Speaking of risks and fire, is there a known limit to the temperature achievable by concentration? I was wondering if I could melt a piece of tungsten with this method.
The fundamental limit is given by the 2nd law of thermodynamics - you can never reach higher temperatures than the surface of the sun, or around 5800 K. We have the atmosphere that absorbs and scatters some of the light, so on the surface of the earth it is a bit lower, but not by a huge amount.
This means that there is a fundamental limit to how small and intense you can make the focal spot in a solar concentrator. The limit is around ~45 MW/m² or 45000 "suns" (which is plenty high, but far from infinite).
Concentrators used for eletricity generation use much lower concentration than this, on the order of 25 suns to 1000 suns depending on the type. There are also solar furnaces designed for reaching much higher concentration by using a different type of optics. The most impressive one is the huge Odeillo solar furnace [1]. I would guess that they could melt tungsten, but I have not actually run the numbers.
I did a talk last week about a concept we are developing for reaching furnace-level concentration ratios with conventional heliostats [2].
The thing that I can't wrap my head around is that if the concentrator "pumps" power into an object, and say you can somehow insulate it to stop the losses, how is this limit not unbounded? Where does the energy go once we reach the cap?
Does the black body radiation send the energy back out?
> Does the black body radiation send the energy back out?
Exactly, this is the issue. If an object is able to absorb sunlight, it is also able to emit blackbody radition back towards the sun. When the temperature limit is reached, these two exactly cancel each other. The object will emit blackbody radiation with the same brightness as the surface of the sun.
Another way to look at it is to imagine yourself standing at the center of the concentrated sunlight and looking out towards the concentrator. The concentrator makes the sun look "bigger" from your perspective, and this is what makes the sunlight concentrated. The limit to this effect is if the sun fills all directions in the whole hemisphere above you. Now it will be as if you are standing on the surface of the sun, and all you can see in any direction is sunlight. Normally, the solar disc fills 1/45000th of the hemisphere above you here on earth, thus the limit of 45000 suns concentration.
Thank you so much. It's the first time I do understand the _why_ of that fact.
But I could build up a lot of solar panels and use the electricity to heat up an oven more than the surface of the sun, right? Is that "cheating" in terms of thermo dynamics?
> I could build up a lot of solar panels and use the electricity to heat up an oven more than the surface of the sun, right?
Yes, this would be like using a hydroelectric dam to power a fountain that sprays higher than the initial reservoir. Machines can convert a large amount of low-quality energy into a small amount of high-quality energy, even when passive components (e.g. mirrors or pipes) cannot.
Great question, and this shows why we could never get a 100% efficient solar panel. Otherwise your scheme would brak thermodynamics.
The most efficient possible way to convert sunlight to electricity is ~86% and is related to the second law of thermodynamics. So we use the heat flow from a hot reservoir (sun) to a cold reservoir (earth) and are able to convert some of that heat into work (electricity) which can then be used to heat something else to a higher temperature without breaking the second law.
Wikipedia says a max temperature of 3500C, which is above Tungsten's melting point. Graphite is the only thing I know of with a melting point above that at 1atm, but I'm not a chemist so I'm sure there are other things.
