Compressible

Compressible describes a property of a material or fluid that undergoes a measurable change in volume when pressurized. In thermodynamics the extent of this change is quantified by compressibility, typically expressed as isothermal compressibility β_T or adiabatic compressibility β_S. In terms of volume V and pressure P, β_T = -(1/V)(∂V/∂P)_T, and the bulk modulus K_T = 1/β_T = -V(∂P/∂V)_T. The corresponding adiabatic form uses entropy instead of temperature. Because volume and density respond to pressure, density can vary with pressure in compressible media and is linked to the speed of sound through (∂P/∂ρ)_s.

Many gases are highly compressible relative to liquids and solids, whose volumes change only slightly under typical pressures. Liquids have small but finite compressibility; solids are even less compressible. Compressibility generally depends on temperature and phase and tends to increase near phase transitions or critical points.

In fluid dynamics, compressible flow refers to flows in which density is not constant and pressure waves (sound) propagate at finite speed. The governing equations are the compressible forms of the Navier–Stokes or Euler equations. A common diagnostic is the Mach number M = v/a, where a is the speed of sound; when M is not small, density changes and pressure waves significantly affect the flow field.

Measurement and characterization typically involve volumetric compression tests, ultrasonic or acoustic methods to infer β_T, or direct observation of pressure–volume data to obtain the bulk modulus. Techniques include piston–cylinder devices, resonant methods, and high-pressure spectroscopy in materials science and geophysics.

Applications span gas dynamics in aerospace, pipeline engineering, and subterranean geology, as well as material science studies of how materials respond to pressure. The concept is contrasted with incompressible behavior, where density is assumed constant and volume changes are neglected.