Crookes Radiometer

The wrong explanation

In 1873, the chemist William Crookes invented a device consisting of four vanes mounted on a spindle inside a partially evacuated glass bulb. Each vane was blackened on one side and silvered on the other. When illuminated, the vanes spin — and Crookes believed he had directly measured the radiation pressure of light, the momentum carried by photons. This was an exciting claim: Maxwell had predicted that light should exert pressure, and here was a beautiful tabletop demonstration. The problem is that the vanes spin the wrong way. If radiation pressure were responsible, the reflective (silver) side should be pushed harder, since it reflects photons and receives twice the momentum transfer. That would make the vanes spin with the black side leading. Instead, they spin with the silver side leading — the black side is being pushed away from the light. Crookes had the mechanism exactly backwards.

The real mechanism: thermal transpiration

The correct explanation was worked out by Osborne Reynolds in 1879 and refined by James Clerk Maxwell in one of his last papers. The black surface absorbs more light and becomes hotter than the reflective surface. Gas molecules near the hot black side gain kinetic energy from the surface and bounce away with greater velocity, exerting more force on the black side. This thermal transpiration (or thermal creep) pushes the black side away from the light. Crucially, this mechanism requires gas molecules to mediate the force. In a perfect vacuum, there are no gas molecules, so the radiometer does not spin — only the negligible true radiation pressure remains, and it is far too weak to overcome friction. At atmospheric pressure, the gas conducts heat too efficiently (equalizing the temperature difference) and viscous drag stops the vanes. The radiometer only works in a narrow intermediate regime of partial vacuum (typically around 1 pascal), where the mean free path of gas molecules is comparable to the size of the vane. This is a beautiful example of a phenomenon that exists only within a specific parameter window.

Edge effects and the full story

Modern analysis (particularly by Scandurra, 2008, and Selden et al., 2009) has shown that the thermal transpiration picture, while correct in spirit, is itself an oversimplification. The dominant force at typical radiometer pressures comes from thermal edge effects: the temperature gradient is steepest at the edges of each vane, where the hot black side and cold silver side are separated by only the vane’s thickness. Gas flowing along this sharp temperature gradient from the cold edge to the hot edge creates a net force. This radiometric force explanation accounts quantitatively for the observed spin rates, while the simple “molecules bouncing off a hot surface” picture underestimates the force by an order of magnitude. The full story involves the Boltzmann equation in the transition regime between free molecular flow and continuum gas dynamics — a notoriously difficult regime to analyze. The Crookes radiometer, far from being a simple demonstration of radiation pressure, turns out to probe one of the most subtle corners of kinetic theory.