Connecting CMOs, ppms, and joules

I have often been asked questions like how many cubic miles of CO₂ 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*10¹⁴ moles of CO₂. As a gas, the volume of CO₂ depends on the pressure and other variables. But let’s say we condense it into a liquid. Liquid CO₂ has a density of close to that of water. As a liquid the amount of CO₂ 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 CO₂, 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 CO₂—about 1.9 cubic miles of liquid CO₂.

To determine by how much the concentration of CO₂ 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*r², 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*10²⁰ moles. Thus, CO₂ introduced from burning a cmo of oil corresponds to 2.7*10¹⁴/1.7*10²⁰ or about 1.5 ppm of the atmosphere.

Table. Volume of liquid CO₂ produced from burning of 1 cmo of various fossil fuels and its concentration if it all ended up in the air.

Fuel	Volume Liquid CO2 (mi3)	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 CO₂ each year from combustion of coal, oil, and natural gas, and that would correspond to about 4.5 ppm. The global CO₂ 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 CO₂ 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 CO₂ 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 CO₂ in air amounts to increasing the radiative forcing by roughly 0.5 W/m². That seems like a small perturbation compared to solar insolation of 1000 W/m² (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 10¹² m²) by the radiative forcing (0.5 W/m²) 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 four-and-a-half 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.