# 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. 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 in most applications.)

Energy density 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

In energy storage applications, 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. And in general, specific energy and energy density are at odds due to charge screening.

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.
This table does not take into account the mass and volume of the oxygen required for many of the chemical reactions, as it is assumed to be freely available and present in the atmosphere. In cases where this is not true (such as rocket fuel), oxygen is included as an oxidizer.
File:Energy Density.PNG
Energy density of various storage media.
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
binding energy of helium-4 nucleus 683,000,000 8.57x1024
nuclear fusion of hydrogen (energy from the sun) 645,000,000
nuclear fission (of U-235) (Used in nuclear power plants) 88,250,000 1,500,000,000
Natural uranium (99.3% U238, 0.7% U235) in fast breeder reactor[1] 24,000,000 50%Template:Smn
Thorium in fast breeder reactor ?
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
liquid hydrogen 143 10.1
compressed gaseous hydrogen at 700 bar[2] 143 5.6
gaseous hydrogen at room temperature[citation needed] 143 0.01079
beryllium (toxic) (burned in air) 67.6 125.1
lithium borohydride (burned in air) 65.2 43.4
boron [3] (burned in air) 58.9 137.8
compressed natural gas at 200 bar 53.6[4]Template:Smn 10
LPG propane [5] 49.6 25.3
LPG butane 49.1 27.7
gasoline[6] 46.9 34.6
diesel fuel/residential heating oil[7] 45.8 38.7
polyethylene plastic 46.3[8]Template:Smn 42.6
polypropylene plastic 46.3[9]Template:Smn 41.7
gasohol (10% ethanol 90% gasoline) 43.54 28.06
lithium (burned in air) 43.1 23.0
Jet A aviation fuel[10] 42.8 33
biodiesel oil (vegetable oil) 42.20 33
DMF (2,5-dimethylfuran) 42[11]Template:Smn 37.8
crude oil (according to the definition of ton of oil equivalent) 41.87 37[12]Template:Smn
polystyrene plastic 41.4[13]Template:Smn 43.5
body fat metabolism 38 35 22-26%[14]Template:Smn
butanol 36.6 29.2
specific orbital energy of Low Earth orbit 33 (approx.)Template:Smn
graphite (burned in air) 32.7 72.9
anthracite coal 32.5 72.4 36%Template:Smn
silicon (burned in air)[15] 32.2 75.1
aluminum (burned in air) 31.0 83.8
ethanol 30 24
polyester plastic 26.0[16]Template:Smn 35.6
magnesium (burned in air) 24.7 43.0
bituminous coal [17] 24 20
PET pop bottle plastic ?23.5 impureTemplate:Smn
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[18]Template:Smn 25.2
sugars, carbohydrates & proteins metabolism 17 26.2(dextrose)Template:Smn 22-26% [19]Template:Smn
Cl2O7 + CH4 - computed 17.4
lignite coal 14-19
calcium (burned in air) 15.9 24.6
dry cowdung and cameldung 15.5[20]Template:Smn
wood 6–17[21]Template:Smn 1.8–3.2Template:Smn
liquid hydrogen + oxygen (as oxidizer) (1:8 (w/w), 14.1:7.0 (v/v)) 13.333 5.7
sodium (burned to wet sodium hydroxide) 13.3 12.8
Cl2O7 decomposition - computed 12.2
nitromethane 11.3 12.9
household waste 8-11[22][23]Template:Smn
sodium (burned to dry sodium oxide) 9.1 8.8
Octanitrocubane explosive - computed 7.4
ammonal (Al+NH4NO3 oxidizer) 6.9 12.7
Tetranitromethane + hydrazine explosive - computed 6.6
Hexanitrobenzene explosive - computed 6.5
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
TNT 4.184 6.92
Copper Thermite (Al + CuO as oxidizer) 4.13 20.9
Thermite (powder Al + Fe2O3 as oxidizer) 4.00 [24]Template:Smn 18.4
compressed air at 300 bar (at 12°C), without container 0.512 0.16
ANFO 3.88
hydrogen peroxide decomposition (as monopropellant) 2.7 3.8
Theoretical highest energy density electrochemical battery Need this!
Lithium ion battery with nanowires 2.54-2.72?Template:Smn Template:Smn 95%[25]Template:Smn
Lithium Thionyl Chloride Battery 2.5
Fluoride ion battery[26] 1.7-4.2Template:Smn 2.8-5.8Template:Smn
Regenerative Fuel Cell (fuel cell with internal Hydrogen reservoir used much as a battery) 1.62[27]Template:Smn
hydrazine(toxic) decomposition (as monopropellant) 1.6 1.6
ammonium nitrate decomposition (as monopropellant) 1.4 2.5
capacitor by EEStor (claimed capacity) 1.0 [28]Template:Smn
Molecular spring ~1Template:Smn
sodium-sulfur battery 1.23[29]Template:Smn 85%[30]Template:Smn
liquid nitrogen 0.77[1]Template:Smn 0.62
lithium ion battery-predicted future capability[2] 0.54–0.9Template:Smn 0.9–1.9Template:Smn 95%[31]Template:Smn
lithium ion battery-present capability[2] 0.23–0.28Template:Smn
lithium sulphur battery 0.54-1.44Template:Smn
kinetic energy penetrator 1.9-3.4Template:Smn 30-54Template:Smn
5.56 × 45 mm NATO bullet 0.4-0.8Template:Smn 3.2-6.4Template:Smn
Zn-air batteries 0.40 to 0.72Template:Smn
flywheel 0.5 81-94%[citation needed]Template:Smn
ice 0.335 0.335
zinc-bromine flow battery 0.27–0.306[32]Template:Smn
compressed air at 20 bar (at 12°C), without container 0.27 0.01 64%[33]Template:Smn
NiMH Battery 0.22[34]Template:Smn 0.36 60% [35]Template:Smn
NiCd Battery 0.14-0.22Template:Smn 80% [36]Template:Smn
lead acid battery 0.09–0.11[37]Template:Smn 0.14–0.17Template:Smn 75-85%[38]Template:Smn
compressed air in fiber-wound bottle at 200 bar (at 24°C) 0.1 0.1
commercial lead acid battery pack 0.072-0.079[39]Template:Smn
vanadium redox battery 0.09[40]Template:Smn 0.1188 70-75%Template:Smn
vanadium bromide redox battery 0.18[41]Template:Smn 0.252 81%
compressed air in steel bottle at 200 bar (at 24°C) 0.04 0.1
ultracapacitor 0.0206 [42]Template:Smn 0.050 [43]
supercapacitor 0.01 98.5% 90%[44]Template:Smn
capacitor 0.002 [45]Template:Smn
water at 100 m dam height 0.001 0.001 85-90%[46]Template:Smn
spring power (clock spring), torsion spring 0.0003[47]Template:Smn 0.0006

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 [48]. 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.

## 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. 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

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

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

## 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. This is 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. Typical values of food energy density for high energy-density foods, such as a hamburger, would be 2.5 kcal/g. Purified fats and oils contain the highest energy densities—about 9 kcal/g. What is popularly referred to as the number of "Calories" in a portion of food is therefore technically the number of kilocalories in the portion.

## External references

### Zero point energy

1. Eric Weisstein's world of physics: energy density [49]
2. Baez physics: Is there a nonzero cosmological constant? [50]; What's the Energy Density of the Vacuum?.
3. Introductory review of cosmic inflation [51]
4. An exposition to inflationary cosmology [52]

### 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

## References

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. Bridging the power gap by Scott Gourney and Francis Tusa: Military Logistics International: November/December 2007 states "Newer, current generation LiIon rechargeable batteries can produce 65-80 Watt hours per kg" and"it is reasonable to assume that LiIon could see a 50% increase in power output, so up to 150 Watt hours per kg." and "ABSL ...is more optimistic...can see a growth path to a stage where LiIon could be capable of outputs of 250 Watt hours per kg". The article also states that the Lockheed Martin LiIon BattPack has a mass of 85lbs and a nominal capacity of 2.5 kWhr. This equates to 0.23 MJ/kg.