitor" (PDF). Skeleton Technologies. Retrieved 13 October 2015.
17. ^
18. ^
19. ^ a b "Vishay STE series tantalum capacitors datasheet" (PDF). Retrieved 2016-01-10.
20. ^ "nichicon TVX aluminum electrolytic capacitors datasheet" (PDF). Retrieved 2016-01-10.
21. ^ "nichicon LGU aluminum electrolytic capacitors datasheet" (PDF). Retrieved 2016-01-10.
22. ^
23. ^ a b
24. ^
25. ^ "Calories in Lay's Classic Potato Chips". CalorieKing. Retrieved 4 March 2017.
26. ^ "Calories in Ham And Cheese Sandwich". Retrieved 22 May 2014.
27. ^ "Green Power Lacks the Energy Density to Run Our Civilization, LENR Might Provide It." LENR & Cold Fusion News. N.p., 24 July 2014. Web.
28. ^ 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.
29. ^ "Panasonic Develops New Higher-Capacity 18650 Li-Ion Cells." Green Car Congress. N.p., 25 Dec. 2009. Web.
30. ^ Stura, Enrico, and Claudio Nicolini. "New nanomaterials for light weight lithium batteries." Analytica chimica acta 568.1 (2006): 57-64.
31. ^ "Energy Density of Coal - Hypertextbook." The Energy Density of Coal. N.p., 2003. Web.
32. ^ "Heat Values of Various Fuels - World Nuclear Association." World Nuclear Association. N.p., Sept. 2016. Web.
33. ^ "Overview of Storage Development DOE Hydrogen Program." Office of Energy Efficiency & Renewable Energy. N.p., May 2000. Web.
34. ^ Wong, Kaufui Vincent and Dia, Sarah, “Nanotechnology in Batteries.” ASME J. Energy Resour. Technol. 2016.
35. ^ "Supply of Uranium". world-nuclear.org. 2014-10-08. Retrieved 2015-06-13.
36. ^ "Facts from Cohen". Formal.stanford.edu. 2007-01-26. Retrieved 2010-05-07.
37. ^ "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.
38. ^ Ionescu-Zanetti, C.; et., al. (2005). "Nanogap capacitors: Sensitivity to sample permittivity changes". 99 (2). Bibcode:2006JAP....99b4305I. doi:10.1063/1.2161818.
39. ^ Naoi, K.; et., al. (2013). "New generation "nanohybrid supercapacitor"". Accounts of Chemical Research. doi:10.1021/ar200308h.
40. ^ Hubler, A.; Osuagwu, O. (2010). "Digital quantum batteries: Energy and information storage in nanovacuum tube arrays". Complexity. 15 (5). doi:10.1002/cplx.20306.
41. ^ 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.