compressibili

Compressibility is a material property that describes how much its volume changes in response to a change in pressure. It is commonly quantified by the isothermal compressibility κ_T, defined as κ_T = - (1/V) (∂V/∂P) at constant temperature. The inverse of this quantity is the bulk modulus K, a measure of a substance’s resistance to uniform compression.

Two related forms are the isothermal κ_T and the adiabatic (or sonic) compressibility κ_S = - (1/V) (∂V/∂P) at constant entropy. In general, κ_S is smaller than κ_T because compressing a system without allowing heat exchange requires more work to change the volume. For an ideal gas, κ_T equals 1/P, while κ_S equals 1/(γ P), where γ is the heat-capacity ratio Cp/Cv.

Compressibility varies with phase and structure. In liquids, κ_T is small but finite; in gases it is large, making gases highly compressible under modest pressures. In solids, compressibility is closely tied to the bulk modulus and can be direction-dependent in anisotropic crystals; the isotropic approximation uses a single bulk modulus to describe volumetric response.

Applications and relevance span multiple fields. In acoustics, compressibility determines the speed of sound through a medium, via c = sqrt(1/(ρ κ_S)) for fluids. In geophysics, mineral compressibilities inform the interpretation of seismic data. In materials science, measured or computed κ_T helps assess mechanical performance, stability, and behavior under high-pressure conditions.

Typical values illustrate the wide range: air at room temperature has κ_T about 1×10^-5 Pa^-1, water about 4.5×10^-10 Pa^-1, and solids like steel around a few ×10^-12 Pa^-1. Compressibility is inherently temperature- and pressure-dependent, reflecting the equation of state of the substance.