h a l f b a k e r yI think this would be a great thing to not do.
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85,000 Suns is apparently more flux than at the surface of the Sun.
The problem that I see with lenses, or parabolic mirrors is that the Sun is focussed as an image. The image is small, but based on the focal length of the lens or mirror (the ratio of the the size of the image to the focal length
refers to the same angle the the Sun subtends - namely about 0.5 degrees). So the image is usually not small enough.
However, if a small flat mirror, say 5mm by 5mm, is used the reflected light will be approx 5mm across. If an array of these little mirrors is orientated correctly, then all the little reflections can be trained on one spot.
An array of 300 x 300 little mirrors would give a similar result to the world record, and only be 1.5m square.
The little spot would most likely be running at over 3000C.
Good for burning and melting almost anything - it could even split water into Hydrogen and Oxygen.
(?) 85,000 Suns
http://members.fort...adamson/solmet.html
See link to University of Chicago, as well [Ling, Jun 16 2005]
(?) Solar Barbecue
http://www.users.bi.../cooker/cooker1.htm
I kind of want one of these. [Zimmy, Jun 17 2005]
DLP --
http://www.ti.com/s...ducts/dlp/index.htm
darn, not reliable at temps in excess of 67C [reensure, Jun 18 2005]
Max temp of a solar furnace cannot be greater than the sun's surface temp
http://www.volker-q...ntals2/index_e.html
That's the law! [ldischler, Jun 19 2005]
Non-imaging secondary concentrator
http://images.googl...%3Dlang_en%26sa%3DN
Takes the focused image and re-concentrates it via total internal reflection [Freefall, Jun 20 2005]
Consumption of entropy at small scales.
http://physicsweb.o...rticles/news/6/7/11
[ldischler, Jun 21 2005]
Thermodynamic limits of light concentrators
http://www.ee.ucla....s/ey1990sem2123.pdf
13 page pdf file [Ling, Jun 21 2005]
Solar Fusion Magnifying Glass
Solar_20Fusion_20Magnifying_20Glass
[AusCan531, Sep 04 2013]
[link]
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what shape will the array of mirrors approximate? I'd guess it'd be a parabola or ellipse. For similar reasons that a Fresnel lens does not work better than a normal lens, I don't think it improves upon the prior art (unless keeping the reflector thin is a priority). |
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I don't see this a being any better than a
curved mirror, every part of which is
reflecting the sun to the same point. |
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Oh, and if your 5mm sq. mirror is only
reflecting part of the Sun, why are you
counting it as a whole Sun in your
calculations? |
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The overall shape of the array is relatively unimportant, but it would be easier to make if it is flat.
Any converging lens makes an image (OK, some Fresnel lenses are not optimised for high quality images, but that's not important for solar concentrators). Once an image is formed, it will be a reduced version of the object. The size of the image depends on the focal length - short focal length means small image - but the focal length cannot be too short, even with a Fresnel lens. Typical examples have the focal length about the same as the diameter of the lens. And then there's the diffraction to worry about; blurring things about. |
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A parabolic mirror can reflect a point source of light to the same spot, but the Sun is 0.5 degrees across, so it isn't reflected to the same spot. |
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In contrast, each little mirror makes a clean reflection onto the same spot. There is no focal length to worry about, so that spot could be several metres from the mirror array. |
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"The overall shape of the array is
relatively unimportant, but it would be
easier to make if it is flat."
If you tilt each mirror to reflect sunlight
to the same spot and attach them all so
that they are in a sheet, that sheet
would approximate a fresnel mirror.
Since the Sun is brightest in the centre,
the true fresnel mirror (which reflects
the centre of the Sun from every point)
will create a brighter/hotter spot than
the one made out of 5mm square tiles.
It wouldn't have thought that it would
be much different, though. |
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Yes, it's based on a Fresnel mirror, although Fresnel mirrors are usually concentric rings, or huge banks of mirrors arranged on the ground. |
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I don't know if the Sun is brightest in the centre (you mean the centre of the disc: not the centre of the sphere, right?). But I'm having trouble with a Fresnel mirror that reflects the centre of the Sun from every point. The light from the periphery of the Sun will also strike the mirror - where does that go? |
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Yeah. I mean the centre of the disk as
seen in the sky. A parabolic mirror
reflects the light from the centre of the
solar disk to the centre of focus and
does so from from *every* point on its
surface of the mirror. The light from
close to the centre of the solar disk will
focus at a point close to the focal point
of the centre of the solar disk. In
essence you are creating a small image
of the Sun at the focal point of the
mirror. The thing you want to heat
you'd generally make the same size as
the image of the Sun that you have
created, so that you can use all the the
solar radiation from on edge of the disk
to another. |
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A fresnel parabolic mirror is essentially
the same thing. Its almost as if you cut
up the parabolic mirror and move the
bits around to put them in more
convenient places. (you have to change
the shape of the pieces a little to
compenstate for the fact that you've
moved them, but that's pretty much it.)
Apart from the discontinuities that you
have created by having more edges, the
fresnel mirror behaves like the real
thing. |
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Your set of small flat mirrors would,
from the centre of each mirror, reflect
the centre of the solar disk to the focal
point of the mirror assembly. From the
edge of each mirror you would reflect
something close to the centre of the
solar disk to the focal point of the
morror assembly. By flattening the
mirrors you are effectively blurring the
image of the Sun that you create,
making a larger, but cooler hot-spot at
the focal point of the assembly. The
larger the flat elements the more
blurred
the image. |
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With the sizes of mirror you're talking
about, the blurring will probably be
quite small, but what you're creating is
an array that is less effiecient than an
equivalently sized parabolic or fresnel
parabolic reflector. |
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There is a critical fault in your logic. You're assuming that the rays striking each individual mirror are fully parallel. As you have said yourself, the sun subtends .5 degrees. The rays from opposite edges of the solar disk striking any given point on the flat mirror will therefore be off-parallel by .5 degrees, and will diverge enroute to the collector by the same amount. Because of this, your flat-mirror approach will suffer from the same limitations as a perfectly parabolic reflector. |
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//with lenses, or parabolic mirrors is
that the Sun is focussed as an image.//
Yeah, but so what? I don't get this. You
can refract or reflect the image down to
any size you want, surely? And
therefore 'concentrate' the energy by
any factor (ie, the ratio betwen the area
of the mirror or lens, and the area of
the focussed spot.
Reverse
thinking: you can create a projecting
microscope which will project a teeny
tiny dot as an image of whatever size
you want. Ergo, you can conversely
focus the sun into a dot of just about
any size you want.
Presumably, there is some upper
limit (eg, you can't focus down to much
below the wavelength of the light, or
the air at the focal point forms a plasma
and screws up your focus, or
something), but your basic premise is
surely wrong? |
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In fact, you can disprove the merit of
this idea by a scaling argument. If you
think about it, the efficiency of your
system will go up as you add more tiny
flat mirrors, if their total area remains
constant. This means that the
efficiency of your system will be
greatest for an infinite number of
infinitesimal flat mirrors. This is a
curved mirror! Proof by r.a.a. |
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See link for solar barbecue which might mimic what you are proposing (it is parabolic however). |
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I had constructed a temporary model of one of these out of cardboard and aluminum foil, but the kids destroyed it before I could get a meat thermometer / hot dog test out of it. |
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It was by no means a great reflecting mirror, but I was dissapointed in the heat generating capability at the focal point. (I imitated a parabolic mirror using an assemblage of triangular and quadrangular flat pieces). |
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I wish I knew more about lasers as there are some people working out using a solar collection system similar to what you mention to make a solar pumped lasers. I have some odd ideas about trying to get a steam engine going with a variation on that theme. |
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Thanks for your comments, everyone. |
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I accept the arguments that:
1. A Parabolic mirror is an extreme version of a fresnel mirror
2. A flat mirror will reflect the Sunlight at an angle of 0.5 diverging degrees |
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(I don't accept that the image can be made any size - the lower limit depends on the focal length of the lens or mirror, and that depends on the diameter) |
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A parabolic mirror minimum focal length is limited roughly, I suppose, to be approx half the diameter of the mirror. The Sun subtends 0.5 degrees; this is equivalent to 1 in 114. So a 1 metre diameter parabolic mirror (area = 785,397mm^2) ought to be able to focus an image of the Sun which is only about 0.5mm diameter (0.196mm^2). Better than my mirror system, and the number of Sun concentrations would be 4,007,132 (since we are reflecting onto 3D image, that's not quite true, but let's not quibble).
This concentration is truly remarkable: why hasn't it been done? Perhaps the optics would need to be precise or expensive; I don't know. |
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on a slightly related topic; is there a noticeable difference between a parabolic and ellipsoidal mirror (when trying to concentrate light from the sun)? a parabola is an ellipse with the second focus at infinity... Is assuming the sun is infinitely far away too rough an approximation? |
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I would like to answer that, just so that I learn. From a quick check: |
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A parabola can be drawn by marking the set of positions that are equidistant from a fixed point and a nominal straight line. I suppose that a fixed point/plane will make the 3D shape. |
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An ellipse can be drawn by marking the set of positions where the distance to two fixed points, added together, is constant. It can also be drawn in the same way as a parabola, except there is a fixed ratio between the distances, instead of being equal. |
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The light from one focus will reflect onto the other focus. Same in both cases. Interesting. |
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Um, "hello?" basic physics: |
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Your optics should be set up to create (the approximation of) single point at the focal point, not just a nice, crisp image of the sun (0.5 degrees). |
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The problem is that I don't know how to do it. Could you explain? |
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There are microchips that focus arrays of tiny mirrors -- perhaps these would be sufficiently adaptable, programmable, and resistant to heat. I don't see another way to tweak individual mirrors into a very narrow focus, i.e., to focus by refringence a square foot of solar radiation to a point smaller than the point of a pin. |
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So, to step back a little, does anyone
know (a) what temperatures are
achieved by the current solar furnaces
and (b) what limits them? |
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"Your optics should be set up to create
(the approximation of) single point at the
focal point, not just a nice, crisp image of
the sun (0.5 degrees)." |
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Er, a single crisp focus creates an image of
the Sun. To can vary the size of that image
by using a different focal length mirror but
you still get an image of the solar disk. To
focus all the rays of the Sun onto a single
point requires, as far as I am aware, magic. |
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Isn't this idea on the verge of violating the second law of theromodyanics, which (sometimes) says, "heat can never pass spontaneously from a colder to a hotter body"? So that the max temp is the surface temp of the sun? See linky. |
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ldischler's right - the limit is the surface temperature of the sun. At this temperature, the black-body emissions from the focal point will have the same energy as the incident radiation from the sun. |
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//on the verge of violating the second law of theromodyanics// |
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I'm smiling after reading that. I imagine getting pulled over and the policeman saying: "You were nearly breaking the limit". |
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"Number of Suns" refers to the light intensity: not temperature. The potential remains the same, but the current is much greater. |
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Thanks for that, Ling. I was on the verge of
digging out a thermodynamics textbook to
craft a rebuttal. |
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NASA has developed a secondary non-imaging solar concentrator (see link) that will take the focused solar image and further concentrate it via total internal reflection to a very small point. |
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As has been stated, the temperature cannot exceed the surface temp of the sun, as blackbody radiation will prevent further temperature rise at this point. However, if there is a mechanism for reducing the surface temperature of the collector by drawing off the heat (isn't that the point of a thermosolar collector?), the total flux is limited only by the rate at which the energy can be drawn off. |
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A secondary concentrator as shown in the link isn't all that useful in power generation, as there wouldn't be a practical way to transport such a hot fluid to the turbines (or whatever is used to transform heat to electricity), but is of vital importance to thermosolar rockets, where higher exhaust temperature (and thus higher exhaust velocity and greater propulsive efficiency) is king. |
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If you could concentrate the flux of solar ration to a level greater than that of the sun’s surface, then you could exceed the solar surface temperature at your target, and as that’s what you need for a perpetual motion machine, scientists long ago made it illegal. So here’s a ticket for violating the second law. I won’t issue an MFD just yet, as I know Ling will want to argue. |
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"'Number of Suns' refers to the light
intensity: not temperature." -- Ling |
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I can't see a violation of the law of
thermodynamics here, just a flat mirror
reflector that'll be a little less efficient that
a curved reflector and a mathematical
error that made Ling think the it might be
better. |
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How is that a perpetual motion engine? You're simply using the energy of the sun, and concentrating it. |
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Recalling the dismal failure Mythbusters had building a solar concentrator of this type (although rather bigger), I'm thinking you ain't gonna find it as easy as all that to get this right. |
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// How is that a perpetual motion engine?//
You can use heat running downhill (from hotter to colder) to run an engine and generate energy. So, if you can get the heat to run back uphill on its own (from colder to hotter), without inputting energy to make it do it, you have the basis of perpetual motion. |
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I think Ling has given up on the original premise of this idea, but I'm fishboning it just because I knew it was wrong. |
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I once watched a solar eclipse using a dentist's mirror (a flat one). I stuck the handle in my front lawn, and reflected the sun in through my front doorway, down the hall and onto a white wall in the back of the house, with all the shades drawn and the lights off. It made a sun image a foot or so across, but I realized the blurriness of the image was exactly the size of the mirror. So I got some tape and masked the mirror down to about a quarter inch, and got a much clearer, but dimmer, image, still the same size. It moved across the wall with the movement of the sun in the sky, and was the most dynamic representation of the sun I have ever seen. A little too dynamic, as I had to keep running out into the yard to reposition the mirror. |
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//NASA has developed a secondary non-imaging solar concentrator ... to a very small point.// [Freefall] I looked at that link and I missed the point--it looks to me like the thing spreads the light out inside a rocket engine. |
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Re: /Max temp of a solar furnace cannot be greater than the sun's surface temp/ - Suppose a mirror were placed in space to reflect the suns light back onto the surface of the sun. Wouldn't the surface there become hotter? It seems to me that the "surface of the sun" rule considers the sun as a point source, which is not really true. |
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// Wouldn't the surface there become hotter?//
That’s the equivalent of insulating part of the sun. The flow of heat out of the sun would no longer be in equilibrium, so its surface would heat up until it again reached equilibrium. You’re not heating up the sun with the sun, if that’s what you’re implying. If that were possible, you could bake a ham just by surrounding it with mirrors. |
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<resisting the temptation to argue, but probably failing> |
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//If you could concentrate the flux of solar ration to a level greater than that of the sun’s surface, then you could exceed the solar surface temperature at your target// |
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I agree that the temperature cannot exceed the surface of the Sun (see? I'm not arguing) |
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What is interesting is the concept of linking flux to temperature. Let me present one test: |
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A 1m diameter flat metal plate is heated to a nominal temperature, let's say 400C. Immediately in front of the plate is a 1m diameter infra red lens which forms a 0.01m diameter image of the plate onto another small metal plate. |
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Now, we know that the black body radiation concept limits the temperature of the small metal plate to a maximum of 400C.
But if we compare the flux at the large and small plate, I would assume that the flux at the small plate is more than at the big plate. |
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So, if sunlight were concentrated enough, the flux could also be more than that at the surface of the Sun. |
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<ticket torn up; patiently waits for court summons> |
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//which forms a 0.01m diameter image of the plate onto another small metal plate//
You assume you can focus like that, and you can, but only for those photons that are emitted perpendicular to the plate—a small proportion of them. Nature conspires to prevent you from doing what you want to do*, like building perpetual motion machines, so it’s simpler just to believe in the laws of thermodynamics, and if something violates then, then you know it’s impossible. So you don’t have to do the math every time.
*It does most of the time, except for really small things. Get small enough, and anything can happen. |
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I agree totally with the example put up by [Ling], for being understandable. When used as arguments, the laws of thermodynamics can be far from easy to grasp; consider the case of locating a point transfixed, of a moment divided to its limit, or of any absolute. I don't totally understand or credit some of the claims of researchers who comment on their achievements without attesting to the limitations imposed by their study. |
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Those examples [reensure], are not from thermo. |
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Sorry, but as I say, I neither know thermodynamics, nor am versed in the QED I'd need to propose examples of the dilemma in thermodynamic prediction. I had to use tangible examples I appreciate. |
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Oh...I didn’t know you were talking to yourself. |
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You're not to be faulted. |
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I've been checking the 2nd law of thermodynamics ('cos I don't want to be jumping into any holes). I think it basically says that the total order of a system always tends to reduce. Applied to a solar concentrator, one could say "I cannot concentrate the Suns light any more than what there is at the source". |
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But I'm having trouble getting to grips with this: I can increase current density in a conductor without any problem. So I thought I would look at it another way: |
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If we use the "number of Suns" as a unit, then at the surface of the Sun, the "number of Suns" is 52,524 (this is (1/tan0.25)^2). But 1 Sun at Earth is 1.3kW/m^2, so the flux at the Sun is 68,281kW/m^2. |
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I double checked this by another quotation of the power developed by the Sun, and the surface area, and arrived at 62,687kW/m^2. So it's in the right ballpark. |
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In the link "Thermodynamics of light concentrators" the maximum number of Suns is not clear: at one point it is 45,000, but further there is mentioned 100,000. The maximum flux *achieved* was quoted at 7.2kW/cm^2 which is the same as 72000kW/m^2. |
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It would seem that someone is claiming that the concentrated flux can be more than that at the surface of the Sun. |
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I am not convinced, either way, at the moment. Just more confused. |
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Good find, Ling. The article suggests that, in a refractive medium, the irradiance can be more than the sun’s surface, even if the temperature has to be less. (And without the medium, both must be less.) |
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An associated factor from entropy of the Sun's ordered photons is obvious. Obvious to me, anyway, since I failed utterly to grasp the wider implications of entropy to the properties of natural forces at first blush. Photon positions are accretive as one is nearer the source, less so at a distance; hence, the behavior/path of an "average" photon from its source is less likely to appear random at increasing distances. I'd propose that the difference between your calculations [Ling] and those stated by others is due to entropy of the sun's flux. The study test intensity at a focus point would exceed the calculated intensity of the source by virtue of a coronal effect of the sun, akin to how light is amplified in a laser. |
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Solar concentrators may be divided into two categories. Imaging and non-imaging. It is impossible to achieve a concentration of more than approximately 46,200. this number is got by squaring the ratio of the earth's orbit to the radius of the sun. For places closer to the sun - eg Venus - less than 46,000 is possible and for places further then a higher figure is possible. |
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There are two ways to demonstrate that 46,200 is the maximum concentration possible. The hard way is to analyse the optics of a concentrator, and is particularly difficult for a non-imaging concentrator. Imaging concentrators of high concentration are also very difficult to analyse since all the standard optics formulas only apply to thin lenses of high F number where they are in any case only approximately correct. Eg the simple theory gives a plane immage. In reality however there is certainly no simple lens that gives a perfect plane image, however acceplable it may be in practice for the typical camera lens. |
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The second proof is very short. The law of conservation of energy is involked and the readers attention is drawn to the fact that if it were possible to produce concentration to greater than the surface temperature of the sun, then this hot surface would radiate more power than it received. This is clearly impossible, so the factor os 46,200 is the largest consentration possible at Earth's distance from the sun. |
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A practical imaging concentrator that would have the maximum possible concentration is got by rotating an elipse around it's long axis. Place the sun at one focus, and all the light leaving the sun is brought to a 3 dimensional focus at the other focus. The image is the same size as the sun. If a smaller object such as the eart is placed there then the image on the earth will not then be in focus, and most of the sun's energy will miss although the temperature achieved will be that of the surface of the sun. |
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The reason for the inability to focus sunlight to a point is because the sun is not a point source but subtends around .5 degrees as noted by others. Basepair is not correct when he says that you can focus the sun down to any size you want. |
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Might not work at midnight, but you could get a bunch of moons then. |
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//cannot be greater than the sun's surface temperature// |
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what if you use quantum dot reflectors that absorb low frequencies and emit higher frequencies ? (so there). |
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Or filter out everything below (say) UV (best done outside the atmosphere). |
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This confuses the hell out of me. |
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See now, we can get a big solar panel, use it to power a laser, and produce a hot spot well in excess of the sun's surface temperature. How is this also not a violation of the 2nd law? |
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Why couldn't all of the little mirrors you use, each themselves be slightly concave so as to reduce the divergence of the reflected light? |
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Somewhere along the line I reasoned that you couldn't directly concentrate EMR to be any hotter than the black-body temperature of its radiation spectrum. |
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I now have no clue how I came to that conclusion but it seemed a pretty simple answer to "Why can't ...?". |
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Lots of discussion of this issue on linked idea. I ended up on the wrong side of a technical discussion with [spidermother]. Bugger. |
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//couldn't directly concentrate EMR to be any hotter than the black-body temperature of its radiation spectrum// |
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Goddamnit, now my head hurts. I’m trying to refute this with logic, but I’m not sure I really can. At least I’ve got something really interesting to go research now. Does this “problem” or “paradox” have a convenient name where info could be found? |
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I'm not sure I buy the convoluted "optics limitations help us out with our potential thermodynamics paradox" bit. It feels like nature's ganging up on us. |
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IIRC my reasoning started with the Sun being a black-body radiator (which Wikipedia says is a "poor approximation", whatever), then things get muddled a bit, then the conclusion that after a certain saturation point the object simply reradiates the incoming radiation at the BBR spectrum, ie: temperature, of the Sun. |
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Which allows me to come to the conclusion that if you filter all but the highest frequencies somewhere between source and (concentrators and) object you can raise the temperature past the original BBR of the source by (crudely and inefficiently) giving the object a higher frequency BBR spectrum. |
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Or you could bear in mind that I flunked high-school physics first time'round (for lack of trying). But it makes as much sense to me as the other explanations proferred. |
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[custardguts] The solar panel and laser example does not violate the laws of thermodynamics because only some of the harvested energy ends up as higher-temperature heat; the rest ends up as waste (low temperature heat), and the overall entropy is greater than that of the sunlight. |
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For example, it's possible to intercept 1 KW of sunlight and use it to produce 1 W of heat energy at a temperature greater than the surface of the sun, and 999 W at a lower temperature, but it's not possible to produce 1 KW of heat at the higher temperature. |
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[FlyingToaster] The temperature reached is not determined simply by the effective temperature of the radiation, but by the flux density as a function of wavelength. |
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It's often helpful to think of radiation as a large (infinite) number of frequency bins, each with a particular power (or power density, as appropriate). If you remove some of those frequencies, you simply decrease the total power. The target will continue to emit those frequencies, though, so its temperature will be lower. |
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yes but if you filter all but the high frequencies out of a bbr, or portion thereof, then you can actually get a higher temperature if sufficiently concentrated. |
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So if all the EM concentrators passed only gamma rays then you could increase the temperature at the focal point into the gazillions of degrees (if you had that much concentration). |
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The difference between this and the solar panel/laser thingie is that it's direct. |
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As an aside, you couldn't get a maser or IR laser to heat something up hotter than the surface of the Sun: at best the object would end up radiating a microwave or IR-based BB spectrum. |
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You may be thinking that wavelength is what limits the achievable power density and/or the achievable temperature. It's not. The flux density at the source is what counts. |
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For example, a domestic microwave oven can deliver a kilowatt of energy to a few square centimetres, thus producing molten glass, plasma, and other wonders, even though the wavelength corresponds to the dominant frequency of a black body at just a few kelvin. The power density at the target can approach the power density at the source - in this case, the magnetron. |
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//you couldn't get a maser or IR laser to heat something up hotter than the surface of the Sun: at best the object would end up radiating a microwave or IR-based BB spectrum// |
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Again, not so. A magnetron effectively is a maser, and I have personally used one to generate temperatures in the thousands of degrees, with much blue light (and probably even some UV) emitted. |
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Exactly, I agree and this was the bit I was struggling with. I don't buy the "limited by the equivalent black body temperature" bit. |
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Black body radiation defines the output frequency spectrum for an object at a given temperature. If you pump more energy in, it's temperature rises (and thus the emission spectrum and intensity increases) until power out = power in, ie equilibrium. |
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So if we focus a couple fucktons of sunlight (whose spectrum matches blackbody temp approx 3000 degrees) - we should be able to push the equilibrium temperature of the target above 3000 degrees. That, or the object must not absorb all of the incident energy. What it can't do, is absorb it all, and somehow radiate it all away to keep it's temperature low due to some arbitrary rule we just made up. |
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The problem is that you *can't* focus that much sunlight into such a small area. It's geometrically impossible. So yes, the universe basically conspires to enforce an arbitrary rule we just made up. |
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You can't pass heat from the cooler to the hotter
Try it if you like but you far better notter
'Cos the cold in the cooler will get hotter as a ruler
'Cos the hotter body's heat will pass to the cooler
Oh, you can't pass heat from the cooler to the hotter
You can try it if you like but you'll only look a fooler
'Cos the cold in the cooler will get hotter as a ruler
That's a physical Law! |
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Yes, but then what of the concept of using a large
solar panel to power a laser (as mooted somewhere
up above)? |
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Or, to extend the point, how do we create high temperatures at all? |
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We can use a large quantity of heat at a medium temperature, and a sink at a low temperature, to produce work (whether electrical, mechanical or whatever). We can use that work to move a *smaller* amount of heat of heat to a higher temperature. But heat can never flow from a cooler to a hotter body, whether by conduction or convection or radiation, without work. |
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But in the case of solar panels powering a laser,
surely the laser can heat a target to a temperature
above that of the sun's surface? And, in this case,
surely heat has flowed from the surface of the sun
to the hotter target? |
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Yeah, I think [spider] is making a solid point about the entropy limitations, I just don't get, in this case, how nature can so agilely change how things work to make it impossible in the case of reflected light. |
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The laser example doesn't prove the entropy case wrong because of the entropy-linked limitations in efficiency of both the solar panel and the laser source. |
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What I don't get are what are the absolute limitations on reflected light that make this situation not work. The explanations thus far feel contrived, not based on actual properties of the light, the mirrors or the target. |
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At what point does the limitation kick in ? Obviously, if you have a low powered laser as source, you can put your hand in front of it and "so what", then put a lens in front and your hand in front of the lens and "ow". |
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Mostly as obviously, if the focal point were a picometre away from the Sun's surface and you had a mirror array to reflect light that otherwise would head off into the distance without impinging on that point, onto the point, then the temperature would rise... no ? |
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1. A (perfect) mirror 1 picometre from the surface of the sun is a good example. It would reflect every photon that leaves the surface back to the surface, resulting in an intensity exactly equalling that of the sun. |
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2. If this is extended to a spherical mirror enclosing the sun 1 picometre from its surface, the result is the same. |
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3. The general case is an ellipsoid, of any size or eccentricity (including spheres), with the sun at a focus. In every case, the image is exactly the same size as the sun, and has exactly the same total flux as the sun. |
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4. Any alternative shape that produces a smaller image will harvest (at best) proportionately less of the sun's total output. The maximum flux density remains the same. |
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I don't have a general proof of 4., but I'm confident that it can be shown for any particular example. |
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Lasers are a special case. They produce an especially low entropy form of light, which corresponds to their ability to be focussed especially tightly and to produce exceptionally high temperatures. In the case of lasers, wavelength is indeed a limiting factor; whereas in the case of sunlight, the relatively large size and low intensity are more important. |
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//n this case, surely heat has flowed from the surface of the sun to the hotter target?// No I don't think so, because some of the heat has been converted into work, and some of that work has been converted back into heat. It's like paying a load of fivers into the bank and then drawing tenners out of the hole in the wall. The fivers have not been sellotaped together in pairs. |
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Or cashing in a ton of lead, and buying a few grams of gold. The lead hasn't been converted into gold. |
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I didn't read all of the above, but here's my
tuppence worth on solar concentration. |
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To calculate the maximum concentration possible,
you would need to work out what area of the sun,
the energy we receive corresponds to. |
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You can do this by calculating the area the sun
would be if it we the size of Earth's orbit, finding
the fraction of that which the Earth's cross-
sectional area represents, and then applying that
fraction to the real area of the sun. |
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With this figure, you can take any area of solar
array, use its proportion to the c-s area of the
Earth and use it to find how small an area it would
be on the sun. |
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If you can focus on a smaller area, it would be
hotter than the surface of the sun, without
accounting for losses. |
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Sun diameter = 1,391,000 km, Earth diameter =
12,742 km, distance from Sun to Earth =
149,600,000 km. |
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If I do the required maths, I'll edit this comment,
but don't hold your breath. |
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Edit: Ok, I'm not going to show my working, but I
calculated that 1.5m2 on Earth = 32.4 mm2 on the
sun (so just more than 5mm x 5mm) but
atmospheric losses will diminish that a lot. |
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I'm sure there is a much simpler formula than the
one I used, but I did make it up myself. |
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Edit2: It is a sobering thought that if all light was
emitted straight out from the sun, the light
hitting you when you sunbath is coming from less
than 1cm2 of sun. |
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