The footprints of coal and nuclear fuels.

In 2007, coal consumption in the United States – just for electric power generation – was 1.046 billion tons (1,046 million tons).

That’s a lot of coal.

Crushed bituminous coal has a bulk density of about 833 kg/m³, so therefore, that coal occupies a total volume of one cubic kilometer.
(1.046 billion tons / 833 kg/m³)^1/3 = 1.04 km.)

Combustion of coal produces carbon dioxide at a rate of about 1.83 kg CO₂ per kg coal.
Of course, CO₂ is just one particular component of the stream of dangerous waste output from coal combustion – there’s the particulate matter, the SO₂, the NO₂, the fly ash, the polycyclic aromatic hydrocarbons, and so forth.

So, each year, the use of coal for electricity generation in the United States generates 1.91 billion tons of CO₂ output to the atmosphere.

Applying the ideal gas equation, we can find the volume that this CO₂ occupies, assuming that it’s at a temperature of 300 K and a pressure of one atmosphere.

(T = 300 K is very frequently used as the value of “room temperature” or “ambient temperature” when performing scientific or engineering calculations in the Kelvin scale, since it’s a nice round number.)

(1.91 x 10⁹ tons * R * 300 K / (44 g/mol * 1 atm))^(1/3) = 9.90 km.)

The volume of CO₂ produced each year from coal-fired generators in the United States corresponds to a cube of CO₂ with a dimension of just under 10 kilometers on a side. Over the course of a decade, that adds up to a column of CO₂ which is 9.90 km on a side and occupies the entire thickness of Earth’s atmosphere.

But what about nuclear fuels?

Coal yields an output of thermal energy when it is combusted of about 24 MJ/kg – therefore, 1.046 gigatons of coal corresponds to about 2.28 x 10¹⁹ J of energy.

One atom of fissile nuclear fuel like uranium-235 generates about 200 MeV of energy in a nuclear fission – and of course, that atom of ²³⁵U has a mass of 235 u (atomic mass units).

So, to generate 2.28 x 10¹⁹ J of thermal energy, we need to fission about 277.7 tonnes of ²³⁵U.

((2.28 x 10¹⁹ J / 200 MeV) x 235 u = 277.7 tonnes.)

(By the way, did I ever mention that I really like Google calculator?)

Uranium is quite a dense material – metallic U has a density of 19.1 g/cm³.

Therefore, the amount of uranium required to replace that billion tonnes of coal is only a volume of uranium metal corresponding to a cube measuring about 2.44 meters, eight feet, on a side.

(((2.28 x 10¹⁹ J / 200 MeV) x 235 u / 19.1 g/cm³)^1/3 = 2.44 m.)

Now, I know what you’re probably thinking. That assumes that we’re using pure ²³⁵U as a nuclear fuel, and that it’s consumed in fission with 100% efficiency, and that is not the case with real, practical nuclear fuels in existing nuclear power reactors.

OK, so let’s revise the calculation a little to reflect the characteristics of a typical, existing light-water reactor more realistically.

A light-water reactor typically uses low-enriched uranium dioxide (UO₂) fuel, and a modern power reactor typically achieves a burnup of something like 50 GWd (thermal energy) per tonne U.

Therefore, the generation of 2.28 x 10¹⁹ J of thermal energy from a conventional, once-through, inefficient LEU fuel cycle in a light-water reactor requires the use of 5987.4 tonnes of low-enriched UO₂ fuel.

((2.28 x 10¹⁹ J / (50 GW days/tonne)) x (270/238) = 5987.4 tonnes.)

UO₂ has a density of 10.97 g/cm³.

Therefore, the amount of LEU uranium oxide fuel required to replace that billion tonnes of coal is a volume corresponding to a cube measuring about 8.17 meters, 27 feet, on a side. The used, irradiated fuel – even before any recycling or recovery of unused uranium and actinides is performed – occupies about the same volume. Yes, you can put it in a garage, or put it in a basement, or something.

(((2.28 x 10¹⁹ J / (50 GW days/tonne)) x (270/238) / 10.97 g/cm³)^1/3 = 8.17 m.)

Perhaps soon I certainly shall download SketchUp and have a play around with it in order to make some visualisations of these quantities.

Finally, a hat tip to Jason at Pro Nuclear Democrats for an interesting and very educational post which was my inspiration in creating this post.