The bulk modulus K of a fluid or solid is the inverse of the compressibility:

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 to other kinds of strain: 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, constant-enthalpy (adiabatic), and other variations are possible. In practice, such distinctions are usually only relevant for gases.

For a gas, the adiabatic bulk modulus K is approximately given by

where

κ is the adiabatic index, sometimes called γ.

p is the pressure.

The 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.

Examples

• Water: 2.2×10⁹ Pa
• Steel: 1.6×10¹¹ Pa
• Solid helium (approximate): 5×10⁷ Pa

References

• Bulk Elastic Properties on hyperphysics at Georgia State University
• Dynamic and thermodynamic properties of solid helium in the reduced all-neighbours approximation of the self-consistent phonon theory, C. Malinowska-Adamska, P. Sŀoma, J. Tomaszewski, physica status solidi (b), Volume 240, Issue 1 , Pages 55 - 67; Published Online: 19 Sep 2003