## Wednesday, March 02, 2011

Crookes Radiometer is device which generates mechanical energy from light. The instrument consists of a shaft with Blades (leaves). The blades are painted black at one side and silver at other side. When light is shown on the device the leaves rotates.
According to the current scientific knowledge base, the explanation of Crookes Radiometer revolves around 'Thermal Transpiration'. However the explanation is very convoluted. Please refer http://math.ucr.edu/home/baez/physics/General/LightMill/light-mill.html for details about the current explanation.
I have better explanation.
First consider what happens at the boundary between the blade and gas around it. The molecules in the gas hit and bounces at the blade. Consider now the temperature of the blade is higher than that of gas. Now heat will flow from blade to gas. How is heat flow from blade to gas? When the molecules hit the blade. When the molecules hit and bounce, it will bounce with faster speed than it was traveling before bouncing*. The increase in speed means increase in energy (the energy transferred from the blade to gas). The increase in speed is depends on the temperature difference between the blade and gas.
Similarly when the temperature of the blade is less than the gas, the molecules will bounce with a lower speed than it was traveling before touching the blade.
In steady state, temperature difference between gas and black side is higher than the temperature difference between the gas and silver side. Hence the molecules at black side bounces faster than the silver side.
As the molecules bounces faster at black side, black side will experience more pressure than silver (note that the pressure = change is momentum; momentum = mass * velocity). This pressure difference causes the rotation of the blade.

* How can a particle travel faster than it's initial speed? Well, actually the real story is not like that. According to quantum theory the particle when hit get absorbed in the surface of the blade and then it get emitted with a higher speed. However this is not important to us.

Lizzie L. said...

What material is the blade made out of? I would be surprised to see much of a temperature difference from the black side to the silver side.

William Helmer said...

Lizzie - A radiometer is typically made out of Mica. The temperature difference is on the order of 0.1-0.5 Kelvin (0.1-0.5 degrees C).
Rejeev -Conceptually you can see that although everything you argued is true it is not quite the full story. After a molecule impacts the black vane of the radiometer it picks up more thermal energy the molecules bouncing off the vane will prevent some incoming molecules from impacting the vane. As the black vane increases in temperature the outgoing molecules will get "better" at preventing some impacts,thus while the black vane molecules leave with more energy, there is also less particle flux off the surface then the respective particle flux off of the white surface (more flux at lower energy). This causes the forces from this heating effect to effectively cancel out along the majority of the vane. However at the edges of the vane this effect does not fully cancel, Einstein showed in the 1920's that there is a force due to your effect, but is is only on the edge and it is not the full story.
Thermal transpiration is a good theory that accounts for the rest of the force. Thermal transpiration is a non-intuitive flow of molecules from cold to hot(this is the reverse of most typical thermal systems). I believe that an important consideration in this problem is that a radiometer is in a partial vacuum, so the flow of gas molecules is on the edge between typical viscous(group) flow and the molecular flow regime that is present at high vac. The low pressure/long mean free path regime of gas can lead to some results that are counter-intuitive.

William Helmer said...

Lizzie - A radiometer is typically made out of Mica. The temperature difference is on the order of 0.1-0.5 Kelvin (0.1-0.5 degrees C).
Rejeev - The effect that you mention has been proved to be false mathematically by J.C. Maxwell. Conceptually you can see that although everything you argued is true it is not quite the full story. After a molecule impacts the black vane of the radiometer it picks up more thermal energy the molecules bouncing off the vane will prevent some incoming molecules from impacting the vane. As the black vane increases in temperature the outgoing molecules will get "better" at preventing some impacts,thus while the black vane molecules leave with more energy, there is also less particle flux off the surface then the respective particle flux off of the white surface (more flux at lower energy). This causes the forces from this heating effect to effectively cancel out along the majority of the vane. However at the edges of the vane this effect does not fully cancel, Einstein showed in the 1920's that there is a force due to your effect, but is is only on the edge and it is not the full story.
Thermal transpiration is a good theory that can account for the rest of the force. Thermal transpiration is a non-intuitive flow of molecules from cold to hot(this is the reverse of most typical thermal systems) due to a pressure difference. I believe that an important consideration in this problem is that a radiometer is in a partial vacuum, so the flow of gas molecules is on the edge between typical viscous(group) flow and the molecular flow regime that is present at high vac. The low pressure/long mean free path regime of gas can lead to some results that are counter-intuitive.