h a l f b a k e r yFewer ducks than estimates indicate.
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We start with a low iron (so it's transparent to UV and IR), low thermal expansion (so it doesn't break) glass tube, shaped into a circle.
We fill our circular tube halfway (as measured by volume / displacement) with solid metallic iodine, and remove as much air as we practically can.
The tube
is attached to an axle or other rotary bearing, and oriented so that it's axis of rotation is horizontal.
A heat source (sunlight focused through a magnifying sheet) is applied to the lowest point of the tube, and a heat sink is applied to the highest point, and the tube is given an initial spin.
The heat source's temperature is hot enough to sublimate the iodine, and the heat sink's temperature is low enough to cause the iodine to desublimate.
As each point on the tube passes through the heat source, all solid iodine within it turns to a gas, and flows upwards faster than the tube is moving.
As each point on the tube passes through the heat sink, all gaseous iodine within it turns into a solid, and sticks to the glass. The solid iodine moves downward at precisely the same speed as the glass tube.
While the solid iodine descends, it's gravitational potential energy is converted to kinetic energy; since the iodine is firmly attached to the glass, this rotationally accelerates the tube.
While the gaseous iodine ascends, gravity slows it down, but since it's not attached to the glass, this slowing of the gaseous iodine does not slow down the glass tube.
I chose iodine as the working "fluid" because it's triple point (113C) is at a temperature above atmospheric (which means our heat sink can be cooled using air), yet easily reachable with common heat sources.
Plus, it's dark color allows it to be easily heated by concentrated sunlight, and it's violet gas phase just plain looks cool :)
An alternative might be the type of dye used in a dye sublimation printer.
Stanley Dryer
Stanley_20Dryer
[theircompetitor, May 11 2010]
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I don't know if this would work, but damn it's a cool mental image. [+] |
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//all solid iodine within it turns to a gas, and flows upwards faster than the tube is moving.// cite ? for the "faster" bit |
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May need something more thermally conductive than glass, or some tricky piping, to provide sufficient coupling to the heatsink. Nevertheless, please build and market these as sciency toys for children and geeks [+] |
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[+] for the idea. It might just work... but it looks
like it will be really slow. |
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A bit of math gives the maximum angular velocity
it can reach as Q/Cm, where Q is the power of the
heat source/sink, C is the specific heat of
sublimation and m is the "angular density" (mass
per radian) of iodine in the tube. If the tube is
half-filled, m is M/Pi where M is the mass of
iodine. |
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Taking the heat of sublimation as 238 kJ/kg
(iodine), 0.01kg mass filled over half a circle, and a
heat source of 100W it's possible to reach 0.04
rpm. |
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Torque is, of course, 2 R M g/Pi and the power
output is 2 Q R g / C. |
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Which raises an interesting situation... C and g are
constants... so if the radius is greater than
12,143m will it become a perpetual motion
machine? :) |
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EDIT: Just realized that according to my model, it
becomes a perpetual motion machine if it turns at
all - I'm extracting the same amount of heat at the
sink that I'm supplying at the source. |
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I think the solution is that it is not possible to
keep the source and the sink both at the triple
point like in my model - some pressure difference
between the bottom and top of the vapour
column is inevitable, otherwise it will not flow up.
Since the heat of sublimation is lower at lower
pressures, this would mean that the heat
extracted at the sink is less than the heat supplied
at the source. There would also be temperature
differences... |
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The problem with a perpetual motion machine,
assuming that you could get one to work, is that it
does nothing but spin and maybe look pretty. As
soon as you try to siphon any energy off it -
mechanical, electrical, karmic, chi, whatever - you
destabilize the equilibrium and it eventually stops. |
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Not if it has an efficiency of more than 100% |
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FT, if we assume a steady state system, and ignore turbulence, then the mass flow rate will be constant for all angles. Furthermore, the gaseous iodine has lower density than the solid iodine. |
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Consequently, a larger *volume* of gas must flow through each angle on the upwards arc than the volume of solid moving downwards through each angle on the downward arc. |
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Arvin, the triple point determines the highest pressure / temperature that the heat source may be (well, at the point at which the heat flows into the iodine), but the heat source doesn't *need* to be that hot, and furthermore, the heat sink must be cooler than the heat source. |
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As the iodine sublimates, it expands, doing work on (accelerating) the gas in front of / above it, thus moving that forward/above gas upwards. In fact, all the way from bottom to top, the gas will be expanding, pushing on the gas in front of it. The heat sink needs to remove heat from this expanded gas, at it's lower-than-initial pressure. |
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Furthermore, the quantity of heat removed from the expanded gas will be less than the quantity of heat that was added by the heat source -- the difference, of course, will be equal to the amount of work that was done. |
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As for the engine's maximum speed.... |
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If we don't remove mechanical energy from the engine fast enough, it will accelerate, just like any other engine. |
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The result of this will be that some, but not all, of the solid iodine passing through the heat source sublimates, and some, but not all, of the gaseous iodine passing through the heat sink desublimates. |
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There will still be a weight imbalance, but less of one than there originally was; torque will decrease, but not go to zero. |
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When the torque decreases to the point that it equals the amount of friction on the axle, the speed of the engine will cease to increase. |
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In practice, since torque decreases as speed increases, there's a maximum amount of power available at some finite, calculable, speed between zero and infinity. |
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