## Friday, December 5, 2008

### Energy density

Energy density

The energy density of coal, i.e. its heating value, is roughly 24 megajoules per kilogram.
The energy density of coal can also be expressed in kilowatt-hours for some unit of mass, the units that electricity is most commonly sold in, to estimate how much coal is required to power electrical appliances. One kilowatt-hour is 3.6 MJ, so the energy density of coal is 6.67 kW·h/kg. The typical thermodynamic efficiency of coal power plants is about 30%, so of the 6.67 kW·h of energy per kilogram of coal, 30% of that—2.0 kW·h—can successfully be turned into electricity; the rest is waste heat. So coal power plants obtain approximately 2.0 kW·h per kilogram of burned coal.
As an example, running one 100 watt computer for one year requires 876 kW·h (100 W × 24 h/day × 365 {days in a year} = 876000 W·h = 876 kW·h). Converting this power usage into physical coal consumption:
876kW.h/2.0kW.h/kg=438 Kg of Coal=966 pounds of Coal
It takes 438 kg (966 lb) of coal to power a computer for one full year. One should also take into account transmission and distribution losses caused by resistance and heating in the power lines, which is in the order of 5–10%, depending on distance from the power station and other factors.
Relative carbon costBecause coal is at least 50% carbon (by mass), then 1 kg of coal contains at least 0.5 kg of carbon, which is
0.5kg/12.kg/kmol=1/24kmol
where 1 mol is equal to NA (Avogadro Number) particles. This combines with oxygen in the atmosphere during combustion, producing carbon dioxide, with an atomic weight of (12 + 16 × 2 = mass(CO2) = 44 kg/kmol), so 1⁄24 kmol of CO2 is produced from the 1⁄24 kmol present in every kilogram of coal, which once trapped in CO2 weighs approximately
1/24kmol.44kg/kmol=11/6kg=1.6kg
. This can be used to put a carbon-cost of energy on the use of coal power. Since the useful energy output of coal is about 30% of the 6.67 kW·h/kg(coal), we can say about 2 kW·h/kg(coal) of energy is produced. Since 1 kg coal roughly translates as 1.83 kg of CO2, we can say that using electricity from coal produces CO2 at a rate of about 0.915 kg/(kW·h), or about 0.254 kg/MJ.
This estimate compares favourably with the U.S. Energy Information Agency's 1999 report on CO2 emissions for energy generation, which quotes a specific emission rate of 950 g CO2/(kW·h). By comparison, generation from oil in the U.S. was 890 g CO2/(kW·h), while natural gas was 600 g CO2/(kW·h). Estimates for specific emission from nuclear power, hydro, and wind energy vary, but are about 100 times lower. See environmental effects of nuclear power for estimates.