# Energy density

(Redirected from List of energy densities)
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 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.

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) Specific energy (Wh/kg) Energy density (MJ/L) Energy density (Wh/L)
Deuterium-Helium-3 (in Fusion reactor) Nuclear fusion 88,200,000[2] 24,700,000,000 3,940,000 1,100,000,000
Deuterium (in Fusion reactor) Nuclear fusion 87,900,000[2] 24,600,000,000 3,930,000 1,100,000,000
Deuterium-Tritium (in Fusion reactor) Nuclear fusion 84,800,000[2] 23,700,000,000 3,790,000 1,060,000,000
Uranium (in breeder) Nuclear fission 80,620,000[3] 22,393,817,400 1,539,842,000 427,734,231,076
Thorium (in breeder) Nuclear fission 79,420,000[3] 22,060,493,400 929,214,000 258,115,206,492
Plutonium 238 Nuclear decay 2,239,000 621,927,030  ?
Tritium Nuclear decay 583,529 162,086,850  ?
Hydrogen (compressed at 700 bar) Chemical 142 39,443 5.6 1,555
Methane or natural gas Chemical 55.5 15,416 0.0364 10
Liquefied natural gas (LNG) Chemical 53.6 14,889 22.2 6,167
Diesel / Fuel oil Chemical 48 13,333 35.8 9,944
LPG (including Propane / Butane) Chemical 46.4 12,889 26 7,222
Jet fuel (Kerosene) Chemical 46[citation needed] 12,777 37.4 10,389
Gasoline (petrol) Chemical 46.4 12,889 34.2 9,500
Fat (animal/vegetable) Chemical 37 10,278 34 9,444
Butanol Fuel Chemical 35 9,722
Dimethyl ether (DME) Chemical 28.8[4] 8,000 19.3 5,361
Ethanol fuel (E100) Chemical 26.4 7,333 20.9 5,806
Coal, anthracite Chemical 26-33 7,222 – 9,166 34-43 9,444-11,944
Coal, bituminous Chemical 24-35 6,667 – 9,722 26-49 7,222-13,611
Methanol fuel (M100) Chemical 19.7 5,472 15.6 4,333
Carbohydrates (including sugars) Chemical 17 4,722
Protein Chemical 16.8 4,667
Wood Chemical 16.2[citation needed] 4,500 13 3,611
TNT Chemical 4.6 1,278
Gunpowder Chemical 3[citation needed] 833
Lithium battery (non-rechargeable) Electrochemical 1.8 500 4.32 1,200
Lithium-ion battery Electrochemical 0.36[5]–0.875[6] 100 – 243 0.9–2.63 250-731
Alkaline battery Electrochemical 0.5[7] 139 1.3[7] 361
Nickel-metal hydride battery Electrochemical 0.288 80 0.504–1.08 140-300
Lead-acid battery Electrochemical 0.17 47 0.56 156
Supercapacitor (EDLC) Electrical (electrostatic) 0.01-0.036[8][9][10][11][12][13] 3 – 10 0.05-0.06[8][9][10][11][12][13] 14-17
Supercapacitor (Pseudo) Electrochemical 0.031[14] 9 0.046[14] 13
Electrostatic capacitor Electrical (electrostatic) 0.00001-0.0002[15] 2.7×10−3 – 55.5×10−3 0.00001-0.001[15][16][17] 0.0027-0.277
Energy capacities of common storage forms
Storage device Energy type Rechargeable / Non Rechargeable Energy content

(Joule)

Energy content

(Wh)

Typical mass (g) Specific energy (Joule/kg) Specific energy (Wh/kg) D X L

(diameter x Length in mm)

Alkaline AAA battery[18] Electrochemical Non Rechargeable 5,076 1.41 12 423,000 117.5 10.5 × 44.5
Alkaline AA battery[18] Electrochemical Non Rechargeable 9,360 2.60 24 390,000 108.3 14.2 × 50
Alkaline C battery[18] Electrochemical Non Rechargeable 34,416 9.56 65 529,477 147 26 × 46
Alkaline D battery[18] Electrochemical Non Rechargeable 74,988 20.83 135 555,467 154.3 33 × 58
NiMH AAA battery Electrochemical Rechargeable 3,456 0.96 12 288,000.0 80.0 10.5 × 44.5
NiMH AA battery Electrochemical Rechargeable 9,072 2.52 26 348,923.1 96.9 14.2 × 50
NiMH C battery Electrochemical Rechargeable 19,440 5.4 82 237,073.2 65.9 26 × 46
NiMH D battery Electrochemical Rechargeable 41,040 11.4 170 241,411.8 67.1 33 × 58
Lithium-ion 18650 battery Electrochemical Rechargeable 28,800 – 46,800 8 – 13[19] 44 – 49[19] 654,545.5 – 955,102 181.8 – 265.3 18 x 65
Lithium-ion 26650 battery Electrochemical Rechargeable 50,400 – 64,800 14 – 19[20] 95 – 100[20] 530,526.3 – 648,000 147.4 – 190.0 26 x 65
Potato Chip Chemical 41,900 J (10-Cal) [21] 11.63 1.89 23,000,000 [22] 6,390 60 × 40 × 1
Ham and Cheese Sandwich[23] Chemical 1,470,000 408.3 145 10,130,000 2,815.9 100 × 100 × 28

## Energy density in energy storage and in fuel

Selected energy densities plot[24][25][26][27][28][29][30][31]

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

The greatest energy source by far 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 (.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,[32] 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.[33] Coal, gas, and petroleum are the current primary energy sources in the U.S.[34] but have a much lower energy density. Burning local biomass fuels supplies household energy needs (cooking fires, oil lamps, etc.) worldwide.

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

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

Many researches proposed new options for energy storage to increase energy density and decrease charging time. [35][36][37]

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

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

### Energy densities ignoring external components

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

Energy densities of energy medium
Storage type Specific energy (MJ/kg) Specific energy (Wh/kg) Energy density (MJ/L) Energy density (Wh/L) Peak recovery efficiency % Practical recovery efficiency %
Antimatter 9×1010 = c² Density would depend on the form the antimatter takes 100
Plutonium-239 83,610 719,000 Depends on crystallographic phase Depends on crystallographic phase
Hydrogen, liquid[38] 141.86 39,405.6 8.491 2,358.6
Hydrogen, at 690 bar and 15°C[38] 141.86 39,405.6 4.5 1,250.0
Hydrogen, gas[38] 141.86 39,405.6 0.01005 2.8
Diborane[39] 78.2 21,722.2
Beryllium 67.6 18,777.8 125.1 34,750.0
Lithium borohydride 65.2 18,111.1 43.4 12,055.6
Boron[40] 58.9 16,361.1 137.8 38,277.8
Methane (1.013 bar, 15 °C) 55.6 15,444.5 0.0378 10.5
Natural gas 53.6[41] 14,888.9 0.0364 10.1
LNG (NG at −160 °C) 53.6[41] 14,888.9 22.2 6,166.7
CNG (NG compressed to 250 bar/~3,600 psi) 53.6[41] 14,888.9 9 2,500.0
LPG propane[42] 49.6 13,777.8 25.3 7,027.8
LPG butane[42] 49.1 13,638.9 27.7 7,694.5
Gasoline (petrol)[42] 46.4 12,888.9 34.2 9,500.0
Polypropylene plastic 46.4[43] 12,888.9 41.7 11,583.3
Polyethylene plastic 46.3[43] 12,861.1 42.6 11,833.3
Crude oil (according to the definition of ton of oil equivalent) 46.3 12,861.1 37[41] 10,277.8
Residential heating oil[42] 46.2 12,833.3 37.3 10,361.1
Diesel fuel[42] 45.6 12,666.7 38.6 10,722.2
100LL Avgas 44.0[44] 12,222.2 31.59 8,775.0
Gasohol E10 (10% ethanol 90% gasoline by volume) 43.54 12,094.5 33.18 9,216.7
Lithium 43.1 11,972.2 23.0 6,388.9
Jet A aviation fuel[45]/kerosene 42.8 11,888.9 33 9,166.7
Biodiesel oil (vegetable oil) 42.20 11,722.2 33 9,166.7
DMF (2,5-dimethylfuran)[clarification needed] 42[46] 11,666.7 37.8 10,500.0
Polystyrene plastic 41.4[43] 11,500.0 43.5 12,083.3
Body fat metabolism 38 10,555.6 35 9,722.2 22[47]
Butanol 36.6 10,166.7 29.2 8,111.1
Gasohol E85 (85% ethanol 15% gasoline by volume) 33.1 9,194.5 25.65[citation needed] 7,125.0
Graphite 32.7 9,083.3 72.9 20,250.0
Coal, anthracite[48] 26 – 33 7,222.2 – 9,166.7 34 – 43 9444.5 – 11944.5 36
Silicon[49] 32.2 8,944.5 75.1 20,861.1
Aluminum 31.0 8,611.1 83.8 23,277.8
Ethanol 30 8,333.3 24 6,666.7
Polyester plastic 26.0[43] 7,222.2 35.6 9,888.9
Magnesium 24.7 6,861.1 43.0 11,944.5
Coal, bituminous[48] 24-35 6666.7 – 9722.2 26 – 49 7222.2 – 13611.1
PET plastic 23.5 (impure)[50] 6,527.8
Methanol 19.7 5,472.2 15.6 4,333.3
Hydrazine (toxic) combusted to N2+H2O 19.5 5,416.7 19.3 5,361.1
Liquid ammonia (combusted to N2+H2O) 18.6 5,166.7 11.5 3,194.5
PVC plastic (improper combustion toxic)[clarification needed] 18.0[43] 5,000.0 25.2 7,000.0
Wood[51] 18.0 5,000.0
Peat briquette[52] 17.7 4,916.7
Sugars, carbohydrates, and protein metabolism[citation needed] 17 4,722.2 26.2 (dextrose) 7,277.8 22[53]
Calcium[citation needed] 15.9 4,416.7 24.6 6,833.3
Glucose 15.55 4,319.5 23.9 6,638.9
Dry cow dung and cameldung 15.5[54] 4,305.6
Coal, lignite[citation needed] 10-20 2777.8 – 5555.6
Sodium (burned to wet sodium hydroxide) 13.3 3,694.5 12.8 3,555.6
Sod peat 12.8 3,555.6
Nitromethane 11.3 3,138.9
Sulfur (burned to sulfur dioxide)[55] 9.23 2,563.9 19.11 5,308.3
Sodium (burned to dry sodium oxide) 9.1 2,527.8 8.8 2,444.5
Battery, lithium-air rechargeable 9.0[56] 2,500.0
Household waste 8.0[57] 2,222.2
Zinc 5.3 1,472.2 38.0 10,555.6
Iron (burned to iron(III) oxide) 5.2 1,444.5 40.68 11,300.0
Teflon plastic (combustion toxic, but flame retardant) 5.1 1,416.7 11.2 3,111.1
Iron (burned to iron(II) oxide) 4.9 1,361.1 38.2 10,611.1
ANFO 3.7 1,027.8
Battery, zinc-air[58] 1.59 441.7 6.02 1,672.2
Liquid nitrogen[clarification needed] 0.77[59] 213.9 0.62 172.2
Compressed air at 300 bar (potential energy) 0.5 138.9 0.2 55.6 >50%[citation needed]
Latent heat of fusion of ice[citation needed] (thermal) 0.335 93.1 0.335 93.1
Water at 100 m dam height (potential energy) 0.001 0.277 0.001 0.3 85-90%[citation needed]
Storage type Energy density by mass (MJ/kg) Specific energy (Wh/kg) Energy density by volume (MJ/L) Energy density (Wh/L) Peak recovery efficiency % Practical recovery efficiency %

Divide joule metre−3 by 109 to get MJ/L. Divide MJ/L by 3.6 to get kWh/L.

## Energy density of electric and magnetic fields

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

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

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

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