Bulk modulus

The bulk modulus ( K {displaystyle K} or B {displaystyle B} ) of a substance is a measure of how resistant to compression that substance is. It is defined as the ratio of the infinitesimal pressure increase to the resulting relative decrease of the volume. 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 a complex 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.There are two valid solutions. The plus sign leads to ν ≥ 0 {displaystyle u geq 0} . The bulk modulus ( K {displaystyle K} or B {displaystyle B} ) of a substance is a measure of how resistant to compression that substance is. It is defined as the ratio of the infinitesimal pressure increase to the resulting relative decrease of the volume. 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 a complex 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. The bulk modulus K > 0 {displaystyle K>0} can be formally defined by the equation where P {displaystyle P} is pressure, V {displaystyle V} is volume, and d P / d V {displaystyle dP/dV} denotes the derivative of pressure with respect to volume. Considering unit mass, where ρ is density and dP/dρ denotes the derivative of pressure with respect to density (i.e. pressure rate of change with volume). The inverse of the bulk modulus gives a substance's compressibility. Strictly speaking, the bulk modulus is a thermodynamic quantity, and in order to specify a bulk modulus it is necessary to specify how the temperature varies during compression: constant-temperature (isothermal K T {displaystyle K_{T}} ), constant-entropy (isentropic K S {displaystyle K_{S}} ), and other variations are possible. Such distinctions are especially relevant for gases. For an ideal gas, the isentropic bulk modulus K S {displaystyle K_{S}} is given by and the isothermal bulk modulus K T {displaystyle K_{T}} is given by