Crookes Radiometer

The Crookes radiometer was invented by the chemist Sir William Crookes as the byproduct 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 devised the device named after him, still manufactured and sold to this day as a curiosity item.

The radiometer consists of 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, are several (usually four) lightweight metal vanes. Each vane is polished on one side, and blackened on the other. In sunlight, or exposed to a source of infrared radiation (even the heat of a hand nearby can be enough), the vanes turn with no apparent motive power.

One misconception (often seen in explanatory leaflets packaged with the device) is that the radiometer is demonstrating the pressure of light, but this is not the case. If this explanation held, the better the vacuum in the bulb, the less air resistance to movement, and the faster the vanes should spin: in fact, the radiometer only works when there is low pressure gas in the bulb, and the vanes stay motionless in a `hard' vacuum. In addition 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, though it exists, and can be measured with devices such as the Nichols radiometer, is far too small to move these vanes.

The actual explanation has to do with temperature differentials between the two sides of the vanes. The blackened side, absorbing radiation, is slightly hotter than the silvered side.

A second misconception was that gas molecules hitting the warmer side of the vane will pick up some of the heat i.e., will bounce off the vane with increased velocity. 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 it only works when the vanes are heating up. After the vanes have heated up and reach thermal equilibirum, the pressure on both sides should be equal. If you imagine a closed cylinder with one end hot and the other end cool, if there was an excess amount of pressure on the hot end, the cylinder would constantly accelerate without any outside force which is impossible. What will instead happen is that the density will decrease on the hot side so that the pressure on each side is equal.

The actual reason for the motion of the radiometer was determined by James Clerk Maxwell and Osborne Reynolds in the later portions of the 1800s. The actual effect occurs at the edges of the vanes. Basically, on the hot side, the gas molecules are moving with higher average speed than the gases on the cold side. When the hot molecules hit the edge of the vane, on average they will produce a force on the vane that is towards the cool side. When the cool molecules that are passing in the other direction hit the vane, they will on average produce a force that is towards the hot side. Since the average speed of the hot molecules is greater than the average speed of the cold molecules, there will be a force on the vane towards the cool side. See the diagram below for an illistration of the effect.

This effect called thermal transpiration gives the vanes their force away from the hot side and thus is the cause of the motion of the radiometer.

External Sources

1. Loeb, Leonard B. (1934) The Kinetic Theory Of Gases (2nd Edition);McGraw-Hill Book Company; pp 353-386
2. Kennard, Earle H. (1938) Kinetic Theory of Gases; McGraw-Hill Book Company; pp 327-337
3. How does a light-mill work?-Physics FAQ