I Am Not a Crooke

At my parents' new condo where I've been staying, we have an interesting scientific trinket that once resided at my grandparents' house: a Crookes radiometer.  For those unfamiliar, they generally look like this (from Wikipedia):

When exposed to a light source, the vanes turn.  For a long time, the process that caused this was misunderstood.  Initially, it was believed that the momentum carried by the light was being transferred to the vanes.  The momentum carried by a photon is given by

where h is Planck's constant, and λ is the wavelength of the photon.  The majority of photons from the sun have a wavelength around 500 nm, giving a momentum of 1.3 x 10^-27 kg m/s.  Assuming the vanes are about 4 cm^2, there is about 1/4 watt worth of photons hitting each one at 500 nm.  Converting this into the actual number of photons gives about 6.3 x 10^17 photons/second.  We can find the force on the vanes by multiplying this by the single-photon momentum we found above.  This gives the miniscule force of 8.2 x 10^-10 Newtons, hardly enough to move anything macroscopic.

Aside from the lack of sufficient force, this explanation would also predict that the vanes would turn with the white side trailing.  The black sides would absorb the photons' momentum, but the white sides would reflect it, gaining twice as much.  However, as you can see from the animation above, the black sides trail.

It turns out the real explanation has to do with the heat the vanes gain from absorbing light.  The black sides heat more quickly than the white, creating a pocket of hotter air in front of them.  Near the edges of the vanes, the cooler air from the white side flows into the hotter air, pushing the vanes forward.