Which way does a Crookes radiometer spin, and why?

Settled in 1879 by Osborne Reynolds (thermal transpiration), refined by Einstein (1924).

Kapitza's problem #194 asks students to analyze how the residual gas pressure and composition in a Crookes radiometer affects its spin rate. William Crookes invented the device in 1873 and initially misattributed its spin to radiation pressure, a claim briefly endorsed by Maxwell; simple radiation pressure predicts the wrong rotation sense and is many orders of magnitude too weak. Osborne Reynolds correctly identified 'thermal transpiration' -- gas flow driven along a temperature gradient at the vane edges -- as the dominant mechanism in 1879, and Einstein's 1924 paper added a complementary edge-force correction, together giving the accepted quantitative explanation.

A toy sold in gift shops spins the 'wrong way' for the explanation most people guess, and getting the right answer took the combined efforts of Maxwell, Reynolds, and Einstein.

Explanations that circulated

• Simple radiation pressure from photons pushes harder on the black (absorbing) side, spinning the wheel black-side-back (this predicts the correct rotation direction only by accident of sign error; actual radiation pressure would push the silvered side more, and is far too weak to explain the observed speed)
• The vanes are pushed by heated air molecules bouncing off the warmer black side like billiard balls (qualitatively closer, but the full quantitative mechanism is thermal transpiration/edge effects, not simple bulk bombardment)

References

• On certain dimensional properties of matter in the gaseous state, Osborne Reynolds, Philosophical Transactions of the Royal Society, 1879
• Einstein's 1924 analysis of radiometer edge forces (secondary summary), Albert Einstein (as described in modern review sources), Zeitschrift fur Physik (1924), summarized on Wikipedia/Physics Forums, 1924