I have often been asked questions like how
many cubic miles of CO_{2} do we produce when we burn a cubic mile of
oil, and how many ppms does that represent. In this post, I will make some
simplifying, yet reasonable, assumptions to provide answers to these and other
questions.
In round numbers, one cubic mile of oil
weighs 3.8 billion tons and contains roughly 3.2 billion tons of carbon. Burning
this quantity of oil produces 153 quadrillion Btu of energy, which we have
defined as 1 cmo. This combustion produces about 12 billion tons or 2.7*10^{14}
moles of CO_{2}. As a gas, the volume of CO_{2} depends on
the pressure and other variables. But let’s say we condense it into a liquid. Liquid
CO_{2} has a density of close to that of water. As a liquid the amount
of CO_{2} from burning a cubic mile of oil will occupy 3 cubic miles. If
we burn coal to get an equivalent amount of energy, we produce 17 billion tons of
CO_{2}, which as a liquid would take up 4.3 cubic miles. Burning
a cmo worth of natural gas will generate 7.5 billion tons of CO_{2}—about
1.9 cubic miles of liquid CO_{2}.
To determine by how much the
concentration of CO_{2} in the atmosphere changes when we burn a cmo of
oil, we need an estimate of the number of moles of gas in the earth’s
atmosphere. Here’s a guesstimate. The radius of the earth is 4000 miles, and so
its surface area, 4*pi*r^{2}, is approx. 200 million square miles, and if
we assume that the atmosphere extends to only 5 miles, the volume of atmosphere
is 1 billion cubic miles. If we assume that the pressure in this 1
billion cubic miles is 1 atmosphere and 27°C (it is not, but then the
atmosphere also extends to over 60 miles) we can estimate the number of moles
of gas in it using the ideal gas equation, PV = nRT. The number turns out to be
1.7*10^{20 }moles. Thus, CO_{2} introduced from burning a cmo
of oil corresponds to 2.7*10^{14}/1.7*10^{20 }or about 1.5 ppm
of the atmosphere.
Table. Volume of liquid CO_{2}
produced from burning of 1 cmo of various fossil fuels and its concentration if it all ended up in
the air.
Fuel

Volume Liquid CO_{2} (mi^{3})

Conc. in Air (ppm)

Gas

1.9

1.0

Oil

3

1.5

Coal

4.3

2.1

The world is currently releasing about
36 billion tons of CO_{2} each year from combustion of coal, oil, and
natural gas, and that would correspond to about 4.5 ppm. The global CO_{2}
level though is rising at the rate of about 2.5 ppm a year or about half the
value estimated. That is because about half of the emitted CO_{2} ends
up in the oceans and thus increasing their acidity. The increased acidity makes
it harder for corals, oysters, and plankton to develop their shells with potentially
dire consequences for the entire food chain!
An estimated
530 billion tons of carbon have been burnt since the start of the industrial
revolution. The expected rise in atmospheric CO_{2} concentration, if all of it
stayed in the air, would have been 245 ppm. The observed rise of 120 ppm
(current concentration of 400 ppm minus 280 ppm, the concentration in 1860)
jibes well with the assumed 50% staying in the air.
The greenhouse gas effect of the CO_{2} in air
amounts to increasing the radiative forcing by roughly 0.5 W/m^{2}. That
seems like a small perturbation compared to solar insolation of 1000 W/m^{2}
(at high noon). There is a nice video
describing how you can measure the solar insolation in your backyard with a
simple experiment. The net heat gained by the earth in a year can be estimated
by multiplying the surface area of the earth (41 10^{12} m^{2}) by the radiative forcing (0.5 W/m^{2})
times the number of hours (8760) in a year, and a factor that corrects for the fact
that only half
of the earth’s surface is facing the sun at a given moment as well as that the sun is
not overhead all the time. The result is a net heat gain of 563 trillion kWh or
12.5 cmo! Since we are currently consuming 2.75 cmo of fossil fuels per year
that the additional heat being trapped from the greenhouse effect is
fourandahalf times the energy released from burning of fossil fuels. There
goes the theory that the global warming is solely due to the heat rejected by
the engines.