# Efficiency of converting sunlight into chemical energy?

#### ltlmissmegan

Hello!
I'm having trouble with this physics question:
A large tree collects sunlight over an area that is 8m in diameter. The average solar radiation is 168W/m^2. The tree grows for 8 months of the year and is dormant for 4 months of the year. After ten years the mass of the tree has increased by 540kg. What is the efficiency of converting sunlight into chemical energy?

I just do not know what formula to use

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#### studiot

1) Have you calculated the energy the tree collects in 10 years?

Don't forget to divide this by 2

2) What is the formula for efficiency?

I don't like formulae, thinking is much better.

You need to look up the heat of combustion of the wood that the tree has made.

That is the 'chemical energy'.

How are you doing now?

#### Pmb

PHF Hall of Fame
Hello!
I'm having trouble with this physics question:
A large tree collects sunlight over an area that is 8m in diameter.
Are you referring to a circle having a diameter 8m?

The average solar radiation is 168W/m^2. The tree grows for 8 months of the year and is dormant for 4 months of the year. After ten years the mass of the tree has increased by 540kg. What is the efficiency of converting sunlight into chemical energy?

I just do not know what formula to use[/QUOTE]

Its unclear to me what the area is that you're supposed to use. If its a circular area then use the area of the circle for the area in which the sunlight falls. Average solar radiation isn't clear to me either. Assume that its an average flux over the area (normal to a surface of that area). What is the energy that falls in that area per day? Per month? etc.

I doubt that you have enough information here to find what you want. You're not taking into account the water, carbon, etc that makes up the tree.

Where did this question come from?

#### studiot

Assume that its an average flux over the area (normal to a surface of that area). What is the energy that falls in that area per day? Per month? etc.
The average insolation is stated as 168 watts/sqm.

This includes time, but don't forget to divide the result by 2.

#### Pmb

PHF Hall of Fame
The average insolation is stated as 168 watts/sqm.

This includes time, but don't forget to divide the result by 2.
Average insolation is not a very precise term. Its unclear whether it means averaged over 24 hours or averaged over the time the sun is out, i.e. 12 hours.

This question doesn't appear to be from a text. If it was then it'd be stated with greater precision.

No offense ltlmissmegan.

#### studiot

Yes you smoked my meaning about the half.

#### ltlmissmegan

This question comes from an assignment written by my professor, so I believe he is referring to the fact that we only have sun 12 hours a day, for the 8 month the tree is growing.

I just don't understand how to calculate the efficiency, or how the tree's weight after 10 years (540kg) plays a part in this question.

#### Pmb

PHF Hall of Fame
This question comes from an assignment written by my professor, so I believe he is referring to the fact that we only have sun 12 hours a day, for the 8 month the tree is growing.

I just don't understand how to calculate the efficiency, or how the tree's weight after 10 years (540kg) plays a part in this question.
What are you studying right now. The subject matter can tell us something about what your professor is asking. Sounds like a strange question to me. I think your professor is making some invalid assumptions here.

#### ltlmissmegan

What are you studying right now. The subject matter can tell us something about what your professor is asking. Sounds like a strange question to me. I think your professor is making some invalid assumptions here.
He probably is, and we've been learning about solar thermal energy, and how PVs work.

#### oz93666

I just don't understand how to calculate the efficiency, or how the tree's weight after 10 years (540kg) plays a part in this question.
520kg of wet leaves and wood has been created , so just find out what energy is released when this is burnt ...

I'm sure a search will get the Joules released in burning a Kg of wood ... find out how much 'green' (fresh wet) wood gives Kg of dry wood ... then you can find the total energy 'harvested' by the tree in 10 years ...

The rest is easy ...