Thermal iimits of solar power.

[halfeye]

I've read in this forum that there is an upper limit of the heat achievable by solar power of the temperature of the sun's surface.

I'm not satisfied that that makes sense.

Thinking about it earlier today, the thought came to me that this is particularly debatable with reference to The Sun and Betelgeuse. The surface of the Sun is much hotter than the surface of Betelgeuse. However, Betelgeuse is brighter, mainly because it is much bigger. It is bigger because it is much more energetic.

The idea that the most energy that could possibly be extracted from Betelgeuse by a system of lenses and mirrors is less than the maximum energy that could be extracted from the Sun by a similar system seems odd to me.

[Bavarian itP]

Maybe start here.

[gomipile]

I've read in this forum that there is an upper limit of the heat achievable by solar power of the temperature of the sun's surface.

I'm not satisfied that that makes sense.

Thinking about it earlier today, the thought came to me that this is particularly debatable with reference to The Sun and Betelgeuse. The surface of the Sun is much hotter than the surface of Betelgeuse. However, Betelgeuse is brighter, mainly because it is much bigger. It is bigger because it is much more energetic.

The idea that the most energy that could possibly be extracted from Betelgeuse by a system of lenses and mirrors is less than the maximum energy that could be extracted from the Sun by a similar system seems odd to me.

You're conflating energy, power, and temperature. These all have precise meanings distinct from each other. I could set 5 million 1500 Watt kettles to boil at the same time, and they'd heat the water to boiling at close to 100 Celsius. An oxygen-acetylene cutting torch would have much less overall power and use less energy than the system of 5 million kettles, yet it can get hot enough to cut through steel plate a couple of centimetres thick.

[crayzz]

The idea that the most energy that could possibly be extracted from Betelgeuse by a system of lenses and mirrors is less than the maximum energy that could be extracted from the Sun by a similar system seems odd to me.

That's not really an accurate summary of the issue. You can almost certainly extract more energy per unit time from Betelgeuse than you can from the sun; what you can't do is concentrate it in a system such that the system becomes hotter than the source.

[Tyndmyr]

The idea that the most energy that could possibly be extracted from Betelgeuse by a system of lenses and mirrors is less than the maximum energy that could be extracted from the Sun by a similar system seems odd to me.

It's a focusing problem. It's not that there isn't a ton of heat, it's that there's no way to concentrate it all in one spot perfectly.

That said, if we're working with insane megastructure level tech, there is a hack. If you put mirrors *all* around the sun(or any other source), you'll increase the heat of the overall system, and thus increase the heat you can focus on any point. For instance, visualize a spherical mirrored surface with a single pinhole. As the only point where light could escape, light striking anywhere else would be reflected and remain in the system. It doesn't truly break the rule, because the sun will heat up, and thus the pinpoint beam escaping will not actually be hotter than the surface, but it will be hotter than the surface would be without the system in place.

This is purely for illustration, the actual construction of such a thing would be more than a little insane for all kinds of practical reason. It's a spherical cow sort of example.

[Chronos]

First time I've ever seen a Dyson cow.

But back to the OP, one way I find helps to think of it is from the point of view of the ant being fried by the magnifying glass. When I look up in the sky, I see mostly cool darkness (well, a little scattered light, but mostly dark), plus a very small spot, a fraction of a square degree, that's at 6000 K. Average those out, and I end up at a temperature of a few hundred K, comfortable for humans (or ants). But when the ant looks up at the magnifying glass that's frying it, it sees the entire magnifying glass, which fills most of its sky, at 6000 K, and so it'll come to an equilibrium temperature that's close to that. Arrange enough mirrors and lenses, and you can make the ant completely surrounded by 6000 K solar surface, and so it'll come to an equilibrium temperature of exactly that. But you can't make the ant see any more than every direction at that temperature, so it can't get any hotter.

[halfeye]

It's a focusing problem. It's not that there isn't a ton of heat, it's that there's no way to concentrate it all in one spot perfectly.

That said, if we're working with insane megastructure level tech, there is a hack. If you put mirrors *all* around the sun(or any other source), you'll increase the heat of the overall system, and thus increase the heat you can focus on any point. For instance, visualize a spherical mirrored surface with a single pinhole. As the only point where light could escape, light striking anywhere else would be reflected and remain in the system. It doesn't truly break the rule, because the sun will heat up, and thus the pinpoint beam escaping will not actually be hotter than the surface, but it will be hotter than the surface would be without the system in place.

This is purely for illustration, the actual construction of such a thing would be more than a little insane for all kinds of practical reason. It's a spherical cow sort of example.

That's one of the ideas that's bugging me. If you put that spherical mirror around Betelgeuse, you'd get more heat out than you would if you put something similar around the sun.

Obviously with current tech we can't do it, but theoretically it seems potentially possible, and the theoretical results seem to be different than this theory of temperature limitation.

[Mechalich]

Note that the maximum temperature humans can currently engineer using concentrated solar is 1000 - 1500 C. This is an area of very active research as industrial groups are working hard to try and hit 1500 C and scale up, allowing solar to be used for things like cement production.

[gomipile]

That's one of the ideas that's bugging me. If you put that spherical mirror around Betelgeuse, you'd get more heat out than you would if you put something similar around the sun.

Obviously with current tech we can't do it, but theoretically it seems potentially possible, and the theoretical results seem to be different than this theory of temperature limitation.

A campfire is not an oven. An oven is not a campfire.

[Anymage]

That's one of the ideas that's bugging me. If you put that spherical mirror around Betelgeuse, you'd get more heat out than you would if you put something similar around the sun.

Obviously with current tech we can't do it, but theoretically it seems potentially possible, and the theoretical results seem to be different than this theory of temperature limitation.

If you put a dyson sphere around Betelguese and channeled all that energy into various contraptions, you could probably concentrate energy down to a point you could probably get that point to be hotter than a point on the surface. With that big an energy source you can do some nuts stuff.

As hinted at in the XKCD linked in the first comment, though, that requires gadgets that have their own energy requirements and failure points. Lenses and mirrors are passive and don't require any additional energy input. They also have various factors that limit their ability to concentrate energy past a certain point. If you leave optics and start using the energy to power different machines you can easily get different outcomes.

[halfeye]

The thing I come down to thinking in the end is how many variables does a photon carry? it obviously must have frequency or wavelength or energy, and it must have position and direction. Does it really have a lot of info about its origin encoded into it? that seems redundant and unnecessary.

[gomipile]

The thing I come down to thinking in the end is how many variables does a photon carry? it obviously must have frequency or wavelength or energy, and it must have position and direction. Does it really have a lot of info about its origin encoded into it? that seems redundant and unnecessary.

Did you read the XKCD What If linked near the beginning of the thread?

[halfeye]

Did you read the XKCD What If linked near the beginning of the thread?

Yes; I didn't get much from it. I don't recall anything about the information in a photon from it.

In theory, there could be anything in a photon, but there are so many photons that it almost has to be the case that there's as little information in there that's just enough to get the job done.

[gomipile]

Yes; I didn't get much from it. I don't recall anything about the information in a photon from it.

In theory, there could be anything in a photon, but there are so many photons that it almost has to be the case that there's as little information in there that's just enough to get the job done.

Re-read the part around the two diagrams of the Sun, a lens, and points A, B, and C.

[NichG]

Since the argument about these limits hinges on reversibility, I wonder if having accelerating lenses/mirrors is enough to beat it (of course at the cost of having to sustain those accelerations against forces exerted by the light).

The thought is based on whether you could e.g. chop a beam and restack it in an irreversible way to get around ettendue.

[factotum]

That's one of the ideas that's bugging me. If you put that spherical mirror around Betelgeuse, you'd get more heat out than you would if you put something similar around the sun.

You would get more *energy* out. The overall temperature would be lower, but Betelgeuse is far larger than the sun so even if the amount of heat per metre squared is lower, there's more energy. You're making the same error in your OP by assuming that something has to be hotter to emit more energy, which is manifestly not the case.

[Khedrac]

First time I've ever seen a Dyson cow.

But back to the OP, one way I find helps to think of it is from the point of view of the ant being fried by the magnifying glass. When I look up in the sky, I see mostly cool darkness (well, a little scattered light, but mostly dark), plus a very small spot, a fraction of a square degree, that's at 6000 K. Average those out, and I end up at a temperature of a few hundred K, comfortable for humans (or ants). But when the ant looks up at the magnifying glass that's frying it, it sees the entire magnifying glass, which fills most of its sky, at 6000 K, and so it'll come to an equilibrium temperature that's close to that. Arrange enough mirrors and lenses, and you can make the ant completely surrounded by 6000 K solar surface, and so it'll come to an equilibrium temperature of exactly that. But you can't make the ant see any more than every direction at that temperature, so it can't get any hotter.

This is the best summary explanation I have seen of this issue - very nice work!

[Mastikator]

In order to get all of the energy out of a star you need to get all the photons, not just the ones that are escaping at an angle perpendicular to the surface.

Using mirrors or lenses can not be used to make all the photons parallel so you can never make make a heated surface smaller than the surface area of the star.

Edit- the only way to use a lens to make an arbitrarily small area arbitrarily warm requires that you have actually parallel light. Only lasers are actually parallel and only lasers can be used to achieve arbitrarily high temperature.

[halfeye]

Re-read the part around the two diagrams of the Sun, a lens, and points A, B, and C.

As I read it that's saying you can't have infinite heat from a lens, which is not controversial at all. Lenses (except concave lenses) produce images, so you can backtrack from the image to the part a particular image came from, what we're hearing here is that you can't make an image smaller than 'x' where x is some proportion of the size of the lens.

Another thing I don't get is how one is supposed to make a perpetual motion device from being able to make an image that is hotter than its original. You need to shrink the size of the image, so you are not getting something as big as the original that is hotter, you are getting something much smaller that is hotter, which has less energy than the original, just in a different form.

You would get more *energy* out. The overall temperature would be lower, but Betelgeuse is far larger than the sun so even if the amount of heat per metre squared is lower, there's more energy. You're making the same error in your OP by assuming that something has to be hotter to emit more energy, which is manifestly not the case.

I thought I was aguing against that, apparently not so clearly as I would like. Betelgeuse is more energetic than the sun, and emits more light, from a much larger surface, so is cooler. What I find odd is the theory that you could get less hear from Betelgeuse, even though it is more energetic.

[Tyndmyr]

That's one of the ideas that's bugging me. If you put that spherical mirror around Betelgeuse, you'd get more heat out than you would if you put something similar around the sun.

While that's true, and you would get more heat out of Betelgeuse(I assume, I haven't actually looked at numbers for total heat output)....the sun is far smaller, and would thus have more heat/square foot, making for a more efficient use of dyson sphere materials.

Yes; I didn't get much from it. I don't recall anything about the information in a photon from it.

In theory, there could be anything in a photon, but there are so many photons that it almost has to be the case that there's as little information in there that's just enough to get the job done.

For this example, the information in a photon is largely irrelevant, we are only caring about the quantity and relative concentration.

Since the argument about these limits hinges on reversibility, I wonder if having accelerating lenses/mirrors is enough to beat it (of course at the cost of having to sustain those accelerations against forces exerted by the light).

The thought is based on whether you could e.g. chop a beam and restack it in an irreversible way to get around ettendue.

Yeah, the impossibility only holds true for an entirely passive system. Active systems can and do break this limit. In theory, you could have some clever device changing angle for every photon(again, wildly into the realm of sci fi) to *make* more parallel. Or absorbing a lot and re-emiting elsewhere, via a solar panel and laser setup.

An extremely rapidly accelerating panel could perhaps briefly reflect enough light to one point to exceed the limit, but the acceleration needed would be a ton of energy.

[gomipile]

Betelgeuse is more energetic than the sun, and emits more light, from a much larger surface, so is cooler. What I find odd is the theory that you could get less hear from Betelgeuse, even though it is more energetic.

You would get less temperature, but potentially more heat from Betelgeuse. Assuming a highly efficient Dyson shell or other heat engine that can process more power than the Sun's output, to make the comparison meaningful.

Heat is transferred energy, not temperature.

[halfeye]

You would get less temperature, but potentially more heat from Betelgeuse. Assuming a highly efficient Dyson shell or other heat engine that can process more power than the Sun's output, to make the comparison meaningful.

Heat is transferred energy, not temperature.

I was walking along the pavement thinking "I should have written "temperature" " after writing that.

I'm even thinking that that Dyson mirror might lower the Sun's temperature (and the equivalent one Betelgeuse's).

For this example, the information in a photon is largely irrelevant, we are only caring about the quantity and relative concentration.

I'm under the impression that with lasers, if you want more temperature, you just add more lasers.

If that is the case with the lasers, and you can't do the same with stars, then the photon has to carry information about the temperature of its source.

[Anymage]

You could certainly use a star to either power a laser directly, or store its energy for future use in lasers. You could then use those lasers to make a given spot as hot as your engineering allows. All those additional gadgets require energy to function and have their own wear and tear issues. Both the lasers themselves, and the energy infrastructure to get the energy from your dyson swarm to whatever devices you want to use.

Optics meanwhile are passive. Mirrors and lenses just sit there and let photons shift their paths. However, the same way that you can make a very good educated guess about where a ball came from if you have sufficient information about its position and momentum, the same could be said for photons. (Ignoring quantum weirdness, since optics cares about collective behavior over individual photons.) This photon here and that photon that landed a millimeter away took slightly different paths, and there's only so much that mirrors and lenses can do to monkey with that. Only being able to concentrate your image so much through optics and can only reasonably gather so much energy from the source, that limits how hot the concentrated image can wind up being.

[Tyndmyr]

I'm under the impression that with lasers, if you want more temperature, you just add more lasers.

If that is the case with the lasers, and you can't do the same with stars, then the photon has to carry information about the temperature of its source.

Nope. No information is being carried in any individual photon. It's not data that enforces this, it's distribution.

Lasers are an active, not a passive system, so they're not subject to this limit. You're putting energy into that system in the form of however you're powering the laser. They're not a good analogy for a star. You're producing a lot of light with very similar wavelengths and orientation with a laser. That's not true for a star, which is radiating light every which way.

That said, even lasers are not truly perfect, and you will hit some eventual limits. While they can be far more precisely focused, the light put out are usually not *exactly* identical in all respects, even if they are very close. Some dissipation will generally happen eventually, putting a hard cap on how many lasers you can add.

Think of it this way. If someone tosses you a pound of sand, you can theoretically catch it if it's in a bucket. If someone throws the same pound of sand into a strong wind, you will not catch it. Each grain of sand is scattered wildly. This is a (very rough) analogy for the photons. With a very large star, they are being scattered from a very large surface area. The more diffusely they are spread, the fewer any given area will catch.

[halfeye]

Optics meanwhile are passive. Mirrors and lenses just sit there and let photons shift their paths.

How does a photon know whether it arrived from a laser and is allowed to heat an area to a particular temperature, or arrived from the surface of a star and isn't allowed to heat that area?

[Tyndmyr]

How does a photon know whether it arrived from a laser and is allowed to heat an area to a particular temperature, or arrived from the surface of a star and isn't allowed to heat that area?

It doesn't know anything. This isn't a decision a photon makes. It's a law about how closely distributed the photons will be.

If you toss the bucket of sand into the wind, the sand doesn't decide to become widely distributed. It just is, because of the nature of wind and sand. This is the same.

[Chronos]

Lasers are subject to the same limitations as any other light source. They don't have a thermal distribution of wavelengths, but a laser of any given wavelength will have an equivalent temperature, and no matter how many of those lasers you have, and no matter what optics you shine them through, you'll never be able to use them to heat a spot to higher than that equivalent temperature. Laser beams are also never truly perfectly unidirectional: You can make them pretty tight, but there will always be some spread, if nothing else from the diffraction limit imposed by the wavelength and the aperture.

[Radar]

Another thing I don't get is how one is supposed to make a perpetual motion device from being able to make an image that is hotter than its original. You need to shrink the size of the image, so you are not getting something as big as the original that is hotter, you are getting something much smaller that is hotter, which has less energy than the original, just in a different form.

Lenses and mirrors do not use energy to do what they do nor do they (in theory) create any losses to the directed and shaped beams of light. This is the key point of the whole problem and it is indeed connected to perpetuum mobile.

If you were able to concentrate light (or anything really) without doing work (and that's what lenses and mirrors do) to obtain higher temperature than in your initial source, this creates temperature difference out of nothing lowering the universes entropy, which is not possible: you can obviously use that temperature difference to extract work out of the system using a standard heat engine. The residual heat from that engine could again be concentrated to the high temperature you need to keep the engine going. So in a closed cycle you convert thermal energy of a single source to useful work without resorting to using some lower temperature reservoir to dump the residual heat into.

I'm under the impression that with lasers, if you want more temperature, you just add more lasers.

If that is the case with the lasers, and you can't do the same with stars, then the photon has to carry information about the temperature of its source.

Even with lasers there will be limitation, but what counts here is the entropy of the light from a given source. Lasers produce by construction light of extremely low entropy so it is easier to obtain high temperatures using those. Stars are pretty much black bodies (as weird as it sounds), so the entropy of emitted light is actually very high - if I remember correctly emission of light with that distribution produces maximum of entropy for a given energy emitted. So if you want to concentrate it you are quite limited unless you put some work into it.

[Quizatzhaderac]

How does a photon know whether it arrived from a laser and is allowed to heat an area to a particular temperature, or arrived from the surface of a star and isn't allowed to heat that area?

If the photon can get to the area, it can heat the area. The question is how many photon can be corralled into the area.

If the photons are well aligned (as in a laser) you can get them to travel together. If they can travel you get get a bunch of lasers to converge on the same spot.

If the photons aren't well aligned (like from a star) they won't travel together. If you try to get light from many points on Betelgeuse to the same spot, you'll lose most along the way since they didn't start out going in the same direction.

[NichG]

The issue isn't so much alignment as it is needing photons traveling on the same path to catch up with eachother. With reversible optics you'd have the problem that at some point on the reverse path, two photons at the same position and direction must spontaneously go in different directions. But with nonlinear optics or active optics (such as stimulated emission in a laser) you can have one point in space absorb two photons from different directions and times, and emit them in the same direction and time.