What is the absolute hottest temp you coild obtain by focusing the suns light into a small spot? I understand there would have to be some logistical restrictions, such as a practical mirror (in size), etc.
Given that we can make huge mirrors - as big as small houses - is there a potential to focus or magnify the light/energy to a small spot and make it insanely hot?
It can only get as hot as the source, so about 6000 degrees. If you could create a higher temperature, you’d be violating the 2nd law of thermodynamics.
You hit this limit when you try to concentrate the light into a small area. Let’s say you have a large parabolic mirror that focuses a parallel light beam into a perfect point. Sunlight is not a perfectly parallel beam of light because it’s emitted by a 1/2-degree disc in the sky, so it creates a circular spot with finite size. Past a certain limit, you can’t increase the size of the mirror without increasing the size of the spot.
From the Department of Energy website describing Solar Two, a concentrating reflector used in a power plant.
At Solar Two, the molten nitrate salt reached approximately 1,050°F (565°C) in the receiver and then traveled to a storage tank, which had a capacity of 3 hours of storage
This is probably not the theoretical maximum. If you could find a mesa at a high altitude (to reduce atmospheric losses) and manufacture mirrors that were large, but also within enough tolerance to set their focal point exactly at the same point as all the others (+/- 10cm ?), you could make a really really large spread of those mirrors. But then the problem becomes what you want to do with the heat. Molten salt sounds like a pretty extreme heat transfer fluid.
Hang on a moment though - you may be right (although my gut feeling is otherwise), but I’m just trying to get my head around this - you could create a number of mirrors that are all focusing a small spot on the same target (actually, isn’t this all that a single mirror would do - focus a number of rays in the same place).
I’m pretty sure we covered this a while back in a thread relating to covering the entire visible surface of the moon with small, posable mirrors.
Somebody already mentioned “Solar II” while I was poking around about “heliostat arrays”. Here’s another blurb about it:
http://rhlx01.rz.fht-esslingen.de/projects/alt_energy/sol_thermal/powertower.html
And here’s another heliostat array setup:
http://www.imp.cnrs.fr/foursol/1000_en.shtml
So, in terms of practical achievement, you can get pretty damned hot. I’ll let others thrash out how small a spot you can theoretically focus, etc.
IANAPhysicyst, but I think that temperature would be more a function of energy density, not total energy. Shouldn’t a large enough lens with a high reduction be able to crate temperatures well over the surface temperature of the sun?
If you want to know how insanely hot people have made things using focused sunlight, the White Sands Solar Furnace “can focus 5,000 degrees Fahrenheit.” A solar furnace in Odeillo, France has a maximum temperature of 3,800 degrees Celsius (2,900C according to the White Sands link.)
Link to the thread I mentioned above.
There are two quantities here: temperature and heat. The temperature cannot be higher than the sun’s surface temperature. However, the heat (thermal energy) is proportional to the cross-sectional area of sunlight captured. So large mirrors will focus more energy.
What happens if we focus a huge mirror into a small volume? The focus volume will heat up, possibly to the sun’s surface temperature. At that point we will have reached thermal equilibrium (with the sun, no less!), and further increases in temperature will not occur.
The thermal equilibrium is the important point. Remember that the mirror (or lens) is a two-way device–thermal radiation from our target is also being sent back to the sun. When our target is much cooler than the sun, the heat transfer is approximately one-way. But when the target is as hot as the sun, equal amounts of heat are being radiated from the target to the sun. We have equilibrium!
I have a bad feeling about this thread.
Nice explanation Pleonast.
Is there a way to beat thermal equilibrium using the fact that the speed of light is finite? Not giving the system enough time to reach equilibrium could the temperature be ‘cheated’ to above the suns surface temperature?
Mangetout 
I don’t like what happens when I think about focusing the sun’s rays back onto the sun’s surface … ( how hot can a brain cell get before it expires )
On the way back to the sun, through the focusing apparatus (in the other direction), the returned energy is being dispersed by the lens/mirror (the opposite of what happens on the way down - I’m not a physicist (which is why I have such grave concern about the future of this thread, based on what has happene in the past when my ‘intuition’ has rubbed up against the science of those better qualified), but I can’t see what would stop the target from heating up to a temperature beyond that of the surface of the sun - we are talking about capturing the energy from a large area and delivering it to a much smaller target.
I guess maybe I just don’t grasp the precise distinction between temperature and heat, as made by Pleonast.
Interesting. I never thought that there might be a two-way thermal equilibrium.
So, lets say that we had a huge system of mirrors and lenses and whatnot that took the entire visible output of the sun and focused it down to a one-centimetre spot on the moon.
I can see that there’d be heat losses all over such a system, and the target spot would boil away, and you’d be shining into and excavating a cave, but the target would never get hotter than the sun’s surface, no matter how much light was concentrated there?
This is exactly the problem I’m having trouble grasping.
Posts running off in all directions.
Temperature is merely a measure of the level of molecular particle activity/motion.
Heat is the manifiestation of said activity/motion and the two terms are frequently use interchangeabley.
As to reflecting the solar energy back to the sun…
A ‘Fools Errand’ if I ever heard of one. The sun is at the center of the celestial sphere and the earth in a fly speck on that sphere. Any mirror man could construct would be a flyspeck on the earth’s surface and infinitesimal as far as the sun is concerned. Now add the rotation of the earth and the mirror would not be forcused on the sun but for a very short part of the day even at the equator, which would of course be the best location for such a financial “rat hole.”
I’m beginning to wonder where common sense went.
Common sense is of course most uncommon these days.
You can’t concentrate all the sun’s output energy into a one-centimeter spot. If you try to design a mirror system that captures all the sun’s output and focus it, the focus spot ends up being the size of the sun.
It’s the same reason you can’t use a fluorescent bulb for a car headlight. You can’t take a diffuse light source and focus it into a smaller and more intense spot. Light intensity can never be intensified with a purely passive optical system. It’s also the reason you cannot build a telescope that can show Bernard’s Loop (a diffuse gas cloud spanning the entire length of the constellation Orion - see first photo on this page). A telescope can enlarge it, but no telescope can amplilfy the surface brightness of an extended object.
Let’s simplify this (as physicists are wont to do 
). Imagine a large cavity, with the sun in the center. The sun and the cavity are in thermal equilibrium. This means they are at the same temperature, and the heat (the thermal energy) from the sun to the cavity is equal to the heat from the cavity to the sun. The photons (which are also in thermal equilibrium) are the mechanism for heat transfer.
Now let’s add a small, cold black sphere to the cavity. It immediately starts absorbing photons. The sphere also emits photons, at its own temperature. Eventually, the temperature of the sphere reaches the sun’s temperature. And the sphere can’t get any hotter, because everything is at the same temperature. Hopefully this is clear to you.
Next, consider adding a small, cold black sphere and a focusing lens to the cavity. The lens focuses photons from the surface of the sun to the surface of the sphere. The photons being focused are just as hot as in the first case, but there’s more of them. So the sphere heats up faster than in the first case. But once it reaches the sun’s temperature, that’s it, everything is the same temperature. Nothing can get hotter.
Summary: the lens (or mirror) increase the thermal coupling (i.e., how much heat can flow) between the two objects. It doesn’t change the final thermal equilibrium, only how quickly it is reached.
Speed of light cheating: I don't think you can cheat thermodynamics by introducing time delays. Maybe get some interesting thermal oscillations, but no temperatures above the original. You might be able to get some strange effects if the objects are moving at relativistic speeds with respect to each other. I think photonic Doppler shifts might make the objects appear hotter/cooler than in their own frames of reference. I'll have to think more about that.Actually I think you could cheat with speed of light. If the light source is moving towards you, the effective (bolometric) temperature of the emission would be greater than the object’s true temperature (in its own intertial frame). I’m not too sure what the 2nd law of thermo has to say about this…
Can you bounce particles off the same focused surface sport more than once to get around the equillibrium?
On second thought, this is bogus. I mean, the first part is true, but motion will simply change the angular distribution of emitted radiation (less towards the back, more towards the front). Since we’re talking about enclosing the light source with mirrors to capture all of it, such effects don’t chane the result.