How much energy is in a tree?

Yesterday Cortex Futura tweeted about an article which seemed to him likely to be bullshit. But in the spirit of fairness and trying to hold a scout mindset, he asked whether he should pay attention to it rather than rejecting it out of hand. I always find those epistemic questions interesting: what is the process by which you decide that something is worth paying attention to or not? The article he pointed to seemed high in crankishness, but not all cranks are wrong.

I took a quick look at the article myself and decided that it probably was indeed nonsense. How did I do so? One thing that caught my eye was the claim, based on the principle that matter is convertible to energy and vice versa, that trees create their wood from the energy of the sunlight. My memory from school science lessons—a long time ago now, admittedly—was that the carbon in plants comes from the carbon atoms in carbon dioxide via photosynthesis. And I had a vague idea that when you convert matter to energy you get a hell of a lot of energy from a small amount of matter.

That was pretty much enough for me to reject it, but then I got totally sidetracked by the question of how much energy there is in a tree, and therefore just how implausible that claim is. We can work this out.

First we need to know how much matter there is in a tree. Googling “how much does a tree weigh?” feels a bit stupid, but helpfully the OneOak project gives us a bunch of stats about a single oak tree, which I hope is sufficiently representative of trees in general for our purposes. From this we can get the weight, the age and the diameter of that tree.

We also need to know how much energy is in matter, and Wikipedia tells us that it’s 25 billion kilowatt-hours per kilogram.

To start with, how much energy is there in the tree?

energy_per_mass = 25,000,000,000 kWh/kg
tree_dry_mass = 7860 kg
tree_energy = (tree_dry_mass * energy_per_mass)
  => 196,500,000,000,000 kWh

Okay, so that sounds like a lot, but we want to put it in context: is it plausible that the matter in the tree could be created from the energy in sunlight? And to work that out we’ll need to know how much sunlight could have fallen on the tree over its lifetime. Very roughly, there’s about a kilowatt of energy from sunlight reaching the earth’s surface per m² at midday, though it depends a lot on latitude, cloud cover, etc. so that’s closer to a maximum figure.

Helpfully, we have the tree radius, so if we assume it’s a circle then that gives us the area (looking top-down).

tree_radius = 8.9 m
tree_area = pi * tree_radius ^ 2 => 248.8456 m^2

Putting that together with the age we can calculate how much energy the tree has received over its lifetime. And of course, it’s night 50% of the time, so we’ll halve the number of hours in which the tree could have received light.

tree_age = 222 years
tree_daylight_time = tree_age / 2

daylight_energy = 1 kW/m^2
tree_energy_received =
  tree_daylight_time * tree_area * daylight_energy 
  in kWh
  => 242,128,222.1806 kWh

This is not looking good for the claim that the matter in the tree was created from the energy in sunlight: 242,128,222 kWh vs 196,500,000,000,000 kWh. So you would need roughly a million times the amount of energy that the tree could have received in order to create all that matter.

All the calculations here were done with Calca. I’ve been using it for years, but not for anything physics-related. I was very pleasantly surprised by its abilities with unit conversions.