# Fermi Problem Friday: How much energy do you save by having a white roof?

This Friday, in honor of my new facebook friend Steven Chu, I’d like to examine his “White Roofs” campaign through a Fermi problem.

Steven Chu has said that we could all save energy simply by painting our roofs white. The idea is the same one behind why I don’t wear a black shirt on a sunny day (and white after Labor Day). Black objects absorb light, and with it, heat, while white objects reflect it. So if you’re trying to keep your house cool in the summer, it makes sense to have a roof that reflects sunlight instead of absorbing it. Here’s the schpiel:

But how much energy do you save, really?

The Fermi Problem:

The solar flux at Earth’s atmosphere is about 1360 watts per square meter. About 0.3 of this is reflected back into space, while the rest is absorbed by the earth. Given the square footage of your roof, how much energy (assumed as heat) would a black roof absorb? How much energy would a white roof absorb?

Now, you could give Secretary Chu the benefit of the doubt and assume that black roofs absorb all of the sun’s energy, while white roofs reflect it all. But we’re talking getting people to actually paint their roofs white. For reals! So we’re going above and beyond the Fermi Problem protocol for this week’s problem.

How can we test the difference in absorption between light and dark materials? Let’s try placing two thermometers in the sunlight. Procure two boxes. Cover one with white paper, and the other with black paper. Put a thermometer in each box. Go inside and reread a few chapters of Dialogue Concerning Two New Sciences. Then check to see which thermometer reads a higher temperature. Let us know what you find out. Now use this information to calculate the energy you will really save by painting your roof white.

On Monday we’ll be posting the results from our own experiment. Send us a photo of your experiment to [email protected] with your name and a mailing address, and we will mail you something fun for your scientific efforts!

Now, are you going to do with all the money you save from lower electric bills minus the cost of the white paint? Buy Swedish fish, of course.