Crookes radiometer

The Crookes radiometer, also known as the light mill or solar engine, consists of an airtight glass bulb, containing a partial vacuum. Inside are a set of vanes which are mounted on a spindle. The vanes rotate when exposed to light, with faster rotation for more intense light, providing a quantitative measurement of electromagnetic radiation intensity. The reason for the rotation has been the cause of much scientific debate.

It was invented in 1873 by the chemist Sir William Crookes as the by-product of some chemical research. In the course of very accurate quantitative chemical work, he was weighing samples in a partially evacuated chamber to reduce the effect of air currents, and noticed the weighings were disturbed when sunlight shone on the balance. Investigating this effect, he created the device named after him. It is still manufactured and sold as a novelty item.

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General description

The radiometer is made from a glass bulb from which much of the air has been removed to form a partial vacuum. Inside the bulb, on a low friction spindle, is a rotor with several (usually four) vertical lightweight metal vanes spaced equally around the axis. The vanes are polished or white on one side, black on the other. When exposed to sunlight, artificial light, or infrared radiation (even the heat of a hand nearby can be enough), the vanes turn with no apparent motive power, the dark sides retreating from the radiation source and the light sides advancing. Cooling the radiometer causes rotation in the opposite direction.

The effect begins to be seen at partial vacuum pressures of a few mm of mercury (torr) , reaches a peak at around 10⁻² torr and has disappeared by the time the vacuum reaches 10⁻⁶ torr (see explanations note 1). At these very high vacuums the effect of photon radiation pressure on the vanes can be observed in very sensitive apparatus (see Nichols radiometer) but this is insufficient to cause rotation.

The word-element "radio" in the title originates from latin and means "I radiate". Here it refers to electromagnetic radiation. A Crookes radiometer, consistent with the word-element "meter" in its title, can provide a quantitative measurement of electromagnetic radiation intensity. This can be done, for example, by visual or by visually-aided means (e.g., a spinning slotted disk, which functions as a simple stroboscope) without interfering with the measurement itself.

Radiometers are now commonly sold worldwide as an interesting household novelty ornament, no batteries needed, just light to get the vanes to turn; strong light gets them spinning furiously. They come in various forms, as the one pictured, and are often used in science museums to illustrate "radiation pressure" — a scientific principle that they do not, in fact, demonstrate.

Thermodynamic explanation

External radiant source motion

For any heat engine to turn, there must be a difference in temperature. In this case, the black side of the vane is hotter than the other side, as radiant energy from a light source warms the black side by black-body absorption faster than the silver or white side. The internal air molecules are "heated up" (i.e. experience an increase in their speed) when they touch the black side of the vane. The details of exactly how this moves the hotter side of the vane forward are given in the section below Explanations for the force on the vanes.

The internal temperature rises as the black vanes impart heat to the partial vacuum molecules, but they are cooled again when they touch the bulb's glass surface which is at ambient temperature. Heat loss through the glass keeps the internal bulb temperature steady so that the two sides of the vanes can develop a temperature difference. The white or silver side of the vanes are slightly warmer than the internal air temperature but cooler than the black side, as some heat conducts through the vane from the black side. The two sides of each vane must be thermally insulated to some degree so that the silver or white side does not immediately reach the temperature of the black side. If the vanes are made of metal, then the black or white paint can be the insulation. The glass stays much closer to ambient temperature than the temperature reached by the black side of the vanes. The higher external air pressure helps conduct heat away from the glass.

A strong vacuum inside the bulb does not permit motion because there are not enough air molecules to cause air currents to move the vanes and to transfer heat to the outside before both sides of each vane reach thermal equilibrium by heat conduction through the vane material. Higher inside pressure does not permit motion because the temperature differences are not enough to move the higher concentration of air. There is too much air resistance for "eddy currents" to occur. The slight air movement caused by the temperature difference is blocked by the higher pressure before the effects can "wrap around" to the other side.

Motion without external radiation

When heating the radiometer in the absence of a light source, it turns in the forward direction (i.e. the black sides trailing). You can place your hands around but not quite touching the glass and it will turn slowly or not at all, but if you touch the glass to warm it quickly, it will turn more noticeably. The directly heated glass gives off enough infrared radiation to turn the vanes, but if the hands are not touching the glass, the glass blocks much of the far-infrared radiation. Near-infrared and visible light more easily penetrate the glass.

If you cool the glass quickly in the absence of a strong light source by placing ice on the glass or in the freezer with the door most of the way closed, it turns backwards (i.e. the silver sides are trailing). This demonstrates black-body radiation from the black sides of the vanes rather than black-body absorption. It turns backwards because the black sides give off more heat and cool more quickly than the other side.

The rotation lasts only as long as the temperature of the glass is increasing or decreasing fast enough to overcome the friction of the spindle and faster than the temperature conduction through the vanes can cause the two sides of the vanes to reach equal temperature.

Explanations for the force on the vanes

Over the years, there have been many attempts to explain how a Crookes radiometer works:

1. Crookes incorrectly suggested that the force was due to the pressure of light. This theory was originally supported by James Clerk Maxwell who had predicted this force. This explanation is still often seen in leaflets packaged with the device. The first experiment to disprove this theory was done by Arthur Schuster in 1876, who observed that there was a force on the glass bulb of the Crookes radiometer that was in the opposite direction to the rotation of the vanes. This showed that the force turning the vanes was generated inside the radiometer. If light pressure was the cause of the rotation, then the better the vacuum in the bulb, the less air resistance to movement, and the faster the vanes should spin. In 1901, with a better vacuum pump, Pyotr Lebedev showed that in fact, the radiometer only works when there is low pressure gas in the bulb, and the vanes stay motionless in a hard vacuum. Finally, if light pressure were the motive force, the radiometer would spin in the opposite direction as the photons on the shiny side being reflected would deposit more momentum than on the black side where the photons are absorbed. The actual pressure exerted by light is far too small to move these vanes but can be measured with devices such as the Nichols radiometer.
2. Another incorrect theory was that the heat on the dark side was causing the material to outgas, which pushed the radiometer around. This was effectively disproved by both Schuster's and Lebedev's experiments.
3. A partial explanation is that gas molecules hitting the warmer side of the vane will pick up some of the heat, bouncing off the vane with increased speed. Giving the molecule this extra boost effectively means that a minute pressure is exerted on the vane. The imbalance of this effect between the warmer black side and the cooler silver side means the net pressure on the vane is equivalent to a push on the black side, and as a result the vanes spin round with the black side trailing. The problem with this idea is that while the faster moving molecules produce more force, they also do a better job of stopping other molecules from reaching the vane, so the net force on the vane should be exactly the same — the greater temperature causes a decrease in local density which results in the same force on both sides. Years after this explanation was dismissed, Albert Einstein showed that the two pressures do not cancel out exactly at the edges of the vanes because of the temperature difference there. The force predicted by Einstein would be enough to move the vanes, but not fast enough.
4. The final piece of the puzzle, thermal transpiration, was theorized by Osborne Reynolds, but first published by James Clerk Maxwell in the last paper before his death in 1879. Reynolds found that if a porous plate is kept hotter on one side than the other, the interactions between gas molecules and the plates are such that gas will flow through from the cooler to the hotter side. The vanes of a typical Crookes radiometer are not porous, but the space past their edges behaves like the pores in Reynolds's plate. On average, the gas molecules move from the cold side toward the hot side whenever the pressure ratio is less than the square root of the (absolute) temperature ratio. The pressure difference causes the vane to move cold (white) side forward.

Both Einstein's and Reynolds's forces appear to cause a Crookes radiometer to rotate, although it still isn't clear which one is stronger.

See also

• photophoresis.

References

• Loeb, Leonard B. (1934) The Kinetic Theory Of Gases (2nd Edition);McGraw-Hill Book Company; pp 353-386
• Kennard, Earle H. (1938) Kinetic Theory of Gases; McGraw-Hill Book Company; pp 327-337