At 4000 deg C it is already in liquid form. At 5008 deg C it will evaporate. Further heating will simply make the vapours hotter.
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When osmium is heated from 4000 to 6000 degrees Celsius, it undergoes a phase transition from a solid to a liquid state. Osmium has a melting point of 3033 degrees Celsius, so it would completely melt at temperatures above this point. As a transition metal, osmium exhibits metallic bonding, which weakens as temperature increases, allowing the atoms to move more freely and transition into a liquid state.
Oh, dude, osmium is a naturally occurring element that exists in a solid state at room temperature. It's like super dense and heavy, so you wouldn't want to accidentally drop a chunk of it on your foot. Just imagine a tiny, solid osmium disco party happenin' on the periodic table.
About 28600 dollars in 2012. Price depends on quality.
Osmium is the densest metal, you can use google for figuring out the rest.
Aerogel, i think. It may be hydrogen.
Osmium and Iridium for normal matter. Otherwise probably Hadrons (Protons or Neutrons for example). Especally big Black Holes aren't as dense as one might think, because the density goes down with increasing masse to very low values for super massive ones.