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In thermodynamics, the compressibility factor (Z), also known as the compression factor or the gas deviation factor, describes the deviation of a real gas from ideal gas behaviour. It is simply defined as the ratio of the molar volume of a gas to the molar volume of an ideal gas at the same temperature and pressure .
The compressibility factor is defined as = where p is the pressure of the gas, T is its temperature, and is its molar volume, all measured independently of one another. In the case of an ideal gas, the compressibility factor Z is equal to unity, and the familiar ideal gas law is recovered:
The compressibility factor is a dimensionless quantity which is equal to 1 for ideal gases and deviates from unity for increasing levels of non-ideality. [ 9 ] Several non-ideal models exist, from the simplest cubic equations of state (such as the Van der Waals [ 4 ] [ 10 ] and the Peng-Robinson [ 11 ] models) up to complex multi-parameter ones ...
It reads: = + [()] where is the number density, g(r) is the radial distribution function and () is the isothermal compressibility. Using the Fourier representation of the Ornstein-Zernike equation the compressibility equation can be rewritten in the form:
Illustration of uniform compression. The bulk modulus (or or ) of a substance is a measure of the resistance of a substance to bulk compression.It is defined as the ratio of the infinitesimal pressure increase to the resulting relative decrease of the volume.
Take for example the chemical potential of a pure fluid: In a state (,,,) that does not satisfy the ideal gas law, but may be a real state for some real fluid. The ideal gas chemical potential computed as a function of temperature, pressure and mole number is
a property in thermodynamics and fluid dynamics, see Compressibility or Incompressible flow; a property of a vector field, see Solenoidal vector field; a topological property, see Incompressible surface; a proof method in mathematics, see Incompressibility method; a property of strings in computer science, see Incompressible string
The fugacity of a condensed phase (liquid or solid) is defined the same way as for a gas: = and = It is difficult to measure fugacity in a condensed phase directly; but if the condensed phase is saturated (in equilibrium with the vapor phase), the chemical potentials of the two phases are equal (μ c = μ g).