The bulk modulus (K) of a substance measures the substance's resistance to uniform compression. It is defined as the pressure increase needed to cause a given relative decrease in volume. Its base unit is Pascal.
The bulk modulus K can be formally defined by the equation:
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 (KT), constant-entropy (adiabatic KS), and other variations are possible. In practice, such distinctions are usually only relevant for gases.
For a gas, the adiabatic bulk modulus KS is approximately given by
For crystalline solids with a symmetry lower than cubic the bulk modulus is not the same in all directions and needs to be described with a tensor with more than one independent value. It is possible to study the tensor elements using powder diffraction under applied pressure.
|Material||Bulk modulus in GPa||Bulk modulus in psi|
|Glass (see also diagram below table)||35 to 55||5.8×106|
|Water||2.2×109 Pa (value increases at higher pressures)|
|Air||1.42×105 Pa (adiabatic bulk modulus)|
|Air||1.01×105 Pa (constant temperature bulk modulus)|
|Solid helium||5×107 Pa (approximate)|
|Homogeneous isotropic linear elastic materials have their elastic properties uniquely determined by any two moduli among these, thus given any two, any other of the elastic moduli can be calculated according to these formulas.|
The content of this section is licensed under the GNU Free Documentation License (local copy). It uses material from the Wikipedia article "Bulk modulus" modified November 23, 2009 with previous authors listed in its history.