Wired Science - In answer to the question - In that scene from Return of the King when Gollum falls into the pit of lava, would he have really just sunk into the lava like that? The answer is no the person would stay on top as the molten rock is denser than the human body.
However there is more to death by lava and molten steel and details depend upon the amount of lava or molten steel and the temperature. Do not read further if you are squeamish.
A man fell more than 20ft into this vat of steel which was 450 degrees celsius
Allen Wardle lived for six hours despite suffering 100% burns when he fell into a vat of molten zinc at a factory in Essex in 1998. He had been servicing a crane used to dip objects in the vat, which was heated to 450°C, when he fell more than 20ft through a temporary plywood covering. Mr Wardle was quickly pulled from the vat by workmates but died later the same day in hospital.
So if there are other people around it is possible to get pulled from on top before the body is destroyed.
Often times the person cannot be saved and pulled out and they become part of the vat or the lava.
The Leidenfrost effect is what happens a steam bubble is formed underneath something exposed to a lot of heat.
So there are cases where the body will skitter across the molten surface for a time while still cooking and catching fire.
Old newspaper clipping from Google about death in vat of molten metal. Only small fragements of bone are recovered.
Here is a picture of someone cooking pork with lava in Hawaii (they shovel lava onto the pork.
From Reddit -
Lava would instantly seer your nerves. You would feel nothing. The worst part is 1-4 feet proximity to the lava. Provided there is a large amount of lava, the proximity to the intense heat would scorch your flesh and your nerves would sense that and make you feel pain according. Once contact has been established there be no sensation.
People falling into metal vats was not a totally uncommon industrial accident particularly before more stringent safety standards. The coal and steel industry had the procedure of poring an equivalent weight of a person from the vat in which they died as a death ingot to be buried.
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