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Compressibility factor values are usually obtained by calculation from equations of state (EOS), such as the virial equation which take compound-specific empirical constants as input. For a gas that is a mixture of two or more pure gases (air or natural gas, for example), the gas composition must be known before compressibility can be calculated.
In thermodynamics and fluid mechanics, the compressibility (also known as the coefficient of compressibility [1] or, if the temperature is held constant, the isothermal compressibility [2]) is a measure of the instantaneous relative volume change of a fluid or solid as a response to a pressure (or mean stress) change.
These dimensionless thermodynamic coordinates, taken together with a substance's compressibility factor, provide the basis for the simplest form of the theorem of corresponding states. [1] Reduced properties are also used to define the Peng–Robinson equation of state, a model designed to provide reasonable accuracy near the critical point. [2]
At present, there is no single equation of state that accurately predicts the properties of all substances under all conditions. An example of an equation of state correlates densities of gases and liquids to temperatures and pressures, known as the ideal gas law, which is roughly accurate for weakly polar gases at low pressures and moderate temperatures.
The following table lists the Van der Waals constants (from the Van der Waals equation) for a number of common gases and volatile liquids. [ 1 ] To convert from L 2 b a r / m o l 2 {\displaystyle \mathrm {L^{2}bar/mol^{2}} } to L 2 k P a / m o l 2 {\displaystyle \mathrm {L^{2}kPa/mol^{2}} } , multiply by 100.
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:
The virial expansion is a model of thermodynamic equations of state.It expresses the pressure P of a gas in local equilibrium as a power series of the density.This equation may be represented in terms of the compressibility factor, Z, as = + + + This equation was first proposed by Kamerlingh Onnes. [1]
Isotherms of an ideal gas for different temperatures. The curved lines are rectangular hyperbolae of the form y = a/x. They represent the relationship between pressure (on the vertical axis) and volume (on the horizontal axis) for an ideal gas at different temperatures: lines that are farther away from the origin (that is, lines that are nearer to the top right-hand corner of the diagram ...