One Gallon of Gasoline

I found this claim by David Archer rather incredible:

If we add up the total amount of energy trapped by the CO2 from the gallon of gas over its atmospheric lifetime, we find that our gallon of gasoline ultimately traps one hundred billion (100,000,000,000) kilocalories of useless and unwanted greenhouse heat. The bad energy from burning that gallon ultimately outweighs the good energy by a factor of about 40 million.

Archer, David (2008-10-06). The Long Thaw: How Humans Are Changing the Next 100,000 Years of Earth's Climate (Science Essentials) (p. 174). Princeton University Press. Kindle Edition.

Is it believable? Let's do the math, but let me start by saying that his statement "energy trapped by the CO2 from the gallon of gas [\$1.59 at the pump for me yesterday, btw] over its atmospheric lifetime..." is a bit odd. CO2 doesn't really "trap" energy, it just sort of impedes its flow. So let me just assume that he means that the heat content of the climate system will increase by that much, and see where that leads.

So far we have added something like 356 Giga-tonnes of carbon (Gtc) to the atmosphere, and one common estimate is that if we add another 565 we will increase the temperature by 2 C. In the (slightly crude) linear approximation that works out to 1 C/460 Gtc or 2.2 x 10^-3 C/Gtc or 2.2 x 10^-18 C/g. One gallon of gasoline contains about 5700 g of carbon, so (still in our linear approx) it should raise the temperature by 1.3 x 10^-14 C.

To determine how much that is in Joules, I need to know the heat capacity of the climate system. Again I will make an approximation, namely that the heat capacity of the system is the heat capacity of the ocean. The specific heat of water (another approximation, since ocean is not pure water) is 4.17 J/(g C), and the mass of the ocean is about 1.35 x 10^24 g. Change in energy content is then mass x specific heat x dTemperature = 7 x 10^10 Joules, which is a factor of more than 5000 less than Archer's 100 billion kilocalories = 4.18 x 10^13 Joules. I guess that he might have meant 100 billion Joules.

So, the answer seems to be that that 1 gallon of gasoline does indeed translate into a hella lot of extra energy in the climate system - which, by the way, is enough to melt more than 200 tonnes of ice, but not enough to melt the million tonnes of ice implied by Archer's number.

Consider my mind blown. I mean, I can handle melting 200 tonnes of ice to go to the McDonald's, but a million tonnes seems excessive.