# Energy density

Energy density is the amount of energy stored in a given system or region of space per unit volume, or per unit mass, depending on the context, although the latter is more formally specific energy [5]. In some cases it is obvious from context which quantity is most useful: for example, in rocketry, energy per unit mass is the most important parameter, but when studying pressurized gas or magnetohydrodynamics the energy per unit volume is more appropriate. In a few applications (comparing, for example, the effectiveness of hydrogen fuel to gasoline) both figures are appropriate and should be called out explicitly. (Hydrogen has a higher energy density per unit mass than does gasoline, but a much lower energy density per unit volume)

Energy per unit volume has the same physical units as pressure, and in many circumstances is an exact synonym: for example, the energy density of the magnetic field may be expressed as (and behaves as) a physical pressure, and the energy required to compress a gas may be determined by multiplying the pressure of the compressed gas times its change in volume.

## Energy density in energy storage and in fuel

Selected Energy Densities Plot

In energy storage application the energy density relates the mass of an energy store to its stored energy. The higher the energy density, the more energy may be stored or transported for the same amount of mass. In the context of fuel selection, that energy density of a fuel is also called the specific energy of that fuel, though in general an engine using that fuel will yield less energy due to inefficiencies and thermodynamic considerations—hence the specific fuel consumption of an engine will be greater than the reciprocal of the specific energy of the fuel.

The highest density sources of energy are fusion and fission. Fusion includes energy from the sun which will be available for billions of years (in the form of sunlight) but humans have not learned to make our own sustained fusion power sources. Fission of U-235 in nuclear power plants will be available for billions of years because of the vast supply of the element on earth [6]. Coal 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.

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 creates environmental impacts: for example, global warming, nuclear waste storage, and deforestation are a few of the consequences of supplying our growing energy demands from fossil fuels, nuclear fission, or biomass.

By dividing by 3.6 the figures for megajoules per kilogram can be converted to kilowatt-hours per kilogram. Unfortunately, the useful energy available by extraction from an energy store is always less than the energy put into the energy store, as explained by the laws of thermodynamics. No single energy storage method boasts the best in specific power, specific energy, and energy density. Peukert's Law describes how the amount of energy we get out depends how quickly we pull it out.

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.

### True energy densities

This table gives the energy density of a complete system, including all needed oxidisers.

Energy Densities Table
Storage type Energy density by mass (MJ/kg) Energy density by volume (MJ/L) Peak recovery efficiency % Practical recovery efficiency %
Mass-energy equivalence 89,876,000,000
Nuclear fusion of hydrogen (energy from the sun) 645,000,000
Deuterium-Tritium fusion 337,000,000
Nuclear fission (of 100% U-235) (Used in nuclear power plants) 88,250,000 1,500,000,000
Natural uranium (99.3% U-238, 0.7% U-235) in fast breeder reactor[7] 24,000,000 50%
Enriched uranium (3.5% U235) in light water reactor 3,456,000 30%
Hf-178m2 isomer 1,326,000 17,649,060
Natural uranium (0.7% U235) in light water reactor 443,000 30%
Ta-180m isomer 41,340 689,964
Specific orbital energy of Low Earth orbit (approximate) 33
Cl2O7 + CH4 - computed 17.4
Cl2O7 decomposition - computed 12.2
Nitromethane 11.3 12.9
Octanitrocubane explosive - computed 8.5 17
Tetranitrotetrahedrane explosive - computed 8.3
Heptanitrocubane explosive - computed 8.2
Dinitroacetylene explosive - computed 7.9
Sodium (reacted with chlorine) 7.0349
Tetranitrocubane explosive - computed 6.95
Ammonal (Al+NH4NO3 oxidizer) 6.9 12.7
Tetranitromethane + hydrazine bipropellant - computed 6.6
Hexanitrobenzene explosive - computed 6.5
Octogen explosive - computed 6.3
ANFO-ANNM 6.26
TNT [Kinney, G.F.; K.J. Graham (1985). Explosive shocks in air. Springer-Verlag. ISBN 3-540-15147-8. ] 4.610 6.92
Copper Thermite (Al + CuO as oxidizer) 4.13 20.9
Thermite (powder Al + Fe2O3 as oxidizer) 4.00 18.4
Hydrogen peroxide decomposition (as monopropellant) 2.7 3.8
battery, Lithium ion nanowire 2.54 95%[8]
battery, Lithium Thionyl Chloride (LiSOCl2) [9] 2.5
Water 220.64 bar, 373.8°C 1.968 0.708
Kinetic energy penetrator 1.9 30
battery, Fluoride ion [10] 1.7 2.8
battery, Hydrogen closed cycle H fuel cell[11] 1.62
Hydrazine(toxic) decomposition (as monopropellant) 1.6 1.6
Ammonium nitrate decomposition (as monopropellant) 1.4 2.5
Capacitor by EEStor (claimed prototype capacity) [12] 1.2 5.7 99% 99%
Thermal energy storage(Molten Salt) approximate 1
Molecular spring approximate 1
battery, Sodium Sulfur 1.23 [13] 85%[14]
Liquid nitrogen 0.77[1] 0.62
battery, Lithium ion[2] 0.54 0.9 95%[3]
battery, Lithium Sulphur 0.54
Flywheel 0.5 1-0.15%/10s [15]
5.56 × 45 mm NATO bullet 0.4 3.2
Ice(Ice) 0.335 0.335
battery, Zinc Bromine flow (ZnBr)[4] 0.27
battery, NiMH[5] 0.250 0.493
battery, NiCd 0.14 80%[3]
battery, Vandium redox 0.09 [16] 0.1188 70-75%
battery, Vandium Bromide redox 0.18 [17] 0.252 81%
Capacitor Ultracapacitor 0.0206 [18] 0.050 [19]
Capacitor Supercapacitor 0.01 98.5% 90%[20]
Capacitor 0.002 [21]
Water at 100 m dam height 0.001 0.001 85-90%[22]
Spring power (clock spring), torsion spring 0.0003 [23] 0.0006
Storage type Energy density by mass (MJ/kg) Energy density by volume (MJ/L) Peak recovery efficiency % Practical recovery efficiency %

### Energy densities excluding oxidisers

This table lists energy densities of fuels that require external oxidisers, such as oxygen. These figures do not take into account the mass and volume of the oxygen required for the chemical reactions, as it is assumed to be freely available and present in the atmosphere. Such systems give a higher energy density than an equivalent system that must hold its own oxidiser.

Energy Densities Table
Storage type Energy density by mass (MJ/kg) Energy density by volume (MJ/L) Peak recovery efficiency % Practical recovery efficiency %
Hydrogen, liquid (burned in air) 143 10.1
Hydrogen, compressed at 700 bar (burned in air) [24] 143 5.6
Hydrogen, gas (burned in air) 143 0.01079
Beryllium (toxic) (burned in air) 67.6 125.1
Lithium borohydride (burned in air) 65.2 43.4
Boron [25] (burned in air) 58.9 137.8
Methane (1.013bar, 15°C) (burned in air) 55.6 0.0378
Natural gas (burned in air) 53.6[6] 10
LPG propane (burned in air)[7] 49.6 25.3
LPG butane (burned in air)[7] 49.1 27.7
Gasoline[7] 46.4 34.2
Diesel fuel/residential heating oil (burned in air)[7] 46.2 37.3
Polyethylene plastic 46.3[8] 42.6
Polypropylene plastic 46.4[8] 41.7
Gasohol E10 (10% ethanol 90% gasoline by volume) 43.54 33.72
Gasohol E85 (85% ethanol 10% gasoline by volume) 33.1 25.65
Lithium (burned in air) 43.1 23.0
Jet A aviation fuel [26] / kerosene 42.8 33
Biodiesel oil (vegetable oil) 42.20 33
DMF (2,5-dimethylfuran) 42 [27] 37.8
Crude oil (according to the definition of ton of oil equivalent) 46.3 37[6]
Polystyrene plastic 41.4[8] 43.5
Body fat metabolism 38 35 22[9]
Butanol 36.6 29.2
Graphite (burned in air) 32.7 72.9
coal, Anthracite 32.5 72.4 36
Silicon (burned in air)[28] 32.2 75.1
Aluminum (burned in air) 31.0 83.8
Ethanol 30 24
Polyester plastic 26.0 [8] 35.6
Magnesium (burned in air) 24.7 43.0
coal, Bituminous [29] 24 20
PET plastic 23.5 (impure) [30]
Methanol 19.7 15.6
Hydrazine (toxic) combusted to N2+H2O 19.5 19.3
Liquid ammonia (combusted to N2+H2O) 18.6 11.5
PVC plastic (improper combustion toxic) 18.0[8] 25.2
Peat briquette [10] 17.7
Sugars, carbohydrates & protein metabolism 17 26.2(dextrose) 22 [31]
coal, Lignite 14.0
Calcium (burned in air) 15.9 24.6
Glucose 15.55 23.9
Dry cowdung and cameldung 15.5 [32]
Wood 6.0
Sodium (burned to wet sodium hydroxide) 13.3 12.8
Household waste 8.0[11][12]
Sod peat 12.8
Sodium (burned to dry sodium oxide) 9.1 8.8
Zinc (burned in air) 5.3 38.0
Teflon plastic (combustion toxic, but flame retardant) 5.1 11.2
iron (burned to iron(III) oxide) 5.2 40.68
iron (burned to iron(II) oxide) 4.9 38.2
battery, Zinc air (wiki 1) 1.33
battery, Zinc air (wiki 2) 0.40 5.9
Storage type Energy density by mass (MJ/kg) Energy density by volume (MJ/L) Peak recovery efficiency % Practical recovery efficiency %

## 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

$U = \frac{\varepsilon_0}{2} \mathbf{E}^2 + \frac{1}{2\mu_0} \mathbf{B}^2$,

where E is the electric field and B is the magnetic field. 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) substances, the energy density (in SI units) is

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

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

## Energy density of empty space

In physics, "vacuum energy" or "zero-point energy" is the volumetric energy density of empty space. More recent developments have expounded on the concept of energy in empty space.

Modern physics is commonly classified into two fundamental theories: quantum field theory and general relativity. Quantum field theory takes quantum mechanics and special relativity into account, and it's a theory of all the forces and particles except gravity. General relativity is a theory of gravity, but it is incompatible with quantum mechanics. Currently these two theories have not yet been reconciled into one unified description, though research into "quantum gravity" seeks to bridge this divide.

In general relativity, the cosmological constant is proportional to the energy density of empty space, and can be measured by the curvature of space. It is subsequently related to the age of the universe, and as energy expands outwards with time its density changes.

Quantum field theory considers the vacuum ground state not to be completely empty, but to consist of a seething mass of virtual particles and fields. These fields are quantified as probabilities—that is, the likelihood of manifestation based on conditions. Since these fields do not have a permanent existence, they are called vacuum fluctuations. In the Casimir effect, two metal plates can cause a change in the vacuum energy density between them which generates a measurable force.

Some believe that vacuum energy might be the "dark energy" (also called Quintessence) associated with the cosmological constant in general relativity, thought to be similar to a negative force of gravity (or antigravity). Observations that the expanding universe appears to be accelerating seem to support the cosmic inflation theory—first proposed by Alan Guth in 1981—in which the nascent universe passed through a phase of exponential expansion driven by a negative vacuum energy density (positive vacuum pressure).

## Energy density of food

Energy density is the amount of energy (kilojoules or calories) per amount of food, with food amount being measured in grams or milliliters of food. Energy density is thus expressed in cal/g, kcal/g, J/g, kJ/g, cal/mL, kcal/mL, J/mL, or kJ/mL. What is popularly referred to as the number of "Calories" in a portion of food (invariably spelled with a capital C to show that it is the food Calorie) is therefore the number of kilocalories (thousands of calories with the small c) in the portion.

Energy density measures the energy released when the food is metabolised by a healthy organism when it ingests the food (see food energy for calculation) and the food is metabolized with oxygen, into waste products such as carbon dioxide and water. Carbohydrates, fats, and proteins are the only sources of energy for an individual abstaining from alcohol, and they make up ninety percent of the dry weight of food.[13] Therefore, water content is the most important factor in energy density. Carbohydrates and proteins provide four calories per gram, whereas fat provides nine calories per gram, 2.25 times as much energy. Foods that derive most of their energy from fat have a much higher energy density than those that derive most of their energy from carbohydrates or proteins, even if the water content is the same. Nutrients with a lower absorption, such as fiber or sugar alcohols, lower the energy density of foods as well. A moderate energy density would be 1.6 to 3 calories per gram; salmon, lean meat, and bread would fall in this category. High-energy foods would have more than three calories per gram and include crackers, cheese, dark chocolate, and peanuts.[14] The energy density of a food can be determined from the label by dividing the calories or joules by the weight in grams.

## External references

### Zero point energy

1. Eric Weisstein's world of physics: energy density [33]
2. Baez physics: Is there a nonzero cosmological constant? [34]; What's the Energy Density of the Vacuum?.
3. Introductory review of cosmic inflation [35]
4. An exposition to inflationary cosmology [36]

### Density data

• ^  "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

### Books

• 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

## Footnotes

1. ^ 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.
2. ^ A typically available lithium ion cell with an Energy Density of 201 wh/kg [1]
3. ^ a b Justin Lemire-Elmore (2004-04-13). "The Energy Cost of Electric and Human-Powered Bicycles". 7. Retrieved on 2009-02-26. "Table 3: Input and Output Energy from Batteries"
4. ^ "ZBB Energy Corp". Archived from the original on 2007-10-15. "75 to 85 watt-hours per kilogram"
5. ^ High Energy Metal Hydride Battery
6. ^ a b Envestra Limited. Natural Gas. Retrieved 2008-10-05
7. ^ a b c d IOR Energy. List of common conversion factors (Engineering conversion factors). Retrieved 2008-10-05
8. ^ a b c d e [2]
9. ^ Justin Lemire-Elmore (2004-04-13). "The Energy Cost of Electric and Human-Powered Bicycles". 5. Retrieved on 2009-02-26. "properly trained athlete will have efficiencies of 22 to 26%"
10. ^ Bord na Mona, Peat for Energy. [3]
11. ^ David E. Dirkse. energy buffers. "household waste 8..11 MJ/kg"
12. ^ [4]
13. ^ Carbohydrates, Proteins, and Fats: Overview of Nutrition. The Merck Manual.
14. ^ The Okinawa Diet: Caloric Density Pyramid.