Energy density

Surname

volumetric energy density

${\ displaystyle w,}$ ${\ displaystyle \ rho}$

Derived from

Size and unit system	unit	dimension
SI	J · m ^-3	M · L ⁻¹ · T ⁻²

Physical size

Surname

gravimetric energy density, specific energy

Formula symbol

${\ displaystyle w,}$ ${\ displaystyle \ rho}$

Size and unit system	unit	dimension
SI	J · kg ^-1	L ² · T ⁻²

In physics, the energy density describes the distribution of energy over a certain quantity and consequently always has the shape ${\ displaystyle E}$ ${\ displaystyle X}$

{\ displaystyle w = {\ frac {\ mathrm {d} E} {\ mathrm {d} X}}.}

Most often it is used as a

volumetric energy density, a measure of the energy per room volume of a substance (SI unit: joules per cubic meter)
Gravimetric energy density or specific energy, a measure of the energy per mass of a substance (SI unit: joules per kilogram).

But ultimately you can define a corresponding energy density for each physical quantity. According to DIN 5485 , the term is the energy density of the dimensional , in particular volumetric indication reserved for specific energy especially in mass; see " Energy " and " Related Quantity ".

The energy density of energy storage devices such as fuels and batteries used in technology is of great practical interest . In vehicle construction in particular , the energy density of the energy storage device used is decisive for the achievable range.

Energy density in electrodynamics

Energy density of electromagnetic waves

From Maxwell's equations one can conclude that the maximum energy output of electromagnetic waves in a substance is proportional to the square of the field amplitudes . Electric and magnetic fields contribute equally:

{\ displaystyle w = {\ frac {1} {2}} \ left ({\ vec {E}} \ cdot {\ vec {D}} + {\ vec {H}} \ cdot {\ vec {B} } \ right)}

Energy density in the plate capacitor

The energy of a charged plate capacitor is calculated as

{\ displaystyle W = {\ frac {1} {2}} CU ^ {2}.}

The following applies to the capacity:

{\ displaystyle C = \ varepsilon _ {0} \ varepsilon _ {r} {\ frac {A} {d}}}

The voltage U results from E · d. By inserting it you get for the energy:

{\ displaystyle W = {\ frac {1} {2}} \ varepsilon _ {0} \ varepsilon _ {r} {\ frac {A} {d}} E ^ {2} d ^ {2}}

This leads to the energy density:

{\ displaystyle w_ {el} = {\ frac {W} {V}} = {\ frac {1} {2}} \ varepsilon _ {0} \ varepsilon _ {r} E ^ {2}}

Energy of the magnetic field of a coil

For the energy of the magnetic field of a coil with the amount of the magnetic flux density , the cross-sectional area , the length , the number of turns, the current strength , the magnetic field constants and the relative permeability results ${\ displaystyle W}$ ${\ displaystyle B}$ ${\ displaystyle A}$ ${\ displaystyle l}$ ${\ displaystyle n}$ ${\ displaystyle I}$ ${\ displaystyle \ mu _ {0}}$ ${\ displaystyle \ mu _ {r}}$

{\ displaystyle W = {\ frac {B ^ {2}} {2 \ cdot \ mu _ {0} \ cdot \ mu _ {r}}} \ cdot A \ cdot l = {\ frac {(n \ cdot I) ^ {2}} {2}} \ cdot \ mu _ {0} \ cdot \ mu _ {r} \ cdot {\ frac {A} {l}}}

and then continue

{\ displaystyle w_ {B} = {\ frac {B ^ {2}} {2 \ cdot \ mu _ {0} \ cdot \ mu _ {r}}} = {\ frac {(n \ cdot I) ^ {2}} {2}} \ cdot \ mu _ {0} \ cdot \ mu _ {r}}

for the energy density of the flux density . ${\ displaystyle w_ {B}}$ ${\ displaystyle B}$

Energy density of energy storage and primary energy carriers

Energy densities of selected energy stores

The energy density of fuels is called the calorific value or calorific value , that of batteries capacity per volume or capacity per mass. For example, the energy density of a lithium polymer battery is 140–180 watt hours per kg mass (140–180 Wh / kg) and that of a nickel metal hydride battery (NiMH) is 80 Wh / kg. In comparison with other types of electrical energy storage of the battery cuts right from favorable.

A high energy density is desired in order to keep transport costs for the energy carrier low, but also in order to achieve long operating times for mobile devices and long ranges for vehicles. For example, model helicopters can fly longer with a lithium polymer battery than with a NiMH battery of the same mass.

The energy density of nutrients is also known as the physiological calorific value .

In addition to accumulators, energy storage devices to support the power grid include superconducting magnetic energy storage devices (SMES), pumped storage power plants and compressed air storage power plants .

Examples

Substance / system	Energy density in MJ / kg	Energy density in MJ / l	comment	Note *	credentials
NdFeB and SmCo magnets	0.000 055		Range: 200-400 kJ / m ³ BH _max , i.e. 30-55 J / kg	like
Electrolytic capacitor	0.000 4		Range: 0.01-0.1 Wh / kg, i.e. 0.04-0.4 kJ / kg	el
Double layer capacitor	0.01		Range: 0.1-3 Wh / kg, i.e. 0.4-10 kJ / kg	el
Lead accumulator	0.11	0.25	a) Range: 3–30 Wh / kg, i.e. 10–110 kJ / kg b) 30–40 Wh / kg Energy density (MJ / l) calculated on the basis of the gross density of a starter battery	chem	a) b)
Adenosine triphosphate (ATP)	0.128		= 64.6 kJ / mol (with cleavage of both bonds) at 0.507 kg / mol	chem	see adenosine triphosphate
NiCd battery	0.14		a) 40 Wh / kg b) Range: 4–70 Wh / kg, i.e. 15–250 kJ / kg c) 40–70 Wh / kg	chem	a) b) c)
Flywheel storage with CFRP	0.18		49 Wh / kg	mech
Carbon-zinc battery	0.23		65 Wh / kg, i.e. 230 kJ / kg	chem
NiMH battery	0.28		a) 2,300 mAh · 1.0 V / 30 g = 76.7 Wh / kg b) 60 Wh / kg c) Range: 15–120 Wh / kg, i.e. 50–400 kJ / kg d) 60–80 Wh / kg	chem	a) b) c) d)
Li-titanate battery	0.32		90 Wh / kg, i.e. 0.32 MJ / kg	chem
Melting energy ice	0.33		at 1013.2 hPa and 0 ° C	Phase transition
Zebra battery	0.43		Range: 100-120 Wh / kg, i.e. 0.36-0.43 MJ / kg	chem	, (but with an unclear unit)
Alkaline manganese battery	0.45		125 Wh / kg, i.e. 450 kJ / kg	chem
Compressed air	0.46	0.14	a) 138 · 10 ⁶ Ws / m ³ at 300 kg / m ³ b) However, the gravimetric energy density is up to a factor of 10 lower if the pressure vessel is also taken into account	mech	a) b) without ref.
Li-polymer battery	0.54		a) 150 Wh / kg, i.e. 540 kJ / kg b) 130–200 Wh / kg	chem	a) b)
Li-ion battery	0.65	0.7-1.8	a) 180 Wh / kg b) 100 Wh / kg c) Range: 40–200 Wh / kg, i.e. 150–700 kJ / kg d)> 160 Wh / kg	chem	a) b) c) d)
Hydrogen (including hydride tank )	1.19			chem, O
Zinc-air battery	1.2		a) 340 Wh / kg, i.e. 1,200 kJ / kg b) three times as large as conventional Li batteries	chem, O	a) b)
Lithium-sulfur accumulator	1.26		350 Wh / kg	chem
Solid state accumulator (mass production)	1.44		> 400 Wh / kg	chem, O
Lithium-air accumulator	1.6		a)> 450 Wh / kg b) should reach 1,000 Wh / kg	chem, O	a) b)
Heat of condensation of water	2.26		at 1013.2 hPa and 100 ° C. 40.7 kJ / mol	Phase transition
Lithium thionyl chloride battery	2.34		650 Wh / kg	chem
Thermite	4.0	18.4		chem	(?)
Trinitrotoluene (TNT)	4.6	6.92	1,046 kJ / mol / (227 g / mol). Oxidizer is contained in the molecule. Note: for the TNT equivalent, an energy density of 4.18 MJ / kg = 1.0 Mcal / kg is used.	chem	see TNT equivalent
Aluminum-air battery	4.7		a) 1,300 Wh / kg, i.e. 4,700 kJ / kg b) Future goal: 8,000 Wh / kg = 28 MJ / kg	chem, O	a) b)
strongest explosives	7th		Oxidizer is contained in the molecule.		see explosives
Residual waste (moist)	11		Range 8-11 MJ / kg	O, Hw
Brown coal	11.3		a) Range 8.4-11.3 MJ / kg b) 9.1 MJ / kg	O, Hw	a) b)
Wood (air dry)	16.8		a) Range 14.6-16.8 MJ / kg b) 14.7 MJ / kg	O, Hw	a) b)
sugar	16.7			O
Sewage sludge	17th		Range 11–17 MJ / kg for dry matter (digested lower value, not digested upper value)	O, Hw
straw	17th			O, Hw
Wood pellets and wood briquettes	18th			O, Hw
Brown coal (briquette)	19.6			O, Hw
Methanol	19.7	15.6		O, Hw
Ammonia (liquid)	22.5	15.3	−33 ° C or 9 bar	O, Hw
Ethanol	26.7	21.1		O, Hw
Old tires	29.5			O, Hw
Silicon	32.6	75.9		O
carbon	32.8	74.2		O
Propane (liquid)	46.3	23.4	liquid at 15 ° C	O, Hw
Hard coal	34		a) Range 27-34 MJ / kg b) 29.3 MJ / kg c) 30 MJ / kg, coke 28.7 MJ / kg, briquettes 31.4 MJ / kg	O, Hw	a) b) c)
diesel	43	35-36		O, Hw
petrol	40-42	29-32		O, Hw
crude oil	41.9		Heavy oil, bunker oil, residual oil has approx. 40 MJ / kg	O, Hw
Heating oil , light	42.8	36		O, Hw
Methane (main component of natural gas )	50	0.0317	a) 50 MJ / kg / 35.9 MJ / m ³ b) 55.5 MJ / kg / 39.8 MJ / m ³ c) 31.7 MJ / m ³	O, Hw	a) b) c)
Hydrogen 1 bar (without tank)	120	0.01079		O	, (?)
Hydrogen 700 bar (without tank)	120	5.6		O	, (?)
Liquid hydrogen (without tank)	120	10.1		O	, (?)
Hydrogen (liquid, bound to LOHC )	13.2	10.4	The calorific value of the LOHC carrier ( methanol ) is not taken into account. Energy density calculated on the basis of the maximum loading of 0.11 kg _H2 / kg _methanol .	O, Hw
Atomic hydrogen	216		spontaneous reaction to form molecular hydrogen	chem
Radioisotope generator	5,000		electrical (60,000 MJ / kg thermal)	nucl.
Nuclear fission natural uranium (0.72% ²³⁵ U)	648,000		corresponds to 7.5 GWd / t SM	nucl.
Burn-up (nuclear technology)	3,801,600		Value based on the average burn-up of around 40 GWd / t today. Fissile material up to 500 GWd / t SM corresponds to 43,200,000 MJ / kg.	nucl.
Decay of the free neutron	74,600,000		780 keV (1.250 10 ⁻¹³ J) per neutron (1.674 10 ⁻²⁷ kg)	nucl.
Nuclear fission ²³⁵ U	79,390,000	1,500,000,000	corresponds to 1,042 GWd / t SM	nucl.
Nuclear fission ²³² Th	79,420,000	929,214,000		nucl.
Nuclear fusion (nuclear weapon, nuclear fusion reactor)	300,000,000		corresponds to 3,472 GWd / t SM	nucl.
Proton-proton reaction	627,000,000		Most important fusion reaction in the sun ; corresponds to 7,256 GWd / t SM	nucl.
complete conversion of mass into energy	89,875,000,000		maximum possible energy density; corresponds to 1,042,000 GWd / t SM	nucl.	E = mc²

Remarks:

likes: magnetic energy
el: electrical energy
chem: enthalpy of reaction
mech: with mechanical conversion
nukl: conversion of atomic nuclei or elementary particles
Hw: calorific value
O = oxidizer is air and is not taken into account in the reference mass.

1 J = 1 W s ; 1 MJ = 0.2778 kWh ; 1 kWh = 3.6 MJ ; 1 G W d = 24 GWh = 86.4 T J

More energy densities

Mechanical energy density: The elastic energy that is stored in a certain volume of a material is referred to as mechanical energy density (formula symbol mostly ) and is determined in mechanical tests (e.g. in a tensile test ) , whereby the mechanical stress and the elongation are . The mechanical energy density in the event of material failure serves as an easily measured parameter for the toughness of a material, but does not always correlate with the fracture toughness measured by fracture mechanics . ${\ displaystyle U}$ ${\ displaystyle \ textstyle U = \ int \ sigma \ cdot \ mathrm {d} \ epsilon}$ ${\ displaystyle \ sigma}$ ${\ displaystyle \ epsilon}$

Spectral energy density: Dependence of the energy of a radiation spectrum on the frequency.

{\ displaystyle \ epsilon _ {\ nu} = {\ tfrac {\ mathrm {d} E} {\ mathrm {d} \ nu}}.}

Sound energy density : The energy density of the sound field.

Calorific value , calorific value (there also the comparison of different energy densities of typical fuels)

Specific or molar latent heat : The energy stored in the physical state.

Gravimetric energy density of food , used in the Volumetrics Diet

Shear energy density : The energy density during a shear .

Individual evidence

↑ Othmar Marti: Energy of the magnetic field. Experimental Physics, Ulm University, January 23, 2003, accessed on November 23, 2014 (lecture slides).

↑ ^a ^b ^c Info energy. Baden-Württemberg Ministry for the Environment, Climate and Energy (UM), accessed on November 23, 2014 .

↑ super magnets. Webcraft GmbH, accessed on November 22, 2014 (commercial manufacturer website ).

↑ ^a ^b ^c ^d ^e ^f ^g Klaus Lipinski: Energy density. DATACOM Buchverlag GmbH, accessed on November 22, 2014 .

↑ kfz.net - car battery sizes . October 9, 2018 ( kfz.net [accessed February 25, 2019]).

↑ ^a ^b ^c ^d ^e ^f ^g ^h Reinhard Löser: ABC of battery systems. Information about the common accumulators. (No longer available online.) BEM / Bundesverband eMobilität eV, April 2012, archived from the original on December 3, 2014 ; accessed on November 23, 2014 . Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice.

↑ ^a ^b ^c ^d ^e ^f ^g Rolf Zinniker: Information sheet on batteries and accumulators. (PDF; 151 kB) (No longer available online.) August 25, 2003, archived from the original on November 28, 2010 ; Retrieved May 3, 2011 . Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice.

↑ Flywheel and flywheel memory. Energy in local transport. Energieprofi.com GmbH i.Gr., accessed on November 23, 2014 .

↑ NiMH battery type AA with 2300 mAh, 1.2 V, 30 g. Energizer, accessed November 22, 2014 (commercial website).

↑ Lithium-ion batteries. Centrales Agrar-Rohstoff Marketing- und Energie-Netzwerk eV, accessed on November 23, 2014 .

↑ ^a ^b E. DT Atkins, PW Atkins, J. de Paula: Physikalische Chemie . John Wiley & Sons, 2013, ISBN 978-3-527-33247-2 ( limited preview in Google Book Search).

↑ Battery manufacturer FZ Sonick is skeptical about the market for Zebra batteries. Heise Zeitschriften Verlag GmbH & Co. KG, April 12, 2010, accessed on November 23, 2014 .

↑ I. Cyphelly, Ph Brückmann, W. Menhardt:. . Technical fundamentals of compressed air storage. (PDF, 1.27 MB) and their use as a replacement for lead batteries. On behalf of the Federal Office for Energy, Bern, September 2004, accessed on November 23, 2014 (page 37).

↑ Lithium-ion batteries. Energy density. Elektronik-Kompendium.de, accessed on November 23, 2014 .

↑ Data sheet lithium-sulfur battery. (PDF, 142 kB) (No longer available online.) Sion Power, archived from the original on December 27, 2014 ; accessed on November 21, 2014 (English, commercial manufacturer's website). Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice.

↑ Hope for solid battery: series production started. Chip, accessed November 24, 2018 .

↑ Steven J. Visco, Eugene Nimon, Bruce Katz, May-Ying Chu, Lutgard De Jonghe: Lithium / Air Semi-fuel Cells: High Energy Density Batteries Based On Lithium Metal Electrodes. August 26, 2009, accessed on November 21, 2014 (English, Almaden Institute 2009. Scalable Energy Storage: Beyond Lithium Ion).

↑ Tadiran lithium batteries. Tadiran GmbH, accessed on December 5, 2015 (commercial manufacturer website).

↑ Hans Goldschmidt: About the energy density of Thermite and some new technical applications of aluminothermics . In: Angewandte Chemie . tape 15 , no. 28 , 1902, pp. 699-702 , doi : 10.1002 / anie.19020152803 .

↑ Shaohua Yang, Harold Knickle: Design and analysis of aluminum / air battery system for electric vehicles . In: Journal of Power Sources . tape 112 , no. 1 , 2002, p. 162-173 , doi : 10.1016 / S0378-7753 (02) 00370-1 ( sciencedirect.com ).

↑ Thomas Kuther: The metal-air cell takes away the fear of range for electric vehicles. (No longer available online.) EmoPraxis, April 8, 2013, archived from the original on March 6, 2015 ; accessed on November 23, 2014 . Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. @1@ 2

↑ ^a ^b ^c ^d ^e ^f ^g ^h Calorific value / calorific value. State of Styria, accessed on November 21, 2014 .

↑ ^a ^b ^c ^d Calorific values of the energy sources and factors for the conversion of natural units into energy units for the 2014 energy balance. AG Energiebilanzen (is cited as a source in the BMWi publication " Energy data "), accessed on January 7, 2017 .

↑ BMI-rechner.net

↑ ^a ^b Josef Rathbauer, Manfred Wörgetter: Standardization of solid biofuels. Federal Institute for Agricultural Engineering, August 2, 1999, accessed on November 27, 2014 .

^ ^A ^b Norbert Auner: Silicon as an intermediary between renewable energy and hydrogen. (PDF; 386 kB) Deutsche Bank Research, May 5, 2004, accessed on November 21, 2014 .

↑ Properties of liquid gas. Retrieved March 11, 2019 .

↑ ^a ^b ^c ^d ^e ^f Energy table for converting various energy units and equivalents. (No longer available online.) German Hydrogen and Fuel Cell Association (DWV), Berlin, archived from the original on May 9, 2015 ; accessed on November 23, 2014 . Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice.

↑ Erich Hahne: Technical Thermodynamics: Introduction and Application . Oldenbourg Verlag, 2010, ISBN 3-486-59231-9 , p. 406, 408 ( limited preview in Google Book search).

^ Matthias Kramer: Integrative Environmental Management: System- Oriented Relationships Between… Springer, 2010, ISBN 3-8349-8602-X , p. 534 ( limited preview in Google Book search).

^ ^A ^b ^c Louis Schlapbach, Andreas Züttel: Hydrogen-storage materials for mobile applications . In: Nature . No. 414 , 2001, p. 353-358 , doi : 10.1038 / 35104634 ( nature.com ).

↑ M. Niermann, S. Drünert, M. Kaltschmitt, K. Bonhoff: Liquid organic hydrogen carriers (LOHCs) - techno-economic analysis of LOHCs in a defined process chain . In: Energy & Environmental Science . tape 12 , no. 1 , 2019, ISSN 1754-5692 , p. 300 , doi : 10.1039 / C8EE02700E ( rsc.org [accessed May 29, 2019]).

↑ Answers To Unanswered Questions. 25th Annual Regulatory Information Conference. US Nuclear Regulatory Commission, March 12, 2013, accessed November 21, 2014 .

↑ ^a ^b Energy density calculations of nuclear fuel. Whatisnuclear, accessed April 10, 2015 .

[1] Othmar Marti: Energy of the magnetic field. Experimental Physics, Ulm University, January 23, 2003, accessed on November 23, 2014 (lecture slides).

[UM-BW-2] Info energy. Baden-Württemberg Ministry for the Environment, Climate and Energy (UM), accessed on November 23, 2014 .

[Webcraft-3] super magnets. Webcraft GmbH, accessed on November 22, 2014 (commercial manufacturer website ).

[Datacom-4] ↑ ^a ^b ^c ^d ^e ^f ^g Klaus Lipinski: Energy density. DATACOM Buchverlag GmbH, accessed on November 22, 2014 .

[5] z.net - car battery sizes . October 9, 2018 ( kfz.net [accessed February 25, 2019]).

[ABC-6] ↑ ^a ^b ^c ^d ^e ^f ^g ^h Reinhard Löser: ABC of battery systems. Information about the common accumulators. (No longer available online.) BEM / Bundesverband eMobilität eV, April 2012, archived from the original on December 3, 2014 ; accessed on November 23, 2014 . Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. @1@ 2

[ETH-7] ↑ ^a ^b ^c ^d ^e ^f ^g Rolf Zinniker: Information sheet on batteries and accumulators. (PDF; 151 kB) (No longer available online.) August 25, 2003, archived from the original on November 28, 2010 ; Retrieved May 3, 2011 . Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. @1@ 2

[Schwungrad-8] Flywheel and flywheel memory. Energy in local transport. Energieprofi.com GmbH i.Gr., accessed on November 23, 2014 .

[EnergizerNiMH-9] NiMH battery type AA with 2300 mAh, 1.2 V, 30 g. Energizer, accessed November 22, 2014 (commercial website).

[CARMEN-10] Lithium-ion batteries. Centrales Agrar-Rohstoff Marketing- und Energie-Netzwerk eV, accessed on November 23, 2014 .

[Atkins-11] E. DT Atkins, PW Atkins, J. de Paula: Physikalische Chemie . John Wiley & Sons, 2013, ISBN 978-3-527-33247-2 ( limited preview in Google Book Search).

[heise-12] Battery manufacturer FZ Sonick is skeptical about the market for Zebra batteries. Heise Zeitschriften Verlag GmbH & Co. KG, April 12, 2010, accessed on November 23, 2014 .

[BOPB-13] I. Cyphelly, Ph Brückmann, W. Menhardt:. . Technical fundamentals of compressed air storage. (PDF, 1.27 MB) and their use as a replacement for lead batteries. On behalf of the Federal Office for Energy, Bern, September 2004, accessed on November 23, 2014 (page 37).

[EK-Li-14] Lithium-ion batteries. Energy density. Elektronik-Kompendium.de, accessed on November 23, 2014 .

[SionPower-15] Data sheet lithium-sulfur battery. (PDF, 142 kB) (No longer available online.) Sion Power, archived from the original on December 27, 2014 ; accessed on November 21, 2014 (English, commercial manufacturer's website). Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. @1@ 2

[efahrer-16] Hope for solid battery: series production started. Chip, accessed November 24, 2018 .

[Visco-17] Steven J. Visco, Eugene Nimon, Bruce Katz, May-Ying Chu, Lutgard De Jonghe: Lithium / Air Semi-fuel Cells: High Energy Density Batteries Based On Lithium Metal Electrodes. August 26, 2009, accessed on November 21, 2014 (English, Almaden Institute 2009. Scalable Energy Storage: Beyond Lithium Ion).

[Tadiran-18] Tadiran lithium batteries. Tadiran GmbH, accessed on December 5, 2015 (commercial manufacturer website).

[Thermit-19] Hans Goldschmidt: About the energy density of Thermite and some new technical applications of aluminothermics . In: Angewandte Chemie . tape 15 , no. 28 , 1902, pp. 699-702 , doi : 10.1002 / anie.19020152803 .

[AlAir-20] Shaohua Yang, Harold Knickle: Design and analysis of aluminum / air battery system for electric vehicles . In: Journal of Power Sources . tape 112 , no. 1 , 2002, p. 162-173 , doi : 10.1016 / S0378-7753 (02) 00370-1 ( sciencedirect.com ).