A Back-Of-The-Envelope Calculation

I was reading Ron Bailey's comments on world energy which cites Daniel G. Nocera's Daedalus article in estimating global energy consumption at 102 TW in 2050. After paying the $10 for the full text, it turns out that Nocera gets his figure from the UNDP World Energy Assessment. Since a terawatt is a measure of energy per unit time (specifically, watts per second) that should come in at 3.22x10²¹ Joules, or 3.22 zetajoules, but the 2000 report suggests something more like 1.041 ZJ, which may be because of the confusion over peak versus average capacity.

Anyway, as a thought exercise, I figured it might be interesting to calculate how much boron such a scenario might be required to fuel all that consumption. From the Wikipedia entry on terrestrial fusion reactions:

8.6x10⁶ eV/atom • 6.02x10²³ atom/mol / 10.811x10^-3 kg/mol •
1.602x10^-19 J/eV = 76.7x10¹² J/kg

So that's almost eighty terajoules per kilogram of boron. Pretty sweet. Now, take a look at this:

1.041x10²¹ J / 76.7x10¹² J/kg = 13.6x10⁶ kg

or about 13,500 tonnes of boron annually. (Of course, this doesn't adjust for inefficiencies in the process; just as a guess, assume the whole process is something like 25% efficient, so consumption is more like 54 kt.) According to Roskill, the world is lately using 1.6 Mt of boron annually, which would make this figure well within reach hardly put a dent in world production.

Update 12/1/06: corrected for the error in Avogadro's number, which makes this look even more obscenely desirable. For a 1 GW power plant running at full capacity all year, that means

86400 s/day • 365.24 day/year • 1x10⁹ W = 31x10¹⁵ J

and

31x10¹⁵ J / 76.7x10¹² J/kg / .25 = 1.6 t

One and a half metric tonnes per year. Now I'm all full of boron-lust... can we just get to fusion... please?