Spoiler: I don't know.
In a previous essay, I argued that Smaug could destroy Toothless. I don't think he'd ever get off a shot to Smaug's weak spot. However, what if he somehow did? Would that even kill the mighty firedrake? In this post I will attempt to find out.
Heat
The raw heat output of Toothless's plasma is not likely to injure Smaug. I demonstrated why in my main analysis. The charge dissipates in far less than a second, as opposed to the molten gold which Smaug sank in, which got in between his scales and stayed there for many seconds.
Therefore, the primary damage would have to be from the blast itself.
Pressure From Blast
Toothless's charged shots (which take a while to prepare) max out at maybe, very generously, 5 TJ. That's 2390060 pounds of TNT equivalent. (Note that this is a huge overestimation, as that big an explosion would do this. The apparent size of the fireball in this explosion can be explained better by overexposure.) Were I trying to be more conservative, I would go with perhaps 400 GJ to 1 TJ.
Smaug's skin took about 30 GPa of pressure at the very least, from the Black Arrow. I will conservatively assume that one sixtieth of that (500 MPa) is all that is required to break through.
The pressure from a maximum-yield Toothless shot at one third of a meter, scaling from the numbers this calculator gives me, might be enough. But I don't really know—it's above my physics level, and I can't find a blast pressure calculator with that much precision.
So: Toothless totally might be able to do it. Might. I simply don't have the mathematical ability to tell for sure. But this does not change my verdict on the fight—Toothless would almost certainly never get that hit.
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