Monday, September 8, 2008

Conjuring Trees From Thin Air?

At TED.COM, Jonathan Drori gave a talk claiming that graduates from MIT could not correctly answer the following four questions:
  1. An apple seed is small, but an apple tree is large. Where did all that extra mass come from?
  2. It's easy to light a flashlight bulb with a 1.5V battery and two wires, but can it be done with just one wire? (Presumably, no "lateral thinking" solutions, such as cutting one long wire to make two wires, are allowed.)
  3. Why is it hotter in summer than in winter?
  4. Draw a diagram of the solar system.
I believe that most students from Caltech would get all four mostly correct, although of course no one would be able to draw a perfect diagram of the solar system off the top of their heads. (However, I did recently have a conversation with one Caltech graduate who, although he could answer question one correctly, tripped up on its inverse. That is, he thought that when a human loses weight, that weight comes out in their poo.)

Question 1 is the one I want to focus on, because I think that the guy who was giving a talk about how people get it wrong, was himself wrong. In his talk, Drori claims that 99% of the mass of a piece of wood comes from the air.

Eighth grade biology gives us the tools to figure this out. Trees are made of cells, and cells bags holding organic molecules floating around in water. So the mass of a tree is mostly organic molecules and water. The organic molecules come in different varieties, but lots of them are carbohydrates having the empirical formula CH2O. The series of reactions that makes these carbohydrates is photosynthesis, summarized by:

CO2 + H2O -> CH2O + O2

So the mass of the tree comes primarily from carbon dioxide and water. There are other things sucked up by the roots - the tree needs plenty of nitrogen to build amino acids, various other chemicals such as phosphorus and iron, and these along probably add up to more than 1%, but let's just think about the carbon dioxide and water.

The carbon dioxide comes from the air - that was Drori's point. The most important element in life is carbon -sometimes people refer to terrestrial beings as carbon-based life forms. Trees get their carbon from the air. Fine. But that's not the whole story. Trees need lots of water, too. And they get it from the ground.

How do I know they get their water from the ground? Because in my new apartment, there are a bunch of trees on the back patio. They're all dead, because the previous tenants believed what Drori said, and thought the trees would suck up water from the air around them. Nope. Empirical evidence in the form of very dead trees now suggests that you have to pour water on the ground around the trees, and then they can suck up that water through the ground.

PS - when you lose weight, you're going the other way from photosynthesis, turning carbohydrate and oxygen into water and carbon dioxide. So the weight you lose comes out partially as water, which has lots of ways to exit the body, and partially as CO2, which is exhaled. Every time you breathe out, you're losing weight - at rate of about a pound every 50,000 breaths (based on breathing 15 times a minute and burning 2000 calories a day).


Nikita said...

Synthesis of carbohydrates in trees, as far as I know, is much more complicated. First sugar (well, glucose) is synthesized from water and CO2. Then there are some long elaborate processes I fail to remember.

You're probably right though. I'm not sure what percentage of a tree's weight is water but I'd guess it's around 50%.

Markkimarkkonnen said...

Photosynthesis is way complicated. You can learn a good amount of chemistry, as well as a bit of statistical mechanics, by studying it carefully. I was simply skipping to the punch line there.

Ian said...

This post reminded me of a line of thought I had once during a hike:

When you look at a coniferous forest from the ground you can see that most of the trees have very tall thin trunks, and don't have present branches or leaves (needles) until they get close to the top. Presumably this is because the forest canopy is dense enough that most of the sunlight doesn't reach the ground, and for each tree it isn't as energetically worthwhile to bear leaves down in the shaded area. In places like the redwood forests of northern California, the trees are so tall that it almost seems like they're having some kind of tree-height arms race, where each tree has to grow as tall or taller than the others in order to collect any of the sunlight for itself. This process takes a great deal of time, energy and resources, and given that most of the tree's mass ends up in the trunk, this competition almost seems a little wasteful.

So the question I came up with of was, if you could somehow get the trees to 'agree' not to compete in such a way, so that each tree didn't have to grow so tall in order to reach the same amount of sunlight at the top of the canopy, where would all the now-absent tree material (and associated free energy) actually be?

And I'm not just presenting this as some sort of pseudo-philosophical koan. I have a rough sketch of the answer mapped out in my head, and it involves a bit of thermodynamics. Actually, I think I'm pretty far off from having a complete explanation. One specific thought experiment is the following: If you could only look straight down on the the forest (say, from a satellite or something) so that you could see only the tops of the trees but not their trunks, would there be some way of measuring how much energy they were devoting to their height? To phrase that from a more scientifically interesting perspective, exactly what observations would you have to collect from an extrasolar planet in order to tell if there was life on it (intelligent or otherwise)?

Markkimarkkonnen said...

Well, I don't know the answer to your question, either, but here's a guess:

You have a forest where the average height of trees, and to take things a little further, the average biomass per acre, is staying constant when averaged over a year.

In that case, it doesn't matter how tall the trees are, since in a forest of short trees or a forest of tall trees, energy is not being stored on average.

However, a tall forest does undoubtedly store more energy than a short forest. So maybe a question would be: what would happen if all the trees in a forest started growing taller and taller?

This would realistically happen after a fire, say. In that case the forest is storing some percentage of the energy that falls on it, as opposed to the equilibrium-height forest, which is not.

So my guess is the growing forest will just be that much colder while it's growing. Then when it reaches its final height, it will return to a slightly higher temperature.

If the tree were getting shorter, on the other hand, their free energy would be released and the forest would be a little hotter for a while.

However, I think it's a small effect because you simply can't store a large percentage of the incident free energy. Imagine all the trees are growing one meter per year, and are filling 4% of the 3D space of the forest (this is one 20-cm thick tree per square meter of floor space). Then I estimate you're getting about 3*10^8 Joules stored per year-square-meter, or 10 watts per square meter of energy being stored by these fast-growing trees.

I believe we average 160W/m^2 of solar energy on the surface of the Earth, so that's actually a pretty significant fraction being captured.

Unfortunately, the temperature of a radiating body scales with the one-fourth power the amount of energy being radiated. So if you capture 5% of the energy, the temperature only goes down 1%.

On the other hand, 1% of 300K is 3K, which could possibly be measured.

But there are probably lots of other effects that plant life has on temperature, so it would be hard to isolate this. Also, I think my estimates were pretty generous in terms of plant growth speed.

Anonymous said...

what do you guys know about a fruit's mineral content as it ripens? on/off the tree?


Markkimarkkonnen said...


i know nothing of such issues. perhaps you can ask the fruit itself?

Ian said...

I found an atmospheric chemistry book chapter that outlines the first principles of the argument I was thinking about. It's actually written buy a Caltech GPS prof, who I guess we should probably talk to if we want a well-informed answer to this question.

Basically, the Earth is in thermal equilibrium with the influx of solar radiation, so the planet is not actually collecting any net enthalphy. The Earth is, however, collecting a great deal of negative entropy. It's accepting energy from a low-entropy state (a parallel beam of short-wavelength photons) and emitting it in a high-entropy state (isotropically radiated long-wavelength photons).

So, although it isn't actually collecting net thermal energy from the sun, it is collecting a net positive amount of Gibbs free energy. I think that's what ends up being stored in the trees. I still can't decide if this would be externally measurable though.

And as far as the fruit thing goes, I think the vitamin content could change while ripening on vs. off the tree, but the mineral content won't.