This wasn't in the book, so I was wondering: in the second Hobbit movie (The Hobbit: The Desolation of Smaug), when:
the dwarves covered Smaug with liquefied gold
could he actually die?
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I have not found any good picture illustrating it yet (contributions are welcome), but in the movie Smaug's belly skin shows visible glowing cracks every time he prepares to breath fire (which is in itself quite a nice cue that you want to run or hide very fast).
This indicates that his fire is not only some kind of flammable gas he only lights up in his mouth, but rather some kind of internal flame he needs to focus and channel before using it.
His inner parts have, indeed, to be very fire resistant, since dragon fire is described as so hot as to be one of the only means to destroy rings of power in the Fellowship of the Ring: That's the way four of the dwarven rings met their fate.
Wondering if this resistance is magical or natural is kind of pointless, since for Tolkien magic is some kind of power or quality native to all beings, in varying amounts depending of their kind, often used quite subtly and involuntary (for more information, see the can-the-elves-do-magic question).
Considering the amount of fire-resistance (more than melting metal temperature 1,948°F) which is then required from his inner parts, a bath of molten gold does not seem that harmful anymore for any fire-breathing dragon...
It might actually kill Smaug, though for completely different reasons than what the movie scene suggests.
As already said, the temperature of molten gold should hardly be impressive to a fire-drake – which does however not imply that they can necessarily cope with getting completely immersed in it.
But, it's rather absurd that Smaug ever sinks in the gold in the first place! Though movies almost always get it wrongTVTropes warning!, gold is really really dense. The linked page actually points out that
Gollum shouldn't have sunken in the lava of Mount Doom
since rock, liquid or not, is much denser that water/biomass. This applies far more strongly to gold: even if Smaug's body was solid lead (11 g·cm−3), he would easily float on liquid gold (19 g·cm−3)! If his body instead had a density comparable to ordinary life forms, he should pretty much be able to walk on it. (Only ≈1/20 of the body needs to be immersed to lift the rest. An actual elephant might be able to do this, as long as it would stand the heat – which it might conceivably do for a few seconds: unlike in the rather hotter (and closer to blackbody) case of lava, radiation heating isn't that effective for liquid gold; it would at first only sear the elephant's legs by direct heat transfer.)
Then again, the high density has another consequence. Even if you hit water at sufficiently high speeds, the impact on the surface will kill you.Yes, TVTropes also has a page on that subject. Apply that to gold, and the result is that if you fall from some height on liquid gold the surface isn't merely "as hard as concrete", but in fact "harder"! And, again contrary to what movies sometimes say, mechanical crushing becomes ever more of a problem, the larger you go, due to the square-cube law. So, if an elephant were to fall onto a lake of gold from, say, 10 metres height, then it would probably die immediately, simply from the shock of hitting the surface.
This doesn't directly apply to the movie scene, since Smaug sits on the ground in front of the liquid-gold statue before it collapses. However, this sheer mechanical power of the high-density liquid would pose a very real problem for any creature in that position: the disintegrating dwarf statue would constitute a tsunami wave that would push stuff out of its way much more powerfully than a comparable water wave. It would not drown the dragon, but push it towards the opposite wall with incredible speed. Impact on that wall then might be rather deadly indeed, certainly for an elphant, man or whatever non-magical creature.
Evidently, dragons have mechanical powers unlike any real lifeform: otherwise they couldn't possibly fly. So they might, in fact, survive a gold tsunami. But at least, the dwarves weren't quite so unrealistic if they hoped in fact to crush the dragon on the opposite wall by that means, rather than actually drowning it in the gold.
Smaug, based on his description and key characteristics, is identifiable as a winged "fire-drake" (of the same ilk as Ancalagon the Black) rather than a "cold-drake" or "long-worm".
Given that the breath of a "fire-drake" burned hot enough to destroy a Ring of Power (four of the Seven were lost in this way) and that one "fire-drake" (Ancalagon the Black, mightiest of them) crushes a volcanic peak without Tolkien even bothering to mention the word lava (hotter by far than liquid gold) I think it is safe to assume that Smaug, being a particularly mighty "fire-drake" (a "most specially strong worm" and in fact "the greatest of the dragons of his day"), would be completely unconcerned by molten gold
This scene, I fear, is another instance of needless Hollywood-style dramatics that at best lack grounding and at worst contradict Middle-Earth canon.
The melting point of gold is 1064 degrees Celsius, which is not really all that hot in the grand scheme of the maximum temperatures that medieval style furnaces could operate at (to get molten iron you need 1200 degrees, glass is even higher, steel is 1500+ etc). This is well within the reach of a good human smith (and certainly a master dwarf blacksmith) with a good permanent furnace in universe I would imagine.
So, on the basis that humans and even dwarves could not unmake the rings through fire you would have to imagine that they were simply unable to generate enough heat in their furnaces, yet a dragon could. Let's imagine that you need at least twice as high a temperature as man would manage to melt a ring of power, just for arguments sake, that's a temperature of roughly 3000 degrees assuming steel is the hottest thing man could smelt.
Take into account that a dragon could, and that the dragon fire they could use to destroy a ring would by definition be considerably higher than what man/dwarf could produce (and you would imagine that their internal temperatures would have to be even higher than that of their flames) then this sort of thing, whilst no doubt uncomfortable, painful, restrictive etc, is not a mortal danger to a dragon, being simply not all that hot (a third of the minimum temperature they were capable of producing externally) from the dragons perspective.
Dragons are magical creatures, and in Tolkien's works, magic is not based on rules and spells - it is always inherent to people/creatures or objects, and its effects are not well defined or predictable. Conventional physics, chemistry or biology on the other hand, are routinely ignored.
So I think it would be consistent with the way Tolkien wrote his stories to assume that since dragons are creatures of fire, they are at least resistant to fiery things like liquid gold and unlikely to be killed by it.
Assuming we believe it makes sense for the gold to neatly fall around Smaug and cover him (which is addressed by the other answers), the problem in the plan is that the pool of gold with Smaug inside couldn't solidify fast enough.
If Smaug could be trapped in a pool of solid gold, he would probably die or stop being a threat anyway.
I've always wondered how much water it would have taken to cool down all that gold. Presumably the dwarves could have emptied a nearby lake, filled the next room with water or whatever, and flooded the gold pool at the same time.
If we assume that the gold was at 1100 °C, a bit above the melting point, that the nearby water is at 20 °C, and that we want to reduce the gold to a mere 100 °C without turning all the water into steam, we can divide the latent heat and specific heat of the gold by the specific heat of the water, which in in kg would make:
( 63.72 kJ/kg + (1100-100 °C) * 0.129 kj/kg-K ) / ( ( 100-20 °C ) * 4.186 kJ/kg-K ) = 0.575
So it would take less than 0.6 kg of water for every 1 kg of gold. Liquid gold is approximately 17.3 times as dense as water, so that neatly translates to about 10 m³ of water for every 1 m³ of gold.
It's not clear how much gold there is, but the gold pool is shown to neatly fill the bottom of the hall, which is shown a moment before to have just 6 steps. So maybe 2 meters? (Absurd that Smaug fits in just 2 meters of height.) In which case you'd need to fill the room with some 20 m of water.
The heat of vaporization for water is a fancy 2257 kJ/kg, or 6.7 times what the specific heat gives us above, so if we let all the water go into steam then you "only" need a volume of water 3 times as big as the gold. You'd definitely have to escape quick enough to avoid getting quickly cooked like vermicelli rice in a steam cooker...
he did show signs of pain, but probably more along the lines of one of us dumb humans sticking their hand in hot water straight out of the facet, 'ouch it stings and burns and its bloody hot' but the worst we really end up with is reddened skin unless of course it happens to be boiling/scalding... which it was probably on the lesser end for Smaug the awesome.
so yeah, it just pissed him off more than he already was.