Compressibility And Rigidity

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Among water, steel, rubber and an ideal gas at fixed temperature, which substance is expected to have the largest compressibility, meaning it changes volume most for a given increase in applied pressure?

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Compressibility is the reciprocal of the bulk modulus, $k = 1/B$, so a substance that yields a large volume change for a small pressure rise has a high compressibility and a low bulk modulus. Solids and liquids have atoms or molecules packed closely with strong intermolecular forces, giving them very large bulk moduli and hence very low compressibility. A gas, by contrast, consists of widely separated molecules with negligible mutual forces, so its volume responds dramatically to pressure changes; at fixed temperature an ideal gas even obeys Boyle's law, $PV = 	ext{constant}$. Steel is wrong because metals are among the least compressible materials. Water is wrong because, although less stiff than steel, it is still nearly incompressible compared with any gas. Rubber deforms easily in shear but resists uniform volume compression almost like other condensed matter, so it is also far less compressible than a gas. This ordering follows directly from the NCERT comparison of mechanical properties of solids, liquids and gases. As a plausibility check, gases are routinely compressed into cylinders to a tiny fraction of their volume, which no solid or liquid permits, confirming the gas has by far the greatest compressibility.

Compressibility And Rigidity

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