A radiometer toy and its reversal
Jearl Walker www.flyingcircusofphysics.com
August 2014 A radiometer was a device invented in 1872 by William Crooke to measure the energy emitted by a light source, but today it is a novelty or toy sold in science shops. Inside a sealed, partially evacuated glass bulb, four vertical metal vanes are attached to a metal hub that can rotate around a vertical needle. The vanes have the same arrangement of colors: white on one side and black on the other side.
When the device is mounted near a light source, the vanes and hub rotate around the vertical needle, rotating faster for brighter light. What causes the rotation, what is its direction (does, for example, the black side of a vane lead), and how can it be reversed?
The motion is often attributed to the pressure of light, but that effect is far too small to observe with the toy and, besides, it would yield a rotation that is opposite what is seen. Here is the argument: Light can push on object, and the push is greater if the light reflects from the object. Thus, light shining on the vanes will push on the white sides more than the black sides, and the vanes should rotate with the black sides leading. Were the bulb almost fully evacuated, the vanes would indeed turn like this.
However, the pressure on the vanes due to the residual air gives a much larger effect. Because light (infrared radiation and visible light) is absorbed more on the black side of a vane than on the white side, the black side becomes slightly warmer than the white side. Because the residual air molecules run into a vane, they push on the vane. The faster the molecule is moving, the greater the push. The air molecules on the black side of a vane move faster than those on the white side because of the temperature difference. Thus, the push on the black side is greater than that on the white side, and the vanes rotate around the support pin with the white side leading. After a while, the two sides of each vane reach the same temperature (they reach thermal equilibrium), and the effect disappears and the vanes stop rotating.
To reverse the motion, put the toy in a refrigerator. The black side of each vane loses thermal energy slightly faster than the white side via infrared radiation, and so the white side then has the higher temperature and the greater push from the air. Again, the rotation continues until thermal equilibrium is reached.
The paper by Jane Wess, listed below, is a delightful review of various (some quite curious) radiometer designs.
Dots · through ··· indicate level of difficulty
Journal reference style: author, title, journal, volume, pages (date)
· Bell, R. E., (letter) “The reversing radiometer,” American Journal of Physics, 51, No. 7, 584 (July 1983)
· Crawford, F. S., “Running Crooke’s radiometer backwards,” American Journal of Physics, 53, No. 11, 1105 (November 1985)
· Bartels, R.A., "Do darker objects really cool faster?" American Journal of Physics, 58, 244-248 (1990)
··· Arenas, A., L. Victoria, F. J. Abellan, and J. A. Ibanez, “Dynamic characterization of a windmill radiometer,” European Journal of Physics, 17, 331-336 (1996)
· Guemez, J., C. Fiolhais, and M. Fiolhais, “Toys in physics lectures and demonstrations---a brief review,” Physics Education, 44, No. 1, 53-64 (January 2009)
· Wess, J., “Crooke’s radiometers: A train of thought manifest,” Notes & Records of the Royal Society, 64, 457-470 (2010, published online 22 September 2010)
··· Chen, S., K. Xu, and C. Lee, “The dynamic mechanism of a moving Crookes radiometer,” Physics of Fluids, 24, article # 111701 (2012)
··· Sheehan, D. P., D. J. Mallin, J. T. Garamella, and W. F. Sheehan, “Experimental test of a thermodynamic paradox,” Foundations of Physics, 44, 235-247 (2014)
· Castellon, E., “Application of the second law of thermodynamics to explain the working of toys,” Journal of Chemical Education, 91, 687-691 (2014)