Picturing a Tonne of Carbon, and Energy from Dog-Excrement.

The question of, "what does a tonne of carbon really mean?", was put to me last night at a meeting of Transition Reading, a member of the rapidly growing Transition Towns movement, which I belong to, and which aims to achieve resilience at the level of local communities, to mitigate vulnerability to such external threats as peak oil, climate change and economic insecurity. Very often, measures of grams, kilograms or tonnes of carbon, or carbon dioxide are referred to, but practically these references are meaningless, since they do not readily convey an image of quantity, according to common experience. As a "visual" aid, let us consider what one tonne of carbon dioxide represents. The molar volume of an ideal gas at 25 degrees C (298 K) and standard pressure (1 atmosphere = 760 mm Hg = 101,300 Pascals) is 24.46 litres.

One mole of carbon dioxide (CO2) weighs (has a mass of) 44 g. Thus one tonne of CO2 contains 1,000,000g/44 g = 22,727.3 moles. Hence its volume under ambient conditions is 555,909 litres, or about 556 cubic metres. Again, this is not desperately helpful, and so to aid the "eye", we can imagine a cube, of side length 8.22 metres (27.0 feet), which is about the size of a fairly roomy two-storey house.

Now, if a tonne of "carbon" is referred to, we must multiply the above volume by a factor of 44/12, which is the ratio of the molecular mass of CO2 to the atomic mass of carbon, making around 2,039 cubic metres. Hence our house, still assumed to be cubic, now has a side length of 12.68 metres, or 41.6 feet and is accordingly a quite spacious dwelling.

As a rider to this, the topic of making biofuel from dog-excrement came up in conversation http://www.independent.co.uk/environment/green-living/fido-strikes-gold-with-britains-most-noxious-biofuel-dog-excrement-8591702.html which is a recent innovation. At a guess, I reckoned that the raw (dry) material probably has an energy density (that released through combustion) of around 15 GJ/tonne, which is close to that deduced from the combustion enthalpy of carbohydrate (glucose), 2801 kJ/mol  while the biodiesel from it is likely to have a much greater energy density, probably close to 38 GJ/tonne http://www.ipst.gatech.edu/faculty/ragauskas_art/technical_reviews/Energy%20Basics.pdf . Now this brings to mind an exhibition that I saw in the Deutsches Museum http://en.wikipedia.org/wiki/Deutsches_Museum in Munich last week, where I noticed a graph of energy density for different kinds of coal, which seemed to indicate that anthracitic coal (getting toward being pure carbon) had an energy density of 40 GJ/tonne, which is much higher than I had thought it to be, at nearer 30 GJ/tonne. So, let's see what the energy density of pure carbon is.

The enthalpy of combustion of solid carbon (in the form of  graphite), C+ O2(g) → CO2(g) = –393.5 kJ/mol. So, that is the amount of energy released by burning 12 g of carbon. Hence, burning a tonne of it would yield 393.5 x 1,000 J x 1,000,000 g/12 g = 32.8 GJ, which is close to my original notion. The quoted values for the energy content of different kinds of coal do vary somewhat, and this link http://rekauk.com/biomass-fuels cites a value for anthracite of 33.8 GJ/tonne. Now, this is very much at the high end of those various estimates that I have seen (typically in the range 27--30 GJ/tonne http://www.greenrationbook.org.uk/resources/biomass-energy/) and maybe it is too high, but the energy density given for chicken litter at 13.5 GJ/tonne is close to my original guess on the energy that might be recovered from burning a tonne of dog-shit, if indeed one felt compelled to do so!