text: The isothermal compressibility is generally related to the isentropic (or adiabatic) compressibility by a few relations:
  where  is the heat capacity ratio,  is the volumetric coefficient of thermal expansion,  is the particle density, and  is the thermal pressure coefficient.
  In an extensive thermodynamic system, the application of statistical mechanics shows that the isothermal compressibility is also related to the relative size of fluctuations in particle density:
  where  is the chemical potential.
  The term "compressibility" is also used in thermodynamics to describe deviations of the thermodynamic properties of a real gas from those expected from an ideal gas.
  The compressibility factor is defined as
  where  is the pressure of the gas,  is its temperature, and  is its molar volume, all measured independently of one another.  In the case of an ideal gas, the compressibility factor  is equal to unity, and the familiar ideal gas law is recovered:
   can, in general, be either greater or less than unity for a real gas.
  The deviation from ideal gas behavior tends to become particularly significant (or, equivalently, the compressibility factor strays far from unity) near the critical point, or in the case of high pressure or low temperature.  In these cases, a generalized compressibility chart or an alternative equation of state better suited to the problem must be utilized to produce accurate results.