Talk:Energy density

Some rambling request

I see that articles on various kinds of batteries claim they have a "high energy density". I want a single table that gives actual numbers. Is this the right place for such a table?

Requests

Thanks to all contributers for an EXCELLENT article!!! If anyone can obtain the information, I would LOVE to know the energy density of the following:

• gunpowder (and other explosives)
• solid rocket fuel
• clockwork spring
• latex (or other elastic materials), which is used in modern catapults

If adding too many materials makes the list too long, perhaps it can be broken into groups (e.g. explosives, nuclear physics, elastic, momentum etc). --New Thought 12:02, 6 August 2006 (UTC)

Would like to see battery energy density covered here, with some common types listed, like lithium ion, alkaline, lead acid, NiCd, etc.

• Added lithium ion. mastodon 22:22, 8 March 2006 (UTC)
• Added clockwork spring (correct term is "power spring") jhallenworld

Thanks very much - much appreciated! New Thought 21:55, 26 October 2006 (UTC)

The flywheel entry should be removed. its not a constant - 66.92.33.119 20:00, 2 September 2006 (UTC)

I strongly disagree. I think most people will know its an approximation - and this is infinitely more useful than no information at all. --New Thought 06:52, 4 September 2006 (UTC)

I was going to suggest that we add the equation for energy in a flywheel, but it's there if you follow the link. --jhallenworld

Liquid hydrogen and compressed gaseous hydrogen at 700 bar should both have a higher energy per mass density than hydrogen at STP, because both do work as they expand. As an approximate calculation, 1 mole of ideal gas expanding isothermally from 700 bar to 1 bar at 300 K does 16340 J of work. Since hydrogren is 0.001 kg per mole, that gives an additional 16.3 MJ/kg for compressed hydrogren at 700 bar vs. hydrogren at STP. However, someone should find the exact numbers, because hydrogen isn't really an ideal gas, and the expansion isn't necessarily isothermal.

Merge

I say we merge. Thoughts? mastodon 22:22, 8 March 2006 (UTC)

• I say don't -- energy density per unit mass is one thing, energy density per unit volume is quite another. Since energy density can mean either in common usage it needs its own page. (A volume energy density has units of pressure, and many volume energy densities act almost exactly like pressure; one is the kinetic energy density of the molecules in an ideal gas (which acts exactly like pressure) and another is magnetic pressure. zowie

---

This page should go into Hydrogen versus Batteries (electric) as the energy storage medium for transportation of the future.

no - link to this page from that page - there's more to energy density than hydrogen v batteries. --New Thought 12:02, 6 August 2006 (UTC)

(Sorry, forgot to sign the last) I haven't seen any discussion in a long while on the merge issue, so I've removed the merge tag.

zowie 23:55, 16 April 2006 (UTC)

From PNA/Physics

• Energy density - Needs cleanup for narrative viewpoint, and would probably be better folded into vacuum energy based on its current content. --Christopher Thomas 22:56, 6 Jun 2005 (UTC)

Why is the Nuclear Fission/Fusion energy density by volume marked n/a?

It seems to me that for a given amount of, say, U235, there should be a given volume associated with that mass, and hence, an energy density by volume.

Are the entries just set to n/a because no one has done this calculation, or because such a calculation can't legitimately be done? And if they can't be done, could someone please add an explanation to the page explaining why they're marked n/a?

Otherwise, I'd guess one could take the average relative density of U235 and use the mass numbers to compute an average energy density by volume. It sounds like it would be very high: uranium is pretty dense, so 1KG of it would be pretty small.

Thoughts?

I don't know why it's that way, but I like it. Many fission devices use forcible implosion, which drastically changes the volume of the fissionable material. Most nuclear fusion in our vicinity takes place in a gaseous medium, which has no definite density -- be it the interior of the Sun, an exploding nuclear weapon, a tokamak, or a detonating inertial confinement fusion pellet. zowie 19:35, 28 July 2006 (UTC)

clarification of table (volume v weight)

I don't know why, but it took me a minute or two to figure out why the numbers in the columns weren't monotonically increasing. I added the "by weight" and "by volume" sections so that no one else has to think too much about it. I couldn't figure out how to make the text normal (no bold, no italics). can any one else make it look better?

Btu/gal

Btu/gal (both US and UK) are non-SI units, non metric system. It's time we got rid of such things, mostly because at the conversion of units page there are 8 different listings for the definition of Btu, and 4 different defintions for the gallon (UK and US). That's ridiculous. The metric system was designed a very long time ago to get rid such idiotic confusions, and make most conversions in metric are as easy as moving the decimal point around, including converting between volume/mass using the aqueous sp.gr≈1 g/cc of water, then multiplying with actual sp.gr. I guess the US being pretty much the only country with nonmetric units, hangs on to confusing units because it's easier to keep the population in the dark to be unable to evaluate prices properly so it's easier to "market to them". In any case, for Btu/US gallon, using 1 Btu=0.0010550 MJ, and 1 gal=3.785412 L, I calculated 1MJ/L=3588.07 Btu/gal, while the factor used in the table seems to be around 4308 (Btu/gal) / (MJ/L). Can anyone highlight the source of such a large discrepancy? Sillybilly 18:46, 26 November 2006 (UTC)

Serious discrepancies between similar data tables

I note that the data table here and the one in Fuel economy in automobiles contain some of the same information but with totally different values. I went through the table in that article and corrected the numbers that I was able to using the Bosch Automotive Handbook, which is a very authorative reference. The numbers in this table that should match are very different. This really does not reflect well on wikipedia in general.

I believe that we need to consider having this type of data contained in a separate article on properties of materials as it makes little sense to have separate tables in separate articles containing different values for the same physical properties. --Athol Mullen 22:53, 26 November 2006 (UTC)

You are right. If you find better updated references, please fix the data. But I'd like to temper the attitude a bit, as far as expecting science to be super accurate. Yes, there are super accurate measurements for the speed of light, or for the unit electric charge, because they are so important, but a lot of the stuff just doesn't get enough lab measurement investment, and sometimes super accurate results are not of interest, but measurement cost and labtime cost is balanced with need. In particular I had to calculate a lot of the values by hand using http://webbook.nist.gov/chemistry/name-ser.html, and by no means am I as authoritative as a published source doing calculations, and I can make mistakes. Futher below there is an outline of what I did. Still small discrepancies in fuel values for crude oil and coal are acceptable, because, for instance, there is a discrepancy between what is meant by "gasoline" because gasoline is a blend of hydrocarbons, and varies from source to source, from oil well to oil well, and varies over time even from the same oil well. For instance aromatic hydrocarbons which have a higher octane values than alkanes, but lower MJ/kg fuel values because benzene's overall formula is C6H6, with a C:H ratio closer to 1:1, while alkanes are CnH2n+2 (n=7 for heptane, n=8 for octane), roughtly C:H closer to 1:2, more hydrogen than carbon meaning more MJ/kg. So small discrepancy between values might be understandable, perhaps a range should be given, instead of a value to 2 decimal places. When you buy gasoline, it is the octane value that's guaranteed, not the fuel value. On the other hand, the values for methanol and ethanol should be exact, because these are pure chemicals, and there is no excuse for the same 22.61 MJ/kg for both methanol and ethanol. So now I took the values from the fuel economy page and entered them here. Of course there is the water distillation azeotrope and 100% pure ethanol issue, which fuel is actually getting used, but the error in the value listed on this page was still huge, listing methanol and ethanol with the same value. It never occured to me to check values in that table that were already there when I came to this page. Note that discrepancy in reported values is not unusual, see [1] and [2] for values all over the place, though true, the error is less than what was originally on this page. I prefer going with the DOE reference on those pages. Still, here is a double check: At http://webbook.nist.gov/chemistry/name-ser.html we enter methanol, click search, click on condensed phase thermochemistry data, because we want to deal with the heat of formation of the liquid, not the gas, and find these values for ΔHf°, depending on reference:

ΔfH°liquid -238.4 kJ/mol Ccr Baroody and Carpenter, 1972 ALS

ΔfH°liquid -239.5 ± 0.2 kJ/mol Ccb Chao and Rossini, 1965 see Rossini, 1934; ALS

ΔfH°liquid -238.9 ± 3.6 kJ/mol Ccb Green, 1960 Reanalyzed by Cox and Pilcher, 1970, Original value = -238.5 ± 0.2 kJ/mol; ALS

ΔfH°liquid -250.6 kJ/mol Ccb Parks, 1925 ALS

I'm assuming these references are all actual lab measurements instead of citing yet another citation, because that's really the only way to tell. No matter how authoritative a published reference is, if you can't measure those values in a lab, then it's worthless. The ultimate authority is always with Nature and experimental measurement. The Ccr and Ccb above mean rotating and static bomb calorimetry methods. In view of using different experimental methods, the values are pretty close. Note the dates of measurements - more recent ones probably have better instrumentation. While the 239.5±0.2 Chao-Rossini value is from 1965, it says see Rossini 1934, it might actually be a 1965 published reference based on a 1934 measurement. Also, note how different the 1925 data is. So when picking a number to calculate with, we still have to pick whose labwork we want to rely on, and these numbers are actually wonderful, have a scientific feel to them, because too perfect data with too many decimal places is sometimes absurd. I don't like authoritative sources that are too accurate, I'd rather have a wild array of different sources with very little authority disregarding each other and each telling me a different number, and then I go an compare. This is real life. Your task is to pick a number out of thin air given these 5 values! You still have to do some picking, and it's better than the situation with an authoritative single answer. Also note that the 1960 Green value has a lot more error, ±3.6, but such numbers are still much preferable to dry numbers such as Baroody-Carpenter and Parks, without ± ranges given. I don't mind if the error is high, but still, give me the error. Technically all of our wikipedia energy density data should have a ± sign next to it, throughout the table, that would be true science. I highly dislike reading Premium Gasoline 32.84 MJ/L, 43.50 MJ/kg on the fuel economy page. 32.84, 4 signifcant digits? You're dreaming! Premium gasoline is not such a pure and uniquely identified material, moreover even the same exact sample will be measured different by different labs, or even the same lab. 32.8, or 33±2 is probably a normal answer. Anyway, back to cherry picking a ΔHf° for methanol, I like the value 238.9 kj/mol. How about you? So now we look at the combustion equation

CH₃OH+1/2 O₂-->CO₂+2 H₂O

ΔHf° for O2 is 0, by definition, but looking up the ΔHf° for CO2 and water both in the gas state at standard conditions - note your car doesn't exhaust gases at STP. In fact I don't even know off first hand what temperature is used for the NIST webbook data, some 3 minute of effort of mine went wasted trying to find out, I'm assuming all their ΔHf° values are given at the same reference temperature throughout, whether it's 20°C, 25°C or 0°C. So back to CO2 gas and H2O gas at reference condition, after doing some cherry picking (with much more accurate numbers), I come up with -393.5 and -241.83 kJ/mol.

So armed with these values, the ΔHf° for the overall reaction is 2*(-241.83)+(-393.5)-(-238.9)=638.26 kJ/mol liquid methanol combusted to water vapor and carbon dioxide cooled back to standard temperature. From the methanol page in wikipedia we find that the molar mass is 32.04 g methanol per mole. So that gives 638.26 kJ/32.04 g methanol, or 19.92 kJ/g, or 19.92 MJ/kg. Bingo, that number matches the fuel efficiency page and the DOE article, yay!, and not the 22.61 value that was on this page, so those two places seem to be more authoritative than the others, more trustworthy, because they match each other, plus they match the calculation I did based on a 3rd source. So now I'll take the values for ethanol found in both these authoritative places that match each other, the fuel efficiency wikipedia page and the DOE article, and hope they will be true. Note the real authoritative way is to redo the calculation for ethanol, and even then, the real authoritative way is going to the lab and doing the measurement yourself, because otherwise you have to trust someone else's labwork, something you read somewhere, and how do you know they didn't just pick it out of thin air? Multiple sources enhance trust, but you never get full certainty. Who's got all day and all life to keep doublechecking and calculating everything? Only paranoid people keep checking and checking things over and over because of mistrust. You mistrust everything by default, as a matter of fact, but you don't go around being obsessed with mistrust. When you come across an error you point it out and correct it, but sometimes false info gets quoted all over the world for a long time til it's realized it's wrong. Still, "given enough eyeballs, all bugs are shallow" is what wikipedia is about. Eventually all bugs should be hammered out, if it wasn't for all the pranksters and more subtle deliberate wikipedia derogators, wikipedia should gravitate to something better and better. By the way, to finish up the calculations, from the methanol wiki page we get the density as 0.7918 g/cm3, and doing a quick google on methanol msds specific gravity, we find 0.7910, 0.795 and 0.8, so the wikipedia number is "nice". Note that density to 4 significant digits probably requires temperature control to 3 significant digits or better. Ever try that, controlling temperature well within 0.1 °C? It's not easy. So, going with 0.7918 g/cm3, or .7918 kg/l, the 19.92 MJ/kg value translates to 19.92 MJ/kg * 0.7918 kg/L = 15.77 MJ/kg. Note 4 decimal place is absurd, because who will ever combust methanol and cool the exhaust vapors to standard conditions exactly? But anyway, you get the method, and you can calculate more such values for yourself, and double check values if you want. Sillybilly 08:54, 28 November 2006 (UTC)

See the heat of combustion and heating value pages for other set of values. Heat of combustion was understood here by me as the energy content, which represents the ΔH, enthalpy change, and then a second column with energy extraction efficiencies is added to deal with the subtle issues. All heat engines have low Carnot-cycle efficiencies, most cars being on the order of 25%, power plants on the order of 35% efficient. Technically, instead of enthalpy the ΔG, Gibbs free energy should be used, because that limits the availability of how much work can be extracted, or more exactly, gives you how much work can be extracted even from reactions without enthalpy change, but a significant ΔS entropy change (a large enough entropy change can drive a "negative heat of reaction" value, such as in ice packs[3], and can drive engines based on only entropy change). So, should we list the ΔG free energy values instead of the ΔH values as customary for fuel heating values? ΔG=ΔH - TΔS, T in Kelvins, (ex. 25°C=273.15K+25=298.15K, plug it in) you can do the above calculations again. But from the methanol combustion reaction 1.5 moles generating 3 moles, and gases at that from a liquid, the entropy change is very positive and a significant driver without even looking up the values, and gives "extra" energy values. The [4] page citing 22.034 MJ/kg for Methanol based on the ΔG Gibbs function instead of the 19.9 MJ/kg based on the ΔH heat of combustion bomb calorimeter value used by the DOE article citation. The difference is using two different meanings of stored energy - technically ΔG is what's correct, but ΔH is easier to measure. Technically there is some extra driving force present as entropy energy and that much more work(handed over as shaft power, battery electricity) could be extracted besides the heat energy driving force, because there is that extra nudge, extra form of thermodynamic energy present, in the form of entropy drive. But in view of the 30-50% efficiencies of even the best fuel cells, hairsplitting doesn't make sense, especially because the ΔG is very application dependent (i.e. is your upper Carnot cycle temperature in a natural gas combined cycle turbine 1200°C , or are you just dealing with just 150°C steam, the carnot efficiencies will vary tremendously, and but so will the ΔG values), so ΔG is very application dependent and highly sensitive to temperature, as noted in the equation ΔG=ΔH - TΔS, while ΔH is relatively constant for all temperatures, and therefore you can provide it as a single value with less confusion, even if it's technically not the "proper" energy storage value to cite. Still the ΔG° values should be the technically proper things to cite, because they represent the energy values that can be theoretically extracted from the system, whether it's more or less than the "heating value" ΔH part, based on how the entropy part happens to drive the system, whether it's positive and giving extra energy, or negative, consuming a large chunk of the heating value away, and in extreme cases, consuming it all. For instance, the reaction 2H₂+O₂--->2H₂O has approx. the same ΔH value at any temperature, but an unfavorable negative entropy change, up to the point that at 2500°C the 3->2 molecule entropy reduction is so severe, that the reaction won't go forward at all, and no energy is extractable at all from hydrogen fuel, because ΔG is 0, or even negative, where water will thermolyse and self split up into H₂ and O₂ instead of H₂ and O₂ reacting together to give water. Thus hydrogen has a high heating value at any temperature, but less and less "free energy" extractable the higher the temperature. This fact is useful for high temperature electrolysis, but "unuseful" for high temperature fuel cells such as solid oxide fuel cells running at 1000°C, with low temperature Proton exchange membrane fuel cell running at 30°C giving better performance, at least as far as the ΔG part is concerned, or at least the "stored energy density" value is concerned. To reiterate again, the same hydrogen will look more energy rich, or have a higher energy density to a PEMFC than to an SOFC, simply because they operate at different temperatures, and if there were a fuel cell that ran at say 2499°C instead of 2500°C where it hits 0, the fuel value of hydrogen for it would be probaly less than 0.001 MJ/kg instead of the 120 listed in this table, calculable by ΔG. Above 2500°C the true fuel value, or ΔG would be 0. It's pointless to cite the standard free energy of formation at 25°C if your engine doesn't operate at 25°C. So that's another aspect of what "energy density" means at all. It's still important to have some kind of hierarchy and table listing these values, to get a good feel for things such as just how good a fuel gasoline is, how different batteries and liquid hydrogen are, and such things as fuel content of plastic, cow dung and household waste, even if the true fuel value, ΔG is such a vague concept without temperatures fixed to actual operating conditions. Sillybilly 09:24, 28 November 2006 (UTC)

an error imho

mass-energy equivalence 89,876,000,000 MJ/kg protons in the Large Hadron Collider 6.7 ×10^14 MJ/kg

I know how the author thought this "protons in the Large Hadron Collider 6.7 ×10^14MJ/kg" but it's some missconception to say that energy of relativistic particle is the total relastivistic energy and the mass is only the rest mass (in stacionary state) so i thing there can't be written that energy densyty of something is grater than equal tu E=mc^2 eqantion, even hadron in hadron colider not, all energy has it's owen mass —The preceding unsigned comment was added by 147.32.122.137 (talk) 00:49, 9 December 2006 (UTC).

This is the energy of protons stored in the collider. Energy is energy-- total relativistic energy counts if you're in a frame to see it. In this case, particles trapped in a collider add "invariant mass" to the collider equal to their rest mass PLUS their kinetic energy. In this case where the net linear momentum is zero, the relativistic energy/c^2 IS the rest mass of the system. The collider is heavier (if you could weigh it) by not only the weight of the protons, but their kinetic energy also. SBHarris 03:38, 9 December 2006 (UTC)

The first writer is right. You cannot have more energy than E=mc^2. Breaking that equation would have quite...interesting consequences.--Darin-0 15:25, 30 January 2007 (UTC)

Storage density limits

Some years back I saw a theorem that related maximum achievable energy storage density to materials strength. (Not just restricted to mechanical-energy storage systems, as I recall.) Unfortunately I can't remember the details, and can't find the theorem now - any chance of somebody including this in the article? --Calair 23:31, 13 December 2006 (UTC)

As materials strength is a mechanical phenomenon, I believe you must have seen a mechanical-energy storage system discussion - such as discussion of the area under stress-strain curve, or discussion of a flywheel. Note that gravitational potential and electric potential energies are directly related to forcefields (usually force is kE, while energy is kE²/2), therefore maximum energy stored automatically means maximum force developed and sustained by load bearing elements, but even in a capacitor, usually the dielectric breakdown issues happen way before mechanical strength limits are reached. I don't see how chemical or nuclear energy storage densities would be related to mechanical strength - e.g. energy released in a fire(reaction) has nothing to do with how strong the fuel was, for instance a liquid or gas is not very strong mechanically (it falls apart) but it may burn a lot hotter than some chunk of solid coal or chunk of steel bar. There are many ways to store energy, and mechanical strength is the pivotal issue for mechanical storage, it can be an issue for electrical field potential storage as in capacitors but usually it's not, and it is a nonissue for chemical potential storage such as electric batteries and fuels, or nuclear storage. Sillybilly 18:36, 10 January 2007 (UTC)

Values and Estimates

Yes, I think there is something wrong here with quoting numbers that can be :-

accurate figures for some chemicals,

calculated from enthapies of formation etc (eg ethanol),

good approximations for imprecise mixtures,

usable in calculations with a reasonable accuracy,

and wild guesses

that cannot be used for proper calculations for example figures for flywheels.

The energy stored in a kilogram of gasoline/petrol is say 43 MJ/kg.

How much energy is stored in a stationary 1kg flywheel? And in one spinning at 10,000 RPM? And at 20,000 RPM. Maybe the article means the stored at the flywheels maximum RPM. Is it a large radius flywhel spinnin slowly, or a small radius flywheel spinning fast. Okay, the maximum energy stored might be independent of the flywheel size. Is it a hollow flywheel? What is it made from?

I believe the rotational speed of a flywheel is limited by the tensile strength of the material used and then the energy it will store is then further defined by the density of the material. I think either flywheel should be dropped from the list, or a very specific example should be quoted, eg solid carbon fibre disc of density 1750 kg/m3 and radius 10cm spinning at 50,000 RPM.

Other examples too like batteries will depend on how thick the container is and what it is made from, etc. If a reader is to have any confidence in the figures on Wikipedia, I think we need to separate usable scientific information eg chemical enthalpies, from rough guides that might indicate whether batteries of flywheels should be considered for a real world application, based on approximate values, or real values for very specific similar but different products.

If table entries can be coloured, I would favour a different colour scheme for measured scientific enthapies of combustion etc, eg ethanol, iso-octane, and finger in the air estimates, eg flywheel, battery.

I been thinking about colouring too, I totally agree with that idea, but I'm mainly offline these days and only get internet at the library, so I can't really sit down and spend a lot of time tinkering with it. I was especially going to take out the redundant "burned in air" comments I put in earlier, because throughout the table it's pretty much assumed, except for uranium, liq h2+o2, thermite, etc. Most practical energy carriers are chemical energy carriers and they imply combustion in atmospheric oxygen, as opposed to most batteries and rocket fuel where the oxidizer has to be carried along. Which is why metal air, or organic-air "batteries" (or other non-thermal-engine ways of getting at the energy) will be the future, IMHO. Sillybilly 21:39, 25 June 2007 (UTC)

Crysta1c1ear 17:55, 24 June 2007 (UTC)

per mole

Is a unit like BTU/scf also considered energy density? scf is not a unit of volume, but a unit of quantity. — Omegatron 03:32, 5 June 2007 (UTC)

other popular candidates

NaBH4 <-> NaBO3 solution ... proposed by millenium for fuel cell chlorine to sodium chloride solution

can some knowledgeable soul run these?--Oldboltonian 21:36, 6 June 2007 (UTC)

LH2/GH2

Liquid hydrogen and gaseous hydrogen do *not* have the same energy content -- gaseous hydrogen (room temp) has significantly more, by virtue of being warmer. The heat capacity of hydrogen is non-trivial. At atmospheric pressure, the difference is about 4MJ/kg. Reference: NIST thermophysical properties of fluid systems, [5].

hydrogen peroxide decomposition

hydrogen peroxide decomposition (as monopropellant) 0.33 MJ/kg ?? -It looks strange that energy density of this redox chemical reaction is as low energy density of melting ice. I made an approximative computation using AM1 semiempirical quantum mechanical method in Arguslab 4.0 and I got about 2.43 MJ/kg, the computation could be wrong of about 10% but not 10times. But I better discuse it before changing.