Density and specific volume depend on stress as well as temperature. A stress consisting of uniform pressure in all directions is known as “hydrostatic” pressure, and the relationship between change of volume or density and hydrostatic pressure may be expressed in terms of a single coefficient, the compressibility β, defined by
$β = − 1 V ( ∂ V ∂ P ) T = 1 ρ ( ∂ ρ ∂ P ) T ,$
where V is the specific volume, and π the density, at pressure P. Since ∂V/∂P is intrinsically negative, β is a positive number having the dimensions of the reciprocal of a pressure or stress. Its reciprocal K is known as the bulk modulus; K and β depend in general upon pressure and temperature. For small compressions, the volume change is often related to the specific volume V 0 or density π0 at P = 0 (or 1 atmosphere) instead of to the volume or density at pressure P; the difference is proportional to the total change of volume between the pressures 0 and P.

Compressibility may be determined directly as a volume change under pressure, or volume changes may be computed from changes of linear dimensions under pressure. If the material is not isotropic, measurements of linear changes in as many as three mutually perpendicular directions may be required to determine the volume change. Unless specified as linear, the tabulated data refer to volume changes. The directions of linear measurements are specified as “parallel” or “perpendicular” with reference to the axis of highest symmetry for crystals of the hexagonal, tetragonal, and trigonal classes; for the others, the directions are the

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