Clifton W. Draper The Pennsylvania State University University Park. 16802
The Crookes Radiometer Revisited A centennial celebration
It was a century ago this year that William Crookes introduced the scientific community to the Radiometer (I), that short-lived messiah of the corpuscular theory of light. Today the Crookes Radiometer (light mill, solar engine, solar wind vanes) has fallen to the rather unprestigious role of a gift shop knickknack. Most people are first acquainted with it in one of their high school science classes, and never hear of it aeain till their children ex~eriencethe same oriei" nal fascination. Even though in the hundred-year interval such renowned scientists as: Crookes, Reynolds, Dewar, Tait, Stoney, Schuster, Maxwell, Knudsen, Hettner, Czernv. Sexl, and Einstein. to mention a few. have worked on the theor; of the radiometric force, i t is tbday still only qualitatively understood ( 2 ) .To he sure it would he a far easier task to invoke quantum mechanics, energy levels, etc.. and e x ~ l a i nlasers to the nonscientist than to recount thekinetic theory necessary for the "correct" description of how the Crookes Radiometer works. Amona our learned faculties most either think they know and are completely wrong, or think they know and are only partly right. The most common explanation of the radiometric force goes something like this. Molecules are striking, accommodating, and then leaving the surfaces of the vanes. The molecules leaving the hot (blackened) side leave with an increased velocity relative to those leaving the cold (silvered) side. Because of this there is a larger momentum change on the hlack sides leading to a force driving the vanes silver side first. Upon closer scrutiny this theory fails. The Crookes Radiometers typically operate in the 10-100-p range: th> transition region from the Knudsen regime (mean free path >> dimensions of apparatus) to hydrodynamic flow. See Figure 2. The molecules with increased speed leaving the blackened surfaces are more efficient a t cutting down the flux (through collisions) of inbound molecules. So the incident flux on the warm side is less than that on the cold, and the two effects compensate. This theory was first proposed by Reynolds, and even though it is wrong it is still widely used today. The Reynolds explanation is often coupled with the idea of the Knudsen re-
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gime, the result of this being that the flux is the same on hoth sides (no collisions). Figure 2 demonstrates the complicated pressure dependence of the radiometer. I t is clear that the coupling is not justified. X for 50torr ?$ mm. Maxwell laid the groundwork for our present understanding of the radiometric force (3). His work showed that a temperature gradient must exist on the surface if tangential stresses are to arise. These stresses are the result of the gas slipping over the surface from colder to hotter places. T h a t such temperature gradients exist on the vanes was shown experimentally by Marsh (4). Einstein presented a simple account of how the length of edge (perimeter) was important in the radiometric force (5). This too was confirmed experimentally by Marsh, Loeh, and Condon ( 6 ) . Even though the instrument is today hut a toy, and the physics necessary to explain its functioning is tedious in the least, the Crookes Radiometer is deserving of far more attention in our exercises in science. Among the reasons: (1) William Crookes himself led a fascinating and diverse life, (2) the radiometer, like so many discoveries in science, has a history rich with accidental observations, lengthy and ingenious experimentation, and incorrect conclusions all leading to a not totally satisfying theory. (3) Finally, and perhaps most important, the Crookes Radiometer lends itself to a number of inexpensive to outfit, simple to perform, and easy to understand experiments that can he attuned to the audiences' level of learning. I wish to address myself to each of these points, though the first two in rather scanty detail as they have been discussed quite fully elsewhere (7-9). William Crookes' life has something for everyone (7). For the scientist a t heart, Crookes' many experiments de-
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Millimeters
Figure 1. Crookes Radiometer (coilrtesy of the Royal Society of London) 356 / Journal of Chemical Education
Figure 2. Values of the force F (in arbitrary units) on a movable vane in a Knudsen type gauge, pioned against log P,..,, for a series of distances b e tween heated surface and the vane. Taken from Dushrnan (ref. (2)).Original work by Bluche and Linwin.
scrihed in the most minute detail offer a wealth of reading. Althoueh his lack of formal schooline in mathematics and physicLleft him a t a distinct disadvantage with his contemuoraries.. Revnolds and Maxwell. his ahilitv to follow " through tedious experiments, jump on the occasional ambiguities, and simply conceive of the various apparatus made him a first rate experimentalist of his time. For antiscientists, who have mandatory credits in science forced on them, there is a four-year period in Crookes' life where he dabbled in the psvchic world of spiritualism, mediums, and . . s8ances. His involvement, announcement of intent t o d o a scientific investigation, the experiments he performed, and the controversy that accompanied his paper; on the subject are all captivating reading-good for the students who find most science "dry." Two fairly recent papers address themselves directly to my second point. They are hoth superh mixtures of science with just the right touch of history. "William Crookes and the Radiometer" (8),by A. E. Woodruff (who is also the author of an article entitled "The Radiometer and How it Does Not Work" (101, easy reading for those who find references (2) too rich) as the title implies, deals with Crookes, the radiometer, and the controversy it brought about. "Maxwell, Oshorne Reynolds, and the Radiometer" (9),by S. G. Brush and W. F. Everitt, presents a detailed look a t the early theories and their development, focusing attention on two of the great minds of the day. The numerous documents, referees' reports, and letters cited, offer a unique look a t these two men whose names are commonplace today. There are several reasons that radiometers lend themselves to being useful classroom tools. First of all, they are inexpensive and relatively easy to come by (for example: Edmund Scientific, 150 Edscorp Bldg., Barrington, N.J. 08007). However, the materials and tools needed to make radiometers are prohahly available in most high school physics or chemistry departments and, certainly, in any junior college. The engineering aspects in their construction is an interesting student project in itself. The radiometric force is dependent on many parameters: light intensity, residual gas pressure, temperature of the vanes, area (edge perimeter) of the vanes, and actual geumetry of construction. The numerous papers published in the 18701; on the radiometer are hoth readable and interesting sources for ideas along these lines. The exercise of traveling to a large university, and searching the library for the Royal Society publications of this period is a useful experience for all students. In order to convince you of hoth the simplicity and heauty of these experiments I will describe one in detail. This is the experiment performed by Arthur Schuster in 1876 (I1). It was the crucial experiment in eliminating one of two rival camps that had developed over the source of the radiometric action: direct uressure of liaht versus residual gas effect. The experiment was to suspekl the radiometer and obsrve the rotation of the casing. Schuster's reasoning was as follows. Newton's Third ~ a ; tells us for every force there is an equal and opposite force. If the radiometric force were due to radiation then the reaction would he on the sun, and the small amount of friction between the vanes and the needle supporting them would drag the casing in the same direction as the vanes rotated. Rut, if the rotation of the vanes were ". . . due to any interior action" the reaction would be imparted to the container, and it would rotate in the opposite sense relative to the vanes. The materials needed include a radiometer (the light weight-no fancy stand type) cork stopper
needle very fine (e.g.. thermocouple) wire or string (unless you have a cocoon fiber as Schuster used)
Figure 3. S c h e m a t i c of "Sehuster's Experiment.
some oil piece of mirror one intense light source (heat lamp, flood light) one focusable light and lens system (a small portahle He-Ne laser adds a dramatic touch) Figure 3 is a schematic of the ex~erimentalsetuo. The needle is fashioned into a hook an2 inserted in the cork. The small piece of mirror is elued to the cork. and the cork is then glued to the top of the radiometer. he fine wire or string is looped to the hook and the whole assembly is suspended from a lab stand into a saucer of oil so that the base of the radiometer just touches the oil. This serves to dampen oscillation and motion due to air currents in the room. The laser is lined up so as to bounce off the mirror and onto a ;creen. Finally the inrense light source is positioned n e a r the radiometer One note of caution-if w i n e a laser do n,lt turn it into your audience as eye damage could occur. The stage is now set. Your reference light dot is steady on the screen. When the intense light source is turned on, the turning of the casing will torque the mirror also, and the dot will move to the right or left. For a setup like Figure 3 (utilizing a 250-W infrared heat lamp, 0.003-in. thermocouple wire, roughing pump oil, 40-50-cm laser to mirror and mirror to screen dimensions) deflections of 15-20 cm are typically obtained. Light on to full deflection takes about 10 s. The motion is rapid and quite dramatic. You will find as A. Schuster did, and as I hope you all expected, that the casing moves opposite to the vanes. That is, that it is a residual gas effect, and not the pressure of light that causes the vanes to spin. For the higher level audience, the explanation can be put in terms of momentum imparted to the gas molecules, and then transversed to the walls. The experiment can he made more quantitative by using a hifilar, or other torsion-halance suspension and making some angle of deflection measurements. The formulas needed for calculations are available. A good starting place is Schuster's original paper (11 ). I hope I have been ahle to impress on yon the injustice we have done to Crookes and his Radiometer because of our neglect of them in these modern times. Let us on this, the occasion of the centennial of the Crookes Radiometer. find a new and higher place for them hoth. If nothing else when your son comes home and tells you of this "space age solar engine" you will he ahle to set him straight, maybe even tell him how it really works. Literature Cited Ill Crookes, W.,Proc. Roy. Soc.. Ser. A. 23.373 118761. 121 Durhman, S.. "Scientific Foundations of Vaeuvm Technique," 2nd Ed., .luhn Wiley and Sons, New York, 1949, D. 259: Kennerd, R.. "Kinetic Theory of Cares." 1st Ed., McCrar-Hill BookCo., Nev York, 1 9 3 8 , ~333: . Loeb. L.."KineticTheoryof G a r e ~ " 2 n dEd.. MrCraw~HillRnnk Cn.. N s r Ynrk. 1914. n 961. 131 ~ a x w e l iJ. , C.. phi!. Trons. Roy Sor. London. SOT.A . 170.291 11879b (41 Marrh. H.E..J. OolicnlSoc. Amer... 12.. I35 119261. 151 Ehstein.A..k. ~ h ; ~ i 27, h . .111920. 181 Mamh.H. E..Cnndon. E.,andLoeb. I.. R.. J. Opiicoi Sot. Arne,.. 11.257 119251. 171 Fournier d'Alhp, E.. "The Life of Sir Wiiiiam Crmkei." D. Appleton. New York. 19Zd; Hall. T.. "The S~iritualists:The Stow of h r e n c e Cook and William Crmkes," Helix P r l s . &w York, 1963. 181 Wmdruff,A. E.. Iris. 57,188 119661. 191 Brush. S. L a n d Rveritt. W. F.. His! Stud. P h w S c i , 1.105 119fi91. 1101 Wmdruff, A. R..Phys Teacher, 6.358 119681. l l i l Schuster.A.Phi1. Tmh*Roy. SDC.London. Ssr. A. 168,715 118761, ~
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Volume 53,Number 6. June 1976 / 357
