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Can elasticity be applied on liquid and gases?

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Yes, but only in compression. A solid material has strong interactions because of 'immobilized matter' (it still vibrates). When you elastically deform a solid material, you stretch the bonds (reversible), any harder and you shear the crystal plane (permanent). Give it more energy and it turns into a liquid or gas. read more

And, yes, gases and liquids are compressible. Of course, the compressibility of gases is much bigger than for liquids. Gases at normal temperature and pressure can be compressed to half their original volume when subjected to nearly double the pressure. read more

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