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Chapter 14: Problem 1

A large tree might have a trunk \(0.5 \mathrm{~m}\) in diameter and be \(40 \mathrm{~m}\) tall. Even though it branches out many times, pretend all the wood fits into a cylinder maintaining this \(0.5 \mathrm{~m}\) diameter for the full height of the tree. Wood floats, \({ }^{33}\) so let's say it has a density around \(800 \mathrm{~kg} / \mathrm{m}^{3}\). How many kilograms of \(\mathrm{CO}_{2}\) did this tree pull out of the atmosphere to get its carbon, if we treat the tree's mass as \(50 \%\) carbon?

Short Answer

Expert verified
Answer: To find the mass of CO₂ removed from the atmosphere, follow the steps in the solution: 1. Calculate the volume of the tree using the formula V = πr²h. 2. Calculate the mass of the tree using the formula m = ρ · V. 3. Calculate the mass of carbon in the tree by multiplying the mass of the tree by 50%. 4. Calculate the mass of CO₂ removed from the atmosphere by converting the mass of carbon to CO₂ using the molar ratio and molar masses. Once these calculations are completed, you will find the mass of CO₂ removed from the atmosphere by the pine tree.

Step by step solution

01

Calculate the volume of the tree

To find the volume of the tree, we will use the formula for the volume of a cylinder: \(V = \pi r^2h\), where \(V\) is the volume, \(r\) is the radius, and \(h\) is the height. We are given a diameter of \(0.5\,\mathrm{m}\), so the radius is \(0.25\,\mathrm{m}\). The height of the tree is given as \(40\,\mathrm{m}\). Thus, the volume is \(V = \pi (0.25\,\mathrm{m})^2 (40\,\mathrm{m})\).
02

Calculate the mass of the tree

To find the mass of the tree, we will use the formula: \(m = \rho \cdot V\), where \(m\) is the mass, \(\rho\) is the density, and \(V\) is the volume. We are given a density of \(800\,\mathrm{kg/m^3}\). Use the volume calculated in Step 1: \(m = (800\,\mathrm{kg/m^3}) \cdot V\).
03

Calculate the mass of carbon in the tree

We are given that the tree's mass is \(50\%\) carbon. To find the mass of carbon in the tree, we will multiply the mass of the tree by the percentage: \(\text{mass of carbon} = m \cdot 50\%\).
04

Calculate the mass of \(\mathrm{CO}_{2}\) removed from the atmosphere

To find the mass of \(\mathrm{CO}_{2}\) that was removed from the atmosphere, we need to convert the mass of carbon into the mass of \(\mathrm{CO}_{2}\). We can use the molar ratio for this conversion: \(1\) mol of carbon forms \(1\) mol of \(\mathrm{CO}_{2}\). The molar mass of carbon is approximately \(12\,\mathrm{g/mol}\), and the molar mass of \(\mathrm{CO}_{2}\) is approximately \(44\,\mathrm{g/mol}\). So, the mass of \(\mathrm{CO}_{2}\) removed from the atmosphere is: \(\frac{44\,\mathrm{g/mol}}{12\,\mathrm{g/mol}} \cdot \text{mass of carbon} = \frac{44}{12} \cdot \text{mass of carbon}\). Convert the result to kilograms.

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Most popular questions from this chapter

Our modern food industry has an EROEI of 0.1:1. In pre-industrial settings, when energy investment for food production was in the form of muscle power (animal and human), why would a 0.1:1 EROEI for food have been untenable? Next, describe the conditions for an exact break-even food EROEI of 1:1. What would this mean in terms of where effort/energy goes? What would this leave for building shelters, cathedrals, or esthetic pursuits?

The U.S. gets \(2.4\) qBtu per year of energy from burning biomass (mostly firewood). At an energy density of 4 kcal per gram, and a population of 330 million, how many 5 kg logs per year does this translate to per person?

If \(50 \mathrm{~kJ}\) of energy are spent to extract \(1 \mathrm{MJ}\) of energy content in the form of coal, what is the EROEI?

What fraction of the earth's 100 TW biological budget (all life on the planet) do you think is justifiable to use in service of human energy needs? Explain your reasoning. What does this become in TW, and how does it compare to our 18 TW current appetite?

Re-express an EROEI of \(1.5: 1\) in terms of how many total units of energy must be produced in order to extract one unit of net energy in a self- supporting operation.
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