Thursday, May 19, 2011

Can Killing Trees Save the World?

Here's my solution to yesterday's Fermi problem.

Just to remind you, I'm trying to determine whether it's possible to rely on trees to capture carbon from the atmosphere rather than developing technology to do it. Of course, once a tree pulls carbon dioxide out of the air, you'd have to get rid of the tree in some way that keeps the carbon locked up. (You can't burn it or let it rot, because that would just send carbon back into the air.)

The average US household produces about 7.5 tons of carbon dioxide. That's a bit under 7000 kilograms.

Carbon dioxide consists of one carbon atom and two oxygen atoms. Carbon is a bit lighter than oxygen, and only about a fourth of the carbon dioxide mass is due to carbon. So the average family is responsible for emitting

7000/4 kilograms of carbon = 1740 kilograms of carbon

Which I'll round up to 2000 kilograms to make the math easy . . .

Now, wood is mostly carbon. Precisely how much is carbon, I don't know, and because I'm lazy I'll just guess that it's at least half carbon. By my estimate, approximately 4000 kilograms of wood contains as much carbon as the typical US family releases into the atmosphere each year.

The US has about 300 million people living in it. I would imagine that most live in households with an average of about 3 people in each, which means there are about 100 million households in the US.

So, we put enough carbon in the air to equal . . .

4000 kilograms/household x 100,000,000 households = 400 billion kilograms of wood.

Is that a lot? I'm not sure. Let's see . . .

According to one reference I found, the US produced about 30 billion board feet of lumber in 2008.

A board foot is a one foot wide by one foot long by one inch thick piece of wood. That's about 30 centimeters by 30 centimeters by 3 centimeters, which is 2700 cubic centimeters.

Wood is about half as dense as water (again, I'm lazy, but that seems about right). And water is one gram per cubic centimeter, so one board foot has a mass of roughly 2700/2 grams = 1.35 kilograms, which I'll round to 1.5 kilograms.

In other words, the US timber industry annually produces about . . .

30 billion board feet x 1.5 kilograms/board foot = 45 billion kilograms of wood

Let's round it to 50 billion kilograms of wood.

That's equivalent to one eighth as much carbon as US households produce (based on the estimate of 400 billion kilograms calculated above).

To wrap it up, if we were to use trees to sequester carbon (by throwing them down a salt mine or encasing them in concrete), we would have to grow 8 times as much lumber as the entire US lumber industry produces annually - all for permanent disposal.

My conclusion - nope, it's not feasible to kill trees to solve our carbon emission problems.

Sorry kids. I guess you have some other way to save the planet.

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