Re: The Crookes Radiometer

In article
<1ilri1a.19m9zu219nihjN@xxxxxxxxxxxxxxxxx>nospam@xxxxxxxxxxxxxxxx (J.
J. Lodder) wrote:
Wortman <W@xxxxxxxxxx> wrote:
In article
<g6n5l3$9u9$3@xxxxxxxxxxxx>baez@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
(John Baez) wrote:

> It seems there's still a lot of mystery about how this gadget
> works. If you have thought deeply about this issue, try:

Gee, the explanation I heard is that the black sides of the veins
run hotter than the gas in the bulb while the white sides are closer
to the temperature of the gas. When a molecule strikes the black
vein it on average increases in energy and leaves at a higher speed
imparting more momentum on average to the vein than a molecule
striking the cooler white side. It may also be critical that the
bulb is run at a reduced gas pressure. This will increase the mean
free pathof the gas molecules. If the pressure is low enough the
mean free path would be comparable to the bulb radius. This would
allow gas molecules carrying heat from the veins to be cooled by
collision with the glass bulb rather than heating the rest of the
gas. This explanationhas always worked for me. Is there something
obviously wrong with it?

Yes. No explanation based on collisions of single molecules
with the vanes can be correct.
In addition you have to consider the distribution function
f(r,v) of all the molecules.
(you can simplify by holding the vane stationary
and calculating the net force on it. Else you get an f(r,v,t)
It becomes difficult because of phenomena like gas flow or creep.

Jan

1 ATM is 101,325 N/m^2 so at 10^-5 ATM which is the pressure these
devices operate at we get a pressure of 1.01 N/m^2. I assume 1 cm^2
vane surface which gives a force of Fs = 1.01*10^-4 N per face at room
temperature. Now let us assume a 10 degree temperature differential
between black and white surfaces. Since PV=nRT should hold at these
low gas pressures the force difference due to all 4 vanes is
4*(DT/T)*Fs or 1.37*10^-5 N. Assuming the vanes at 1 cm radius I get a
net torque of 1.37*10^-7 N-m. My guesstimate for the vane mass is 0.1
gram which yields an angular acceleration of 6.85*10^-2 radian/sec^2.
Seems to me this really isn't peppy enough by ~10 to 100 but I could
easily envision lighter vanes and larger temperature differentials. I
also can't recall how long these thingstake to spin up.

Regards
Paul

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