An open letter to Steve Levitt

Globe

So already you should be beginning to suspect that this is a pretty trivial part of the Earth’s surface, and maybe unlikely to have much of an effect on the overall absorbed sunlight. In fact, it’s only 0.01% of the Earth’s surface. The numbers I used to do this calculation can all be found in Wikipedia, or even in a good paperbound World Almanac.

But we should go further, and look at the actual amount of extra solar energy absorbed. As many reviewers of Superfreakonomics have noted, solar cells aren’t actually black, but that’s not the main issue. For the sake of argument, let’s just assume they absorb all the sunlight that falls on them. In my business, we call that “zero albedo” (i.e. zero reflectivity). As many commentators also noted, the albedo of real solar cells is no lower than materials like roofs that they are often placed on, so that solar cells don’t necessarily increase absorbed solar energy at all. Let’s ignore that, though. After all, you might want to put your solar cells in the desert, and you might try to cool the planet by painting your roof white. The albedo of desert sand can also be found easily by doing a Google search on “Albedo Sahara Desert,” for example. Here’s what you get:

GoogleSand

So, let’s say that sand has a 50% albedo. That means that each square meter of black solar cell absorbs an extra 125 Watts that otherwise would have been reflected by the sand (i.e. 50% of the 250 Watts per square meter of sunlight). Multiplying by the area of solar cell, we get 6.66 trillion Watts.

That 6.66 trillion Watts is the “waste heat” that is a byproduct of generating electricity by using solar cells. All means of generating electricity involve waste heat, and fossil fuels are not an exception. A typical coal-fired power plant only is around 33% efficient, so you would need to release 6 trillion Watts of heat to burn the coal to make our 2 trillion Watts of electricity. That makes the waste heat of solar cells vs. coal basically a wash, and we could stop right there, but let’s continue our exercise in thinking with numbers anyway.

Wherever it comes from, waste heat is not usually taken into account in global climate calculations for the simple reason that it is utterly trivial in comparison to the heat trapped by the carbon dioxide that is released when you burn fossil fuels to supply energy. For example, that 6 trillion Watts of waste heat from coal burning would amount to only 0.012 Watts per square meter of the Earth’s surface. Without even thinking very hard, you can realize that this is a tiny number compared to the heat-trapping effect of CO2. As a general point of reference, the extra heat trapped by CO2 at the point where you’ve burned enough coal to double the atmospheric CO2 concentration is about 4 Watts per square meter of the Earth’s surface — over 300 times the effect of the waste heat.

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