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What-If 0145: "Fire From Moonlight"

Posted: Wed Feb 10, 2016 8:58 am UTC
Fire From Moonlight

Rogier Spoor wrote:Can you use a magnifying glass and moonlight to light a fire?

xkcd wrote:At first, this sounds like a pretty easy question.

Why can't you "smoosh" light? Go from θOut to θIn and light is smooshed.

Also assuming the mirrors and lenses are lossless, wouldn't you be able to add the light from multiple different angles, using multiple mirrors and lenses, effectively creating a point source?

And an alternate option is LOTS of solar panels powering a bulb, or spark ignition source, but that is off topic.

Re: What-If 0145: "Fire From Moonlight"

Posted: Wed Feb 10, 2016 9:02 am UTC
Hi there,

I'm afraid the discussion in the article is not quite correct.

There are three main points:

1) The final temperature depends neither on how tightly the incident light
is focussed, nor on the power density in the focus, but only on the spectral
composition.

2) A rock on the moon barely sees the moon's surface, but mostly the empty
universe.

3) The temperature of the object in focus will end up between that of the
moon's and the sun's surfaces.

Perhaps the easiest way to see a problem in the argumentation is to consider
a parabolic mirror instead of the moon as a reflector: It is clearly cooler
than an object placed in its focus. One could argue that these two reflectors
cannot be compared, because the moon does not reflect specularly. However,
this is actually irrelevant for the principle, it just makes the moon a
horribly inefficient reflector.
I hope the following will be convincing.

The temperature of a body 'A' in equilibrium with the electromagnetic field
is the temperature of all objects visible from 'A' averaged over the whole
solid angle and weighted with their respective emissivities.
As you correctly pointed out, a lens mainly trades illuminated area for solid
angle of illumination. By focusing the sun on an object you simply modify the
solid angle distribution when the object "averages" the objects it sees. If
the lens is directed toward the sun, the object "sees" the sun over a larger
solid angle and gets hotter.
Incidentally, if the lens is directed towards empty sky on a sunny day, the
object in focus will actually cool below ambient temperature.

Now let's get to the point: the moon.
The moon is a reflector that weakly couples the sun to our object. In addition,
the moon is a thermal radiator whose equilibrium temperature is defined by the
solid angle of the sun (as seen from the moon) and the sun's temperature (we
can pretty much ignore the temperature of the rest of the universe). The moon's
thermal emissivity is proportional to its "blackness" (something like 1-minus-albedo).
On the other hand, the effective emissivity of the sun via the moon is (apart
from some boring prefactors) the product of the sun's original emissivity, the
moon's albedo, the moon's solid angle (as seen from the receiver) and the sun's
solid angle (as seen from the moon). The solid angles enter because the
reflection is assumed to be diffuse.
If we now place 'A' under a lens with very high numeric aperture directed
towards the moon while insulating the back against thermal loss (or if we buy
two mirrors and another lens to illuminate both sides of 'A' with moon light),
the object is in thermal contact with two reservoirs: The moon (directly) and
the sun (via the moon). The equilibrium temperature is then the temperature of
the moon's surface weighted by its native emissivity and the sun's surface
weighted by its effective emissivity via the moon. The equilibrium temperature
will therefore always end up between the temperatures of the moon's and the
sun's surfaces.
It can be increased e.g. by increasing the reflector's reflectivity (reducing
its own emissivity at the same time). An extreme case for this is a mirror:
very high and specular (eliminates the solid angles in the effective emissivity)
reflectivity, barely any thermal emission on its own.

So what does the power density in the focus mean? Nothing for the equilibrium
temperature. It just defines how susceptible the effect is to parasitic thermal
coupling (a.k.a. loss).

In conclusion: I agree that it's probably impossible to light a fire by
focussing light from our moon (just my belly speaking at this point), but it
would be possible if painted the moon with a very bright white paint. It might
also be possible with a highly reflective artificial satellite as depicted
in "Die another day"

Cheers, Christian.

Re: What-If 0145: "Fire From Moonlight"

Posted: Wed Feb 10, 2016 9:14 am UTC
tagno25 wrote:Why can't you "smoosh" light? Go from θOut to θIn and light is smooshed.

The light beams coming out the θOut side are more aligned with each other, but spaced further apart. Conversely, the light beams coming out the θIn side are spaced more closely together, but less aligned with each other. To smoosh light you have to make the beams close together and aligned, but the best you can do is trade one of those things for the other. That's the conservation of what the French call a certain I-can't-spell-that-word-and-I'm-too-lazy-to-copy-paste that Randall talked about.

Now here's a thought experiment. On the other end of that lense that squishes light closer together at the cost of misaligning it, you have a mirror tube, and at the end of that tube a flat mirror, and you put the thing you want to light on fire inside that setup. All the light that got squished-but-scattered is now being confined in a small space and impinging on the thing you want to burn from all sides. How does this not circumvent the problem and effectively give you "smooshed light"? (It's still just the equivalent of making the moon fill the whole sky of the thing-to-be-burned, and so things still won't get hotter than moon rocks, but it seems that it does give you what you were going for with the attempt to smooth the light together).

Re: What-If 0145: "Fire From Moonlight"

Posted: Wed Feb 10, 2016 9:19 am UTC
A lens that spreads out parallel light seems to violate conservation of étendue. For the input, area times angle is 0 since the angle is 0. But the output is not zero.

Re: What-If 0145: "Fire From Moonlight"

Posted: Wed Feb 10, 2016 9:23 am UTC
This is a fairly well-studied problem for engineers of solar thermal energy (those big power stations in the desert using mirrors to make steam to run a turbine & generator). In fact, it's very useful in that field that you can't light a fire using moonlight, as moonlight is used to calibrate the mirrors sometimes.

I mean, the idea of all those mirrors is that they focus the sun's image several thousand times onto something... you don't want to miss whatever you're aiming at, otherwise you'll fry your support structure. And, it's annoying to manually cover and uncover individual mirrors... so just do it at night under a full moon. You need to change the sun-tracking algorithm a bit, but the moon has basically the same solid angle (see: solar eclipse) and doesn't come with the problem of accidentally melting your stuff.

Re: What-If 0145: "Fire From Moonlight"

Posted: Wed Feb 10, 2016 9:41 am UTC
"But wait," you might say. "The Moon's light isn't like the Sun's! The Sun is a blackbody—its light output is related to its high temperature. The Moon shines with reflected sunlight, which has a "temperature" of thousands of degrees—that argument doesn't work!"

I still don't understand how this argument fails.

If the moon were a perfect mirror orbiting earth, you clearly could use its light to light a fire.

If, on the other hand, the moon were a perfect black body, this would not work for the reasons given by Randall.

In reality the moon is something in between (or different, since it scatters light). I don't see a compelling argument why it is could not be close enough to being a mirror for the fire lighting to work.

Re: What-If 0145: "Fire From Moonlight"

Posted: Wed Feb 10, 2016 10:33 am UTC
SubReal wrote:
"But wait," you might say. "The Moon's light isn't like the Sun's! The Sun is a blackbody—its light output is related to its high temperature. The Moon shines with reflected sunlight, which has a "temperature" of thousands of degrees—that argument doesn't work!"

I still don't understand how this argument fails.

If the moon were a perfect mirror orbiting earth, you clearly could use its light to light a fire.

If, on the other hand, the moon were a perfect black body, this would not work for the reasons given by Randall.

In reality the moon is something in between (or different, since it scatters light). I don't see a compelling argument why it is could not be close enough to being a mirror for the fire lighting to work.

I had the same issue. The article follows that original quote with "It turns out it does work, for reasons we'll get to later", but I don't see an explanation of why the moon can't be regarded as an imperfect mirror reflecting the surface of the sun.

Re: What-If 0145: "Fire From Moonlight"

Posted: Wed Feb 10, 2016 11:52 am UTC
The argument is that moon rocks don't get that hot, and they being hit by moonlight from many directions, plus the sun, for two weeks at a time.

Re: What-If 0145: "Fire From Moonlight"

Posted: Wed Feb 10, 2016 11:54 am UTC
SubReal wrote:
"But wait," you might say. "The Moon's light isn't like the Sun's! The Sun is a blackbody—its light output is related to its high temperature. The Moon shines with reflected sunlight, which has a "temperature" of thousands of degrees—that argument doesn't work!"

I still don't understand how this argument fails.

If the moon were a perfect mirror orbiting earth, you clearly could use its light to light a fire.

If, on the other hand, the moon were a perfect black body, this would not work for the reasons given by Randall.

In reality the moon is something in between (or different, since it scatters light). I don't see a compelling argument why it is could not be close enough to being a mirror for the fire lighting to work.

Yes, this. Replace the moon with a gigantic parabolic mirror, would you be happy to sit in its focus? I wouldn't.
Also:

If you're surrounded by the bright surface of the Moon, what temperature will you reach? Well, rocks on the Moon's surface are nearly surrounded by the surface of the Moon, and they reach the temperature of the surface of the Moon (since they are the surface of the Moon.) So a lens system focusing moonlight can't really make something hotter than a well-placed rock sitting on the Moon's surface.

Here lies the trick, I think. The starting condition should be: "If you're surrounded by the bright surface of the Moon and you have the same reflectivity of the surface of the Moon". Surely a carbon black stone dropped in the middle of the surface of the Moon would raise at a higher temperature - just like on Earth asphalt ends up hotter than limestone if both are left in the sunlight in summer. So I really think the argument is at least incomplete - it can be fixed if we take into account that, say, the Moon's surface average reflectivity is roughly the same order of magnitude of anything you may reasonably be trying to set on fire, or possibly smaller.

I'm also kind of disappointed that Randall didn't go there but - forget a regular magnifying lens, what if I used a gravitational lens? I mean, the 2nd principle apparently still holds even for black holes, so I don't expect to be able to violate that, but I don't think the conservation of etendue would still hold either. After all squeezing world-lines in a tighter space is what distorted spacetime is all about. And a black hole fundamentally does exactly that - focusing all light from any source into a single point. Of course in that sense it also seems to destroy the information contained in that light, which is in itself an apparent paradox and a problem with black holes. So maybe the no-hair problem and conservation of etendue are somewhat related.

Re: What-If 0145: "Fire From Moonlight"

Posted: Wed Feb 10, 2016 12:06 pm UTC
Caesar wrote:A lens that spreads out parallel light seems to violate conservation of étendue. For the input, area times angle is 0 since the angle is 0. But the output is not zero.

The formula for étendue is not using an angle directly, but cosine of an angle, so it's fine.

I still don't get the argument. If you replace the moon by a reflective sphere, will it be possible light the fire with moonlight? How close is the moon to the reflective sphere?

Someone should conduct an experiment: is it possible to light a fire using sunlight reflected by a sheet of paper/a bright wall.

Re: What-If 0145: "Fire From Moonlight"

Posted: Wed Feb 10, 2016 12:22 pm UTC
SubReal wrote:If the moon were a perfect mirror orbiting earth, you clearly could use its light to light a fire.
If it were a perfect mirror, then it should be treated as an actual lens for the sun, not the shining moon as we know it (which absorbs sunlight and reflects/re-emits energies differently... noting that standard mirrors aren't perfect, themselves, but I'm considering them in this example), and thus it would be possible.

My actual first thoughts for what you meant about the "perfect mirror" moon first made me strayed through the concept of 'disco ball', but even more so that perfect sphere of reflectivity would disperse the light and make the 'sun reflection' appear as a much smaller pin-prick than the entire moon-width, but then with an additional 'corrective' lens between ourselves and the moon you could gather enough of that light back in again to emulate the collection of the Sun with a 'regular' hand-lens, I think.

A flat mirror a moon-radius in size, and aimed just so, would reflect the Sun as if it was a second sun (or as much of the Sun as it would let us see, which is basically the whole Sun anyway) so would be a 'sun' that wouldn't need anything more than your regular Boy Scout magnifying glass to use exactly as you would with the Sun itself.

[Meant to add the following (related) puzzle, paraphrasing something that came in a (rather intellectual) cracker at Christmas... If a man six feet in height wants a mirror that he can see his whole self in, when standing three feet away, what's the shortest mirror he can get away with? What if he stands twelve feet away from the mirror?]

A focussing-mirror would already be (in effect) a magnifying glass the size of the moon focussing the Sun. Which is overkill, and one small step along the route towards What-If 141. But it would mean that we wouldn't need to carry around a magnifying glass. (Just some form of communication with the focussing-moon-mirror's main control room, to get them to angle it to aim particularly at your small pile of kindling, rather than any other part of the planet where combustible or heat-damageable materials might well exist.)

...but that's just my first thoughts, ICBW.

(m1el posted whilst I was writing this - see first example)

Re: What-If 0145: "Fire From Moonlight"

Posted: Wed Feb 10, 2016 12:26 pm UTC
Gan_HOPE326 wrote:Surely a carbon black stone dropped in the middle of the surface of the Moon would raise at a higher temperature - just like on Earth asphalt ends up hotter than limestone if both are left in the sunlight in summer. So I really think the argument is at least incomplete - it can be fixed if we take into account that, say, the Moon's surface average reflectivity is roughly the same order of magnitude of anything you may reasonably be trying to set on fire, or possibly smaller.

I think that is a short term effect, the stone and the limestone would eventually get the the same temperature. Also, the moon is actually quite dark.

I'm also kind of disappointed that Randall didn't go there but - forget a regular magnifying lens, what if I used a gravitational lens? I mean, the 2nd principle apparently still holds even for black holes, so I don't expect to be able to violate that, but I don't think the conservation of etendue would still hold either. After all squeezing world-lines in a tighter space is what distorted spacetime is all about. And a black hole fundamentally does exactly that - focusing all light from any source into a single point. Of course in that sense it also seems to destroy the information contained in that light, which is in itself an apparent paradox and a problem with black holes. So maybe the no-hair problem and conservation of etendue are somewhat related.

In gravitational lensing we do have the surface brightness theorem, which still holds. Sources only appear to be brightened because they are magnified. The sun is exactly as bright as any other similar star, per angular size. The sun is only 10 billion times brighter than Alpha Centauri because it is 10 billion times larger in the sky.

Re: What-If 0145: "Fire From Moonlight"

Posted: Wed Feb 10, 2016 12:26 pm UTC
m1el wrote:
Caesar wrote:Someone should conduct an experiment: is it possible to light a fire using sunlight reflected by a sheet of paper/a bright wall.

We KNOW it's possible to light a fire using a parabolic mirror:

and I very much doubt the mirror itself reached a temperature higher than that of the paper. Why would it need to? Thermodynamics doesn't forbid very efficient near-reversible processes, and that's what light reflecting off a mirror is. It never degrades to thermal energy ON THE MIRROR - it is just a mediated exchange between sun and piece of paper. The thermodynamic rule would apply only if you heated a body with sunlight, then used its own blackbody radiation to heat up something else. THEN the temperature of the mediating body would be the upper limit.

Nicias wrote:
Gan_HOPE326 wrote:Surely a carbon black stone dropped in the middle of the surface of the Moon would raise at a higher temperature - just like on Earth asphalt ends up hotter than limestone if both are left in the sunlight in summer. So I really think the argument is at least incomplete - it can be fixed if we take into account that, say, the Moon's surface average reflectivity is roughly the same order of magnitude of anything you may reasonably be trying to set on fire, or possibly smaller.

I think that is a short term effect, the stone and the limestone would eventually get the the same temperature. Also, the moon is actually quite dark.

I know. That's why I think the argument is right, it's just that he disregarded mentioning the key point of the moon's reflectivity.

And the stones would get to the same temperature because they are in thermal contact. If the stone was isolated by conduction (convection being obviously impossible because duh, Moon), then its temperature would be a function of total incoming radiation, meaning the radiation received from both the Sun and the surface of the Moon (reflected and blackbody), and its own emissivity/reflectivity. Hence, it could end up being hotter.

Re: What-If 0145: "Fire From Moonlight"

Posted: Wed Feb 10, 2016 12:36 pm UTC
I'm still confused a bit here as to why you wouldn't be able to take, say, 5 ideal convex lenses refracting different points of the moon's reflection and overlap their outputs to get a theoretical max of 500 degrees. It seems to violate the basic thermodynamics argument presented (the cumulative total is reversible, and you're boosting 100 degrees theoretical max up to 500 ("something for free")). But I don't see anything in the rules about optics mentioned that says you can't since there wouldn't be a single source point exceeding it's origin or a single lens with multiple "choices" of reverse paths...

Re: What-If 0145: "Fire From Moonlight"

Posted: Wed Feb 10, 2016 12:40 pm UTC
Nicias wrote: Also, the moon is actually quite dark.

INB4 There is no dark side of the moon. Actually the entire moon is dark.

FWIW, the radiance of a full moon, despite looking very bright in the night sky, is about as bright as a dusty blackboard (the old kind, actually black, w/ white chalkdust on it).

Re: What-If 0145: "Fire From Moonlight"

Posted: Wed Feb 10, 2016 12:48 pm UTC
Positron wrote:I'm still confused a bit here as to why you wouldn't be able to take, say, 5 ideal convex lenses refracting different points of the moon's reflection and overlap their outputs to get a theoretical max of 500 degrees. It seems to violate the basic thermodynamics argument presented (the cumulative total is reversible, and you're boosting 100 degrees theoretical max up to 500 ("something for free")). But I don't see anything in the rules about optics mentioned that says you can't since there wouldn't be a single source point exceeding it's origin or a single lens with multiple "choices" of reverse paths...

I think you could, except it wouldn't be 500 degrees because it's not linear. But in the end it all boils down to the same argument - is this light bound by the temperature of the Moon, or is it not, since it's reflected light?

https://en.wikipedia.org/wiki/Solar_furnace

Apparently, solar mirrors can reach temperatures up to 4000 C, which is pretty damn close to the thermodynamic limit imposed by the temperature of the Sun. I very much doubt the mirror's surface itself withstands such temperatures as well. I think the mirror is certainly going to be hot but not nearly that hot, and it can heat up the furnace because it's merely *reflecting* light. By the same principle, I don't think the temperature of the Moon is an intrinsic upper limit to how much you can heat up something with its light. Though it may as well be that Randall's conclusions are correct, they probably stem more from the numbers and aren't as trivial as he makes them to be.

Re: What-If 0145: "Fire From Moonlight"

Posted: Wed Feb 10, 2016 12:53 pm UTC
Positron wrote:I'm still confused a bit here as to why you wouldn't be able to take, say, 5 ideal convex lenses refracting different points of the moon's reflection and overlap their outputs to get a theoretical max of 500 degrees. It seems to violate the basic thermodynamics argument presented (the cumulative total is reversible, and you're boosting 100 degrees theoretical max up to 500 ("something for free")). But I don't see anything in the rules about optics mentioned that says you can't since there wouldn't be a single source point exceeding it's origin or a single lens with multiple "choices" of reverse paths...

I think there's something someone could probably say here about "heat" being different from "temperature". I'm actually surprised Randall didn't go into that, so maybe I'm wrong in assuming that this is a vital part of the moon-lens argument, but it's still something that people should realise is 'a thing'.

(But if you get five cups of warm water, each at 20C, consider how you would then convert that into a mug of water boiling at 100C. Also, give than 20 Celsius is 293 Kelvin, why wouldn't you get something that is 1458K, instead? Either way, I'm pretty sure that's a related problem.)

Re: What-If 0145: "Fire From Moonlight"

Posted: Wed Feb 10, 2016 1:22 pm UTC
If the moon were only a black body object emitting light at a black body temperature of 100°C it would not be visible in the night's sky with our eyes.
If it only reflected diffusely the albedo would not change during phases. And it does with approximately this graph.
If it were purely a mirror it would be as bright as the sun.
Ergo the truth is somewhere in between. The average albedo (≈reflectivity) is 0.12. The maximum albedo is higher, but I can't find it.

Re: What-If 0145: "Fire From Moonlight"

Posted: Wed Feb 10, 2016 1:26 pm UTC
Neil_Boekend wrote: The maximum albedo is higher, but I can't find it.

Did you look under the bed?

Re: What-If 0145: "Fire From Moonlight"

Posted: Wed Feb 10, 2016 1:41 pm UTC
Neil_Boekend wrote:If it only reflected diffusely the albedo would not change during phases. And it does with approximately this graph.

My snap thought is that it's something to do with the intrinsic retroreflectivity of the lunar regolith1, such that the full-moon phase has a near-parallel bounce-back of light from even the angled edges of the Moon, whereas in partial phases the light has to bounce off at some other angle to reach our eyes.

But that's just a guess.

(ETA: And it's also roughly what you linked to in the Opposition Surge link. I really shouldn't be a snap-replier before checking out links, but at least now I know the proper name for it.)

1 Actually the generalised problem regarding light from almost directly behind being more obvious on a complex and textured/obstacle-strewn surface than that which arrives and departs at differing angles. See also the enhanced 'halo' surrounding the 'brockenspectre' effect, similarly acting with the diffuse aerosol of the cloud/mist and adding to the contrast against your own 'eclipsed' shadow area.

Re: What-If 0145: "Fire From Moonlight"

Posted: Wed Feb 10, 2016 1:50 pm UTC
I must say, this is the best What If in a long time. I'd always heard the rule about not being able to change temperature with optical systems, but it never really made sense until now.

Re: What-If 0145: "Fire From Moonlight"

Posted: Wed Feb 10, 2016 1:59 pm UTC
So, what would stop someone from building a giant optical resonation cavity to turn the moonlight into a giant laser?

Re: What-If 0145: "Fire From Moonlight"

Posted: Wed Feb 10, 2016 2:01 pm UTC
nick012000 wrote:So, what would stop someone from building a giant optical resonation cavity to turn the moonlight into a giant laser?

Difficulty with planning regulations?

Re: What-If 0145: "Fire From Moonlight"

Posted: Wed Feb 10, 2016 2:02 pm UTC
I learned something today.

Re: What-If 0145: "Fire From Moonlight"

Posted: Wed Feb 10, 2016 2:53 pm UTC
The moon is a convex surface so it scatters sunlight in all directions rather than focusing it. That's why it can't act as a mirror.

Re: What-If 0145: "Fire From Moonlight"

Posted: Wed Feb 10, 2016 3:07 pm UTC
sevenperforce wrote:The moon is a convex surface so it scatters sunlight in all directions rather than focusing it. That's why it can't act as a mirror.

Yes and it's also rough so it scatters rather than reflecting geometrically. The issue is, the fact that it DOES reflect light means however that the thermodynamic argument doesn't hold alone, because if it did then it would hold for anything, including a mirror. The thermodynamical argument does not rely on the shape or properties of the object as Randall presented it. I think the conclusion is right, I just think it takes more hypotheses and considerations on the nature of the lunar surface and its properties to come to it rather than just say "because the 2nd law says so".

Re: What-If 0145: "Fire From Moonlight"

Posted: Wed Feb 10, 2016 4:01 pm UTC
sevenperforce wrote:The moon is a convex surface so it scatters sunlight in all directions rather than focusing it. That's why it can't act as a mirror.

A convex retroreflector would reflect light in one direction. Your argument does not completely hold. As for the moon, it does something similar, as the extreme increase in brightness during full moon versus half moon indicates.

Re: What-If 0145: "Fire From Moonlight"

Posted: Wed Feb 10, 2016 4:20 pm UTC
Yeah, this one was just wrong, and it's disappointing that Randall got it wrong with thermodynamics, of all things.

The flaw in the answer is that the Laws of Thermodynamics only apply on closed systems. The sun-moon-lens-paper system isn't a closed one (in the classical sense), as there's a frikin' star-sized fusion reactor acting as an external power supply; laws of thermodynamics only come to fuck you up when the sun runs out of fuel.

With a large enough perfect mirror (think of a dyson sphere with sun-tracking hole the size of the moon) you could set the moon on fire with moonlight.

Re: What-If 0145: "Fire From Moonlight"

Posted: Wed Feb 10, 2016 4:45 pm UTC
paha arkkitehti wrote:With a large enough perfect mirror (think of a dyson sphere with sun-tracking hole the size of the moon) you could set the moon on fire with moonlight.

You mean with sunlight? I don't think you could set the *Moon* on fire with moonlight because it already receives it and it fares pretty well (you could, arguably, concentrate it all in one point and that point wouldn't be very happy).

Re: What-If 0145: "Fire From Moonlight"

Posted: Wed Feb 10, 2016 4:57 pm UTC
paha arkkitehti wrote:The sun-moon-lens-paper system isn't a closed one (in the classical sense), as there's a frikin' star-sized fusion reactor acting as an external power supply

That fusion reactor is the sun, which is obviously a part of the sun-moon-lens-paper system, not external to it.

If you go into a closed room with a Mr. Fusion generator, you won't be able to use the power of that generator to decrease the total entropy of the room; specifically, if you use Mr. Fusion to power a lightbulb, you won't be able to use lenses to make anything hotter than that lightbulb.

To more clearly understand why, take note of the fact that there is light flying around everywhere in the room at all times, bulb or not, most of it's just not visible. If lenses could do what we wanted here, you could set up some lenses to focus that light on one side of the room, making it hotter than the other side, and then use that temperature differential to drive an engine and bam you got useful work out of a system at thermodynamic equilibrium in violation of the second law of thermodynamics.

Re: What-If 0145: "Fire From Moonlight"

Posted: Wed Feb 10, 2016 5:11 pm UTC
Pfhorrest wrote:To more clearly understand why, take note of the fact that there is light flying around everywhere in the room at all times, bulb or not, most of it's just not visible. If lenses could do what we wanted here, you could set up some lenses to focus that light on one side of the room, making it hotter than the other side, and then use that temperature differential to drive an engine and bam you got useful work out of a system at thermodynamic equilibrium in violation of the second law of thermodynamics.

Thermodynamics have nothing to do with temperature, but everything to do with energy. You can increase temperature differential without breaking rules of thermodynamics, you can't increase energy differential. Otherwise you couldn't burn anything; lighting a match clearly increases temperature differential, but in the process chemical energy is lost. In case of the sun-moon-lens-paper system mass is lost in the fusion reaction.

Gan_HOPE326 wrote:You mean with sunlight? I don't think you could set the *Moon* on fire with moonlight because it already receives it and it fares pretty well (you could, arguably, concentrate it all in one point and that point wouldn't be very happy).

Yeah, that was kind of the point. There is no "moonlight", only sunlight reflected by the moon. If you stop energy from escaping the moon while allowing more to enter (using the dyson's mirror with a hole towards the sun), eventually the temperature of the moon will reach ignition point (or melting point, as there's not enough oxygen in moon to actually burn anything).

Re: What-If 0145: "Fire From Moonlight"

Posted: Wed Feb 10, 2016 5:33 pm UTC
paha arkkitehti wrote:Yeah, that was kind of the point. There is no "moonlight", only sunlight reflected by the moon. If you stop energy from escaping the moon while allowing more to enter (using the dyson's mirror with a hole towards the sun), eventually the temperature of the moon will reach ignition point (or melting point, as there's not enough oxygen in moon to actually burn anything).

I imagine so. Surround the whole solar system with a Dyson sphere of mirror satellites and you can bring anything within it to 6000 C, instantaneously.

It's also interesting to think what would happen *then*. I believe equilibrium would be reached because the thing would start emitting roughly black-body 6000 C radiation too, which would go back to the Sun, so the energy balance gets evened out. However if a significant fraction of the Sun's own solid angle is covered by this Dyson sphere (and therefore by this hypothetical new star-hot object), then the Sun couldn't get rid of all its energy any more, and its nuclear fusion reaction would begin to heat it up. Which would lead to it expanding or probably ending up even hotter.

I think you could *heat up the Sun* in this way .

Re: What-If 0145: "Fire From Moonlight"

Posted: Wed Feb 10, 2016 6:00 pm UTC
I believe he is probably correct, however, as many have said the argument he makes is probably wrong. The moon is acting as a mirror (a poor mirror, but one nonetheless), and the thermodynamic argument will not hold because the emitting source is still the sun and not the moon.

Consider a simple thought experiment, say I increase the absorption (decrease the albedo) of the moon. This would cause the moons temperature to go up (more solar radiation retained), but the reflected radiation would be less intense. Go the opposite direction and you get the moon cooling and the intensity of the light going up. Thus the moon's surface temp is actually inverse with the temp achievable by moonlight.

Now my gut tells me that if you were to do the problem of a spherical mirror with reflectivity equal to the moons albedo, and the geometric constraints of the earth moon sun system, there will be no lense that can achieve a very high temperature (certainly not a practical one, not that practical is a consideration for whatif). That being said I do not believe the argument presented in the post holds up. The temperature will be lower than that of the surface of the sun, but the bound will not be set by the temperature of the moon (though I imagine it will be much closer to 100 C than 5600 C). I think you actually need to do the radiation heat transfer problem to know for sure.

Re: What-If 0145: "Fire From Moonlight"

Posted: Wed Feb 10, 2016 6:10 pm UTC
Caesar wrote:A lens that spreads out parallel light seems to violate conservation of étendue. For the input, area times angle is 0 since the angle is 0. But the output is not zero.

The cosine bit that someone else pointed out is one answer. The other is that there is no such thing as perfectly parallel light. All beams have divergence.

This is a great What If, and is tied in to the recent one about focusing all the Sun's light on Earth, which can't be done for the same reasons of conservation of entendue.

I've seen some highly educated scientists tripped up on this, even PhD physicists. They think that simply adding another lens will somehow magically increase the brightness of a laser beam or IR source.

Re: What-If 0145: "Fire From Moonlight"

Posted: Wed Feb 10, 2016 6:50 pm UTC
(But if you get five cups of warm water, each at 20C, consider how you would then convert that into a mug of water boiling at 100C. Also, give than 20 Celsius is 293 Kelvin, why wouldn't you get something that is 1458K, instead? Either way, I'm pretty sure that's a related problem.)
Probably because you're not concentrating anything? 5 individual cups at 20C combined is still 5 cups at 20C

Re: What-If 0145: "Fire From Moonlight"

Posted: Wed Feb 10, 2016 7:12 pm UTC
Alright, did some thinking and yes, I was wrong. You can't use lenses to set things on fire using moonlight. But it's not because of thermodynamics, it's because of optics, just as Randall explained.

You'd need photovoltaics or some similar energy conversion method in addition to optics to burn things with moonlight.

Re: What-If 0145: "Fire From Moonlight"

Posted: Wed Feb 10, 2016 7:25 pm UTC
paha arkkitehti wrote:Alright, did some thinking and yes, I was wrong. You can't use lenses to set things on fire using moonlight. But it's not because of thermodynamics, it's because of optics, just as Randall explained.

You'd need photovoltaics or some similar energy conversion method in addition to optics to burn things with moonlight.

And those photovoltaics or whatever are not entropy-neutral like lenses are, and that's why they let you get around the thermodynamic problem.

The whole thermodynamic argument hinges on lenses being static, passive "devices". I put that in quote because they're not really doing anything, which is why they are entropically neutral additions to the system, and why adding or rearranging lenses in a system can't cause it to lose entropy.

If you start doing something to the system then yeah, you can cause a decrease of entropy.

Re: What-If 0145: "Fire From Moonlight"

Posted: Wed Feb 10, 2016 8:34 pm UTC
He got to here...
The Moon's sunlit surface is a little over 100°C, so you can't focus moonlight to make something hotter than about 100°C.

That's too cold to set most things on fire.

...and I kept waiting for the "but what if we..." part of the WhatIf. Most things?? What are the few things??

Re: What-If 0145: "Fire From Moonlight"

Posted: Wed Feb 10, 2016 8:50 pm UTC
Keyman wrote:He got to here...
The Moon's sunlit surface is a little over 100°C, so you can't focus moonlight to make something hotter than about 100°C.

That's too cold to set most things on fire.

...and I kept waiting for the "but what if we..." part of the WhatIf. Most things?? What are the few things??

Just about anything, assuming a F2O2 environment (including sand!).
In air: silane and white phosphorus

Re: What-If 0145: "Fire From Moonlight"

Posted: Wed Feb 10, 2016 8:51 pm UTC
Soupspoon wrote:if you get five cups of warm water, each at 20C, consider how you would then convert that into a mug of water boiling at 100C.

Stick four cups in the freezer, and wait for the first law of thermodynamics to kick in.