- For calculating the greenhouse gas production due to burning any fossil fuel, all you need is the energy content and a rough chemical formula.
Reasonable quality coal of the type used in power stations has an energy content (higher heating value, or HHV) of around 30 MJ/kg. This number varies considerably depending on the source of coal. The chemical formula for coal is roughly (CH)n. Let's calculate how much coal we have to burn in a typical large power station to produce 1 GWe for a year. For this we have to assume a conversion efficiency η for thermal to electrical energy. Really good modern steam generators have η ≈ 0.4, so to generate 1 GWe we'll need a a thermal power of 1/0.4 = 2.5 GWth.
The total amount of thermal energy required to generate 2.5 GWth for one year is
(2.5)(3600 s/h)(24 h/d)(365 d/y)(109 W) = 7.9 x 1016 J.
The mass of coal that needs to be burnt to produce this energy is
(7.9 x 1016 J)/(30 x 106 J/kg) = 2.6 x 109 kg = 2.6 Mtonnes.
To convert this mass of coal to the mass of CO2 produced on burning, consider the chemical reaction:
4CH + 5O2 → 4CO2 + 2H2O
As, always when burning fossil fuels, every carbon atom in the fuel ends up in a CO2 molecule. The molecular mass of CH is 13; that of CO2 is 44. Thus 13 tonnes of coal produce 44 tonnes of CO2.
In other words, the 2.6 Mtonnes of coal burnt each year in a 1 GWe power station produces (2.6)(44/14) = 8.9 Mtonnes of CO2.
As we are using some rough numbers here and also ignoring CO2 emissions caused by mining and transportation of coal, let's call our result 10 Mtonnes of CO2 per GWe per year. Its hard to know what to do with 10 million tonnes of anything, let alone a gas (which at STP1 would fill 5 cubic km). However, this is the CO2 production from only one large coal-fired plant in one year. Two such plants are being opened in China every week2. Although ideas and plans abound3, no plant yet disposes of its CO2 anywhere other than in the atmosphere.
- 1. Hyper Physics. Ideal Gas Law (online). http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/idegas.html [9 June 2010].
- 2. BBC News. China Building More Power Plants (online). http://news.bbc.co.uk/2/hi/asia-pacific/6769743.stm [9 June 2010].
- 3. Wikipedia. Carbon Capture and Storage (online). http://en.wikipedia.org/wiki/Carbon_capture_and_storage [9 June 2010].
© Physics and Astronomy Outreach Program at the University of British Columbia (Chris Waltham 2010-06-09)