Bulk modulus
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The bulk modulus (or incompressibility) K of a fluid or solid is the inverse of the compressibility:
- <math>K=-V\frac{\partial P}{\partial V}</math>
where P is pressure and V is volume.
The bulk modulus thus measures the response in pressure due to a change in relative volume, essentially measuring the substance's resistance to uniform compression. Other moduli describe the material's response (strain) to other kinds of stress: the shear modulus describes the response to shear, and Young's modulus describes the response to linear strain. For a fluid, only the bulk modulus is meaningful. For an anisotropic solid such as wood or paper, these three moduli do not contain enough information to describe its behaviour, and one must use the full generalized Hooke's law.
Strictly speaking, the bulk modulus is a thermodynamic quantity, and it is necessary to specify how the temperature varies in order to specify a bulk modulus: constant-temperature (<math>K_T</math>), constant-enthalpy (adiabatic <math>K_S</math>), and other variations are possible. In practice, such distinctions are usually only relevant for gases.
The inverse of the bulk modulus gives a substance's compressibility.
For a gas, the adiabatic bulk modulus <math>K_S</math> is approximately given by
- <math>
K_S=\kappa\, P </math>
where
- κ is the adiabatic index, sometimes called γ.
- P is the pressure.
The adiabatic bulk modulus governs the speed of sound (for pressure waves) in a material. Solids can also sustain transverse waves; for these the shear modulus is the key determining factor.
