Golf balls and elephants – energy density in 9 seconds

I’m currently developing a short (2 minute, 30 second) animated video on nuclear power and climate change, with help from friend Ben Heard and the skills of Ron Furner and his team at Fury Films. Near the end of the vid, we talk about the vast amount of energy embodied in so-called ‘nuclear waste’ (or indeed, depleted uranium, or thorium). Here is a 9-second teaser (this is a draft, the final version looks better):

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So, the premise here is that 1 golf ball of uranium equates to a lifetime of energy for a person in a high-energy-use society like Australia or the US, and that if this same energy was supplied instead by fossil fuels, it would be the equivalent to about 800 elephants worth of coal (or thereabouts).

Here is how I came up with the comparison.

First to the golf ball of uranium (Nuclear waste is mostly uranium-238 and various minor actinides; we also have large stockpiles of depleted uranium that is left over from enrichment. Further, a lump of thorium-232, if used in an appropriate reactor that can breed uranium-233 [such as a molten salt isobreeder], would also have essentially the same energy equivalence. It’s a matter of picking your preferred heavy metal).

Density of uranium = 19.1 g/cc and Volume of a golf ball = 40.7 cc

So, the mass of a golf-ball-sized lump of uranium = 19.1 x 40.7… let’s say 780 grams.

Okay, what is its energy content?

Well, 1 fission of a Pu-239 nucleus (bred from fertile U-238 in a reactor) yields about 190 MeV of useable (non-neutrino) energy. A mole of it yields 6.023 E23 (Avagadro’s constant) x 190 x 1.602 E-13 (joules/MeV) = 18.3 TJ of energy. Thus completely fissioning 780 g of Pu-239 (its atomic mass is obviously 239) gives (780/239)*18.3 = 60 TJ (terajoules) of thermal energy.

Now, assume a 35 to 40% thermal-to-electrical conversion rate (e.g., higher-temperature reactor like the IFR or LFTR), and we have ~23 TJ of electrical energy, which is ~6.4 million kilowatt hours (kWh). This constitutes all of your lifetime energy use (stationary electricity, synthetic fuels, transport, food production, etc.). To put this into an everyday context, if you live 85 years, that’s an average of  a little over 200 kWh per day, which is in line with what David Mackay has estimated for places like Australia and the US. Maybe with future energy efficiency we will do better.

Right, so what if we did this with coal, instead?

The burning of 1 kg coal produces about 2 kWh of electricity. So to get the same electricity as the golf ball of uranium, we need to burn 3,200 tonnes of coal. Coal has a density of ~800 kg/m3 (kilograms per cubic metre), meaning 3,200 t/coal occupies ~4,000 m3. A single cube of coal of this mass would have dimensions of 15.9 m sides. A big block, to be sure.

Now, the important part — let’s turn this into elephant equivalents! (for fun illustrative purposes…)

A large elephant weighs about 5 tonnes, and this animal occupies about 5 m3 (given the handy fact that 1 m3 water = 1 tonne, and elephants, like people, are mostly water or at least made of other stuff that is approximately water’s density). So, the coal mass calculated above is equivalent to (4000/5) = 800 adult [coal] elephants.

An elephant of this mass is about 3 m tall at the shoulder. If the elephant was a solid cube, we might expect it to weight 3^3 or 27 t, but it’s obviously not (after all, there’s lots of legs and air space), so the ratio of height to mass is 27/5, or roughly a factor of 5.

From this, you can guess that a single very large elephant, weighing 3,200 t, would be expected to be roughly (15.9 x 5) = 80 m height at the shoulder (with its dimensions otherwise the same as a perfectly ordinary elephant).

A familiar visual icon, the Sydney Opera House, is 65 m high at its top wave. So another comparison is you can have a golf ball or uranium or a coal-elephant that towers over the Opera House, as illustrated below:

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That’s just the coal fuel, of course. Once it gets combusted in a power station, its carbon gets combined with atmospheric oxygen, and it ends up weighing 44/12 or about 3.66 times more in carbon dioxide. That’s almost 3,000 elephants worth of greenhouse gases.

So, which do you want hovering behind you as your energy legacy? A lump of metal that you can put in your pocket, or an army of  ‘energy pachyderms’ that would make Hannibal gape in awe? It’s surely a rather obvious choice. Energy density matters, and nuclear fuel is incredibly dense.

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26 Comments

  1. Actually mass will scale as the cube of linear dimension. So a single elephant massing 800 times as much as a 3m tall elephant – no matter what they are both made of – will be “only” about 28m tall.

    Your calculation would give the same result if you had taken the cube root of 27/5.

  2. With coal, the relevant volume might be considered as that of the CO2 at standard temperature and pressure.

    (Although it is interesting that coal plant effluent, if it were passed through a several-megatonne pile of olivine chips, would release several percent more heat than the initial burning of the coal with air yields. The CO2 would exothermically becomes solid mineral in the pile.)

  3. Hi Barry,

    The video will be great when finished. I haven’t checked the figures or calculations but have two minor niggles to point out.

    1. You mention the density of coal. However, you need to say whther that is the density in situ (before it is mined) or the density in a coal truck or coal dump. The latter is bulked up by about 1/3 so the density is less than in situ. Which value are you using?

    2. “cc” are not an SI unit. In fact they are strongly discouraged in the SI system as is “cm”. The correct unit is mL (and for others who may not be aware, capital L is the correct symbol for litre).

  4. Thanks for the comments. The full video will be featured in the next BNC blog post, as Ron is delivering it to me today.

    Joffan, you may be correct, I need to think about it. But for the final video, I went with the safer bet of 800 elephants spelling coal, as we thought it had more impact anyway.

    Peter, those cc units won’t be in the final vid, it was just for this blog post, but thanks for being a standards ninja! For coal density, I went with bulk density, see: http://www.engineeringtoolbox.com/classification-coal-d_164.html

  5. Heck Barry, this is addressed to a pretty stupid audience. For a start, it dignifies the anti-nuke concept of “nuclear waste” as in “waste, waste, nuclear waste! hiss, hiss…”. Then it uses the jargon of the wilfully ignorant*, as in “billions of kWh”. Strewth, if they are too ignorant to learn SI units, they won’t be hearing you out. Then to cap it off, you dignify their presumption that CO2 waste is okay, measuring it in terms of pink fluffy elephants!

    May I suggest that it be written as if the audience is someone who enjoyed doing science at school? Because s/he understands SI, the laborious arithmetic collapses into a couple of simple lines. The pitch can run then in terms of “nuclear leftovers” being converted across a lifetime into a golf ball sized lump of “fission products”. This in shocking contrast to the equivalent waste from coal of a thousand tonnes of CO2.

    It is at that point that evocative imagery can come in, that is, about the carbon waste. Waste! Half a million cubic metres of greenhouse gas! Up there forever, bringing storm, floods, drought, famines, all over the world, over and over, for thousands of years, to young people … just like you. All just because your superstitious elders were afraid of this little golf ball, buried deep underground.

    *(Electrical engineers, don’t hit me please. You know that using jargon is naughty, and you should be using SI when speaking to the public!)

  6. If a person uses 10 MWh per year, they need 10e6/(1500*24*365*0.15)=5
    (assuming a 15% capacity factor) 1.5kW solar PV systems + storage (times 3 if the PV panels last 25 years and a person lives till 75).

    And if you live on cereals, assume, 3.4 kCal/gm, 2500 kCal per day, wheat yield 2.5 tonne per hectare ((2500/3.4)*365)/250=1073 square meters of crop land (+storage).

  7. These sort of calculations are lots of fun, I’ve taken a stab at it some time ago and made some visual comparisons as well:

    http://energyfromthorium.com/forum/viewtopic.php?f=39&t=2757

    Calcs are for a molten salt reactor but it is very comparable to a sodium cooled fast reactor.

    Energy density is one of the main reasons I changed my mind about nuclear power. It vanishes many of the problems that nuclear power is critiqued about by people who haven’t ran these kind of simple numbers.

  8. Nuclear Submarines provide another great example. I’m borrowing a bit from Rod Adams and from some on-line info, but basically the nuclear reactor can drive a 9000 ton submarine at 20 knots underwater, almost indefinitely. The subs are only fueled once and it lasts for 35 years! The reactor also purifies the air. Typically the subs may stay under for 3-4 months. It is only the need for food (and crew morale) that it needs to surface at all.

  9. For a convenient check of my calculation, Barry, note that increasing an object’s linear dimensions by a factor of 10 will multiply its volume (and mass) by a factor of 10^3 =1000. So a scaled elephant 30m tall will mass one thousand times an elephant 3m tall.

  10. @Mark Robinowitz – Rossi has been analyzed before. He’s keeping the details secret and not letting them be independently verified. The best scientific take I’ve seen on the ‘Energy Catalyzer’ comes from the blog post Rossi energy catalyst – a big hoax or new physics? The comment from experimental physicist Joshua Cude identifies 5 easy measurements that need to be made on the setup. Measurements that Rossi isn’t doing.

    A friend of mine who knows some stage magic suggested that if skeptic James Randi were at the demo, he’d wander over to where the heater was plugged into the wall and joggle the plug enough to disconnect it. And see what happens.

  11. Bary,

    Quote
    Thus completely fissioning 780 g of Pu-239 . . . thermal energy.
    Unquote

    I think you may need to adjust your numbers (of elephants) a little bit because complete fissioning of a “lump” of fuel might not be possible.

    Is it possible to cause fission of all atoms in a given quantity of nuclear fuel? Does the fuel (U, Pu) not have an absorption cross section for neutrons that does not result in fission? And as a result of that absorption, and subsequent nuclear decay chain, the fuel might become “non-fuel”?

    Also, due to fission product build up, a given “lump” of fuel in a reactor may require several cycles of reprocessing and re-irradiation to get all the atoms get fissioned.

    I do realize that you are assuming use of fuel in a liquid form with continuous (on-line) reprocessing and its return back to the core. I feel that, in the present state of technology, building and operating viable power plants of this concept (LFTR) may take a long time yet. Reprocessing is a trouble-prone operation due to the difficult-to-deal-with chemical properties of the reactants and very high radiation fields which make maintenance a nightmare. With on-line reprocessing, any unavailability of the reprocessing part of the plant, would adversely impact plant’s capacity factor for electricity generation as well.

  12. Sanatanan – according to Charles Barton at NuclearGreen the Energy From Thorium site has been suspended for using too much bandwidth.

    Energy from Thorium has been suspended by its host, for allegedly using too much bandwidth. Kirk’s account was suspended after the first warning. This is silly and unprofessional. The suspension includes the discussion form and the document repository as well as the EfT blog.

    While Energy From Thorium is offline, you could check out a couple of the Google Tech Talks about thorium:

    Thorium Remix 2009 – LFTR in 25 Minutes edits several thorium presentations together.
    Energy From Thorium: A Nuclear Waste Burning Liquid Salt Thorium Reactor is one of the older talks. Kirk is an excellent speaker.
    Aim High: Using Thorium Energy to Address Environmental Problems takes a broader view.

    The Thorium Energy Alliance is also a good starting point.

    I hope Kirk gets his hosting problem sorted out quickly!

  13. Hmm, in the age of gigabite free email accounts and free streaming videos, suspending sites for using too much bandwith is not only unprofessional, it is also a sign of incompetence. Let’s hope the site goes up again, there’s lots of useful stuff there.

  14. Pingback: Safe, zero-carbon and proven: is fourth-generation nuclear the energy solution? » Zero Carbon City Gazette

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