How much heat/energy would be needed to turn a large section of desert sand into glass?

Question

I'd like to include a locale in my world that would be a massive glass crater in the middle of the desert. Originally, I imagined an orbital laser cannon or solar "Icarus"-style weapon from the mediocre James Bond movie, "Die Another Day", firing a concentrated blast of energy that would both melt the sand and blast the sand away to make the glass form into a crater.

-Would either a laser or solar mirror be able to get hot enough to melt sand into its liquid form(at least 1700 degrees C)?

-If the temperature is attainable, can a beam impact the sand with enough force to actually cause a blast crater?

-How would a weapon this strong impact climate and the environment? My guess is the atmosphere would get a hole torn in it.

Answer 1

Yes, We Can Melt It.

You can use mirrors or lasers to melt sand. Doing so from orbit is a bit over-the-top and impractical. Not only do you need to deliver the energy to melt the glass, but you first need to get the energy past the atmosphere (which would involve heating that up to or above the target's melting temperature), and then you need to deliver that energy and move the soil out of the way!

Let's do Some Physics!

We need to know a few things first. I'm assuming the sand is made of mostly quartz, or $SiO_2$, even though real glass has a bunch of other things in it.

• The heat capacity of (quartz) sand is about $830 \frac{J}{kg ^{\circ}C}$
• Sand melts when heated to about $1700 ^{\circ}C$.
• The heat of fusion for sand is... actually really hard to find! I've found an enthalpy of fusion for quartz to be around $9.4 \frac{kJ}{mol}$ Using the molar mass of silicon dioxide ($.06008 \frac{kg}{mol}$), I figure the latent heat of fusion for sand is about $156 \frac{kJ}{kg}$.

How Much Sand?

I'm going to do my calculations for 1 kg of sand. You'll need to figure out how much glass you're making on your own.

Making Glass

Using a simple $Q=mC_p \Delta T$, and thinking this sand is already in a hot desert (~40C), the sand requires 1.378 MJ just to get to melting. To completely melt, the sand requires another 156 kJ, so it takes 1.534 MJ to melt a kilo of sand into glass. This calculation does not include penetrating the atmosphere, or any cooling effects at the target.

Impact Craters?

Here is a nifty crater calculator. Modeling this weapon as an explosion above the surface (with the equivalent energy of 0.0003667 Tons of TNT), this calculator says the surface crater is a measly half a meter, and only 15.6 cm at maximum depth! Even so, any energy we use to make the crater is less energy we use to make the glass.

In any case, this calculator can be used to estimate the energy needed to form a crater. It should be noted that the Trinity test did melt sand into a green glass, and it had a payload of 84 TJ. Its crater was only 1.5 m deep and 9.1 m wide.

Given all this, it seems an orbital glass maker may be able to make glass, but it will not form a crater without ridiculous amounts of energy!

Answer 2

A nuclear bomb is probably your best bet. Then wait until the radiation goes away (sadly not an option in reality, but when you are preparing a planet before there is any life on it...).

Using a bomb with many stages you should be able to scale the explosion as much as you want (nobody tried this in reality, because thermonuclear bombs with two stages are already huge enough).

Existing thermonuclear bombs are around 10^16J, so by scaling this up massively using like 10^4 "stages" (blobs of radioactive stuff which are almost critical in size) this sounds doable (when using the energy amount kindly calculated by Joshua in the other answer).

On the other hand using the data (from the other answer) about the Trinity test saying that one thermonuclear bomb generated a crater of around 10m in diameter and assuming that energy is more or less proportional to the square of the diameter, then with 10^4 times the energy you should get a sizable crater around 10m*sqrt(10^4)=1km in diameter.

This seems to be more or less coherent, and that's all I aimed for. Should be in the right ballpark.

Answer 3

For a real life example read up on Libyan Desert Glass.

Located in a 60x100 kilometer area on the Libyan/Egyptian desert, the glass is scattered over the area. Various theories have been put forward as to its source. From ancient nukes, to an air-burst from a meteor or comet. Fairly recently, a very weathered, very large crater (30 km) has been found that could be the remnants of an actual impact.

Answer 4

In answer to your question about the amount of energy required, let's say the amount of sand that was melted was 1 cubic mile's worth. That translates to 4.168e+9 cubic meters. Using the measurement for the mass of dry sand (http://www.simetric.co.uk/si_materials.htm), we are given 1602 kg/cu.m That translates to a total of 6.677e+12 kg of sand. A rough estimate of the energy required to melt 1 kg of sand into glass (http://www.lowtechmagazine.com/what-is-the-embodied-energy-of-materials.html) is 18-35MJ, depending on various elements involved in the process, type of sand, etc. Taking the lowest possible from those figures, at 18 MJ per kg, you're still looking at a TON of energy required, at 1.202e+14 MJ, or 3.4e+16 watt-hours.

I don't think we have anything even close to the tech that would be required to do what you are asking, at least not in the span of a few seconds or minutes. The solar mirror would be your best bet at a realistic possibility, because it uses "free energy", instead of something that has to be compacted into a laser. As for the looks, I would conjecture that the process, if feasible, would look like an upside down glass volcano. I would love to watch that!