- Bulk modulus
The bulk modulus (K) of a substance measures the substance's resistance to uniform compression. It is defined as the pressure increase needed to decrease the volume by a factor of 1/e. Its base unit is the pascal.
The bulk modulus K>0 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 stress. 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 (isothermal 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
and the isothermal bulk modulus KT is approximately given by
- γ is the adiabatic index, sometimes called κ.
- P is the pressure.
Solids can also sustain transverse waves: for these materials one additional elastic modulus, for example the shear modulus, is needed to determine wave speeds.
It is possible to measure the bulk modulus using powder diffraction under applied pressure.
Approximate bulk modulus (K) for common materials Material Bulk modulus in GPa Bulk modulus in ksi Glass (see also diagram below table) 35 to 55 5.8×103 Steel 160 23×103 Diamond 442 64×103
Material with bulk modulus value of 35GPa needs external pressure of 0.35 GPa (~3500Bar) to reduce the volume by one percent.
Approximate bulk modulus (K) for other substances 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)
- ^ "Bulk Elastic Properties". hyperphysics. Georgia State University. http://hyperphysics.phy-astr.gsu.edu/hbase/permot3.html.
- ^ Cohen, Marvin (1985). "Calculation of bulk moduli of diamond and zinc-blende solids". Phys. Rev. B 32: 7988–7991. Bibcode 1985PhRvB..32.7988C. doi:10.1103/PhysRevB.32.7988.
- ^ Fluegel, Alexander. "Bulk modulus calculation of glasses". glassproperties.com. http://www.glassproperties.com/bulk_modulus/.
Elastic moduli for homogeneous isotropic materials Conversion formulas 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.
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