compressibility

Compressibility is a property that describes how much the volume of a material changes in response to a change in pressure. It is defined as the relative volume change per unit pressure and depends on temperature and phase.

The isothermal compressibility κ_T is defined as κ_T = - (1/V) (∂V/∂P)_T, describing how V changes with P at constant temperature. The adiabatic compressibility κ_S is defined as κ_S = - (1/V) (∂V/∂P)_S, describing changes when heat exchange is absent. In general κ_S ≤ κ_T because heating during compression tends to reduce volume change.

Compressibility is related to the bulk modulus K by K_T = 1/κ_T and K_S = 1/κ_S, where the bulk modulus measures resistance to uniform compression at constant temperature or constant entropy, respectively. The speed of sound in a fluid is connected to compressibility: c^2 = 1/(κ_S ρ) for an adiabatic process, or equivalently c = sqrt(K_S/ρ).

Substances vary widely in compressibility. Gases are highly compressible, liquids are relatively incompressible, and solids are near-incompressible under ordinary conditions. For an ideal gas, κ_T = 1/P, so compressibility decreases as pressure rises.

Compressibility depends on temperature and pressure, and can change across phase transitions. It is measured by ultrasonic techniques, volumetric P–V measurements, or other specialized methods, and is essential in fields such as thermodynamics, materials science, geophysics, and engineering. See also bulk modulus, equation of state, and speed of sound.