The Crookes Radiometer, Part II

Sorry for the extremely long delay in this post—I just finished up my first semester of graduate school, and I felt clobbered. But now I am on break, and while we take a refresher and celebrate the New Year, let’s learn some science!

Since you’ve probably forgotten by now, I recommend you re-read my first post about the Crookes Radiometer, which is a bulb with a vane on the inside. Recall the problem: radiation pressure from light comes in two forms, reflection and absorption—though absorption is twice as weak, when light shines on the radiometer, it moves the wrong way, as if absorption is actually stronger. So what’s going on?

Well, I posed a challenge to readers of this blog to figure it out, and fellow reader/blogger Alexandra Greenbaum of comic writing fame came up with a partially correct answer! It was initially believed that this conundrum was caused by a temperature difference between the dark and light side of the vanes. Do you know how it’s bad to wear a dark colored shirt out on a very hot day? That’s because dark color shirts absorb light and heat up more quickly than light colors do, and so dark clothes will heat up more than light clothes. The same happens here—the dark part of the vane absorbs light while the light side reflects light, so the dark side becomes hotter than the light side! Inside the bulb, while it is a partial vacuum, it’s not a complete vacuum…there’s still some air in there. Therefore, when molecules of air hit the dark side, it absorbs some of the heat energy and pushes off with greater speed, causing a net force on the dark side. This solves the paradox, right?

Well, there’s a problem (womp womp). Even though the air molecules are producing this force on the dark side, they are also stopping the other molecules from hitting the vane! This ends up causing a balance that cancels out the force caused by the temperature difference, or so the scientists believed, so they threw this explanation out. It took none other than Albert Einstein to prove that scientists shouldn’t overlook this effect. While this balance occurs over most of the pane’s surface, it does not cancel out at the edges. This second order effect does indeed provide a force to push the vanes in the light-side-forward direction, but it is not large enough to fully explain this motion.

Ok, so we have a partial answer. What are we missing? A neat piece of physics called thermal transpiration. Though James Clerk Maxwell (see: Maxwell’s equations) published the answer in 1879 (the last paper prior to his death), he didn’t come up with it…it was actually an idea of Osbourne Reynolds (of “Reynold’s Number” science fame). The idea is that if you have a porous plate surrounded by a rarified (very small density) gas, and you have one side hotter than the other, then the gas interacting with the hot side will actually flow through to the cold side! This will create a pressure difference between the two sides of the plate, and when there’s a pressure difference, there’s a force. “But Dan,” you may be thinking, “the vanes are not porous. So why are you teaching me about thermal transpiration?” Great question! Well, if the temperature (and therefore pressure) difference is great enough, the air molecules will flow around the edges to the cool side, and will create this additional force.

If you combine the forces from each of these explanations, you can fully explain the Crookes Radiometer! In very sensitive radiometers, with near-vacuums much better than that of the Crookes Radiometer, you can actually detect the radiation pressure we discussed in the Part I. Pretty neat.

That’s all folks! Sorry again for taking so long. Stay tuned for more cool stuff!

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