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.