# Crookes radiometer explanation / heat conduction forces

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I looked up an explanation of why a Crookes radiometer spins in light, and the accepted answer that I've seen---"thermal transpiration"---sounds like bull. Even if the effect is real, the force on the edges of the vanes would have to be small, and nowhere do I see even a suggestion that anyone has ever calculated the force. In fact it's claimed that "The correct solution to the problem was provided qualitatively":

I came to a different conclusion (as have many; there are a lot of incorrect explanations). Assuming that the black surfaces are heated by the light, and are hotter than the ambient air temperature, then the black surfaces will heat the air via conduction. This involves air molecules arriving at the surface with relatively low energy, and leaving with higher energy ie. faster than they arrived. By conservation of momentum or Newton's third law, there must be a force pushing on the surface of the vane.

This seems so simple, but is it wrong?

More generally, it seems that for any conduction of heat, there must be a force acting on each of the hot and cold sides, pushing them away from each other. Is this true?

Edited by md65536
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I looked up an explanation of why a Crookes radiometer spins in light, and the accepted answer that I've seen---"thermal transpiration"---sounds like bull. Even if the effect is real, the force on the edges of the vanes would have to be small, and nowhere do I see even a suggestion that anyone has ever calculated the force. In fact it's claimed that "The correct solution to the problem was provided qualitatively":

http://math.ucr.edu/home/baez/physics/General/LightMill/light-mill.html

I came to a different conclusion (as have many; there are a lot of incorrect explanations). Assuming that the black surfaces are heated by the light, and are hotter than the ambient air temperature, then the black surfaces will heat the air via conduction. This involves air molecules arriving at the surface with relatively low energy, and leaving with higher energy ie. faster than they arrived. By conservation of momentum or Newton's third law, there must be a force pushing on the surface of the vane.

This seems so simple, but is it wrong?

More generally, it seems that for any conduction of heat, there must be a force acting on each of the hot and cold sides, pushing them away from each other. Is this true?

The problem with that is that in leaving with a high energy and thus speed, they will tend to collide with other, slower-moving molecules and knock them away from the surface. Meaning there is a lower pressure there, and the reduction is force cancels the increase. However, there is an effect at the edge that doesn't cancel.

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The problem with that is that in leaving with a high energy and thus speed, they will tend to collide with other, slower-moving molecules and knock them away from the surface. Meaning there is a lower pressure there, and the reduction is force cancels the increase. However, there is an effect at the edge that doesn't cancel.

The heated air molecules tend to knock slower colder molecules away, which is equalizing the pressure among any pockets of air. The warmer air on the black side is less dense, with higher energetic particles, and the colder air on the silver side is more dense but slower particles... the force on the surfaces of the vane from air pressure would also equalize, otherwise there is a pressure difference that would quickly equalize.

Yes, it makes sense that the state of air pressure in the device would not have a net force on the wind vane, but that doesn't rule out my hypothesis. There are two things here: 1 is the heating of the air through conduction, and 2 is the forces imparted by the heated air. Even if (2) is shown to have no effect on the surfaces, it doesn't consider the effect of (1).

If there is a significant force acting on the edge of the vanes due to molecules colliding with it, could this force be removed by making the vanes vanishingly thin? Is the thermal transpiration force proportional to the surface area of the edge, so the effect could be experimentally tested by measuring the effect with vanes of different thickness?

Edited by md65536
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I think the argument is that if there is less air to be heated, because you knock it away, you will have a smaller force. That balances the larger force imparted to/by each molecule. The wikipedia article unfortunately doesn't go through the math or link to any analysis.

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I think the argument is that if there is less air to be heated, because you knock it away, you will have a smaller force. That balances the larger force imparted to/by each molecule. The wikipedia article unfortunately doesn't go through the math or link to any analysis.

Okay that makes sense and complicates my oversimplistic view. Certainly there's more to this than I understand.

There must be an effect from knocking molecules out of the way, but I don't think that that explanation can completely nullify the effect I propose. If it could, then a material that outgasses would also have no net force acting on it, because the force of the outgassing would be balanced by having air molecules knocked out of the way. Perhaps it's true with weak enough outgassing, and perhaps it's true in the radiometer.

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When vanes don't start turning what is the reason? Answer: Static friction is larger than the propelling force. Air resistance is not an answer.

When air is being pumped away from the radiometer bulb, the propelling force increases.

What changes when air is being pumped away from the radiometer bulb? Diffusion speed increases.

Are there other ways to increase diffusion? 1: Make vanes porous. 2: Increase temperature. 3: Shaking. 4: Stirring.

Edited by Toffo
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The working theories agree to say that the warmer black sides heat air more, which is accelerated and pushes the vanes.

Apparently it needed big science names to find out that air has to converge to the warmer area in order to be pushed away from there... But remember that before 1900, very little was known about fluid dynamics. Eiffel experimented from his tower built in 1899. I'd say this part doesn't need a long explanation nowadays. And we better avoid the word "transpiration" which I feel misleading; it's a flow with nothing special.

Is air heated by direct contact or, as the OP suggests, by conduction? This is just a matter of gas density. The mean free path of gas molecules is said to be ~ 1mm, so conduction is more important - by little. Operation with 10 times less pressure and 10mm ean free path would make heating by direct contact predominant.

OP, my feeling is that you have all to understand it. Add "air comes from the sides" to your explanation - done.

Fun to see that ol' James Clerk approved an explanation that obviously rotates in the wrong direction... To keep in mind when, for instance, referring to Helmholtz about sound quality and "harmonic" spectrum.

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