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I know, the human skin can get damaged as quickly as 2 seconds, when exposed to temperature above 80 Celsius.

However, what about human bones, say the skull?

For example, when you cook a meal, at great temperature, the chicken bones, still stay hard and intact, that's why I am asking.

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Boiling point of hydroxyapatite is around 1500°C so you will need this temperature to make bone literally evaporate. Prolonged exposure to lower temperature (like reference in other answer 220°C) will break collagen and make bones weak and extremely fragile.

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The mechanical properties of bone (like Elastic modulus) are generally dependent on a protein called collagen and its cross links. According to this paper, collagen denatures at temperatures around 220 degrees Celsius in a dehydrated environment after gradual heating at transitional temperature intervals.

When you cook a meal, at great temperature, the chicken bones, still stay hard and intact.

The typical (and of course recommended) temperatures for cooking poultry (like chicken) are below 100 degrees Celsius. I think this is why chicken bones are usually still hard after cooking as they normally become fragile after collagen denatures.

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While this answer shows that collagen denatures at 220°C under dry heat, it is possible to break down the collagen in bones at much lower temperatures by means of hot hydrolysis.

This hydrolysis can be accelerated by use of either strong bases or acids (as shown in this paper), which help to break down the peptide bonds between the collagen and release the calcium phosphate deposits. Once the matrix is destroyed, the bone quickly loses its strength.

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