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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:
According to van der Waals, the theorem of corresponding states (or principle/law of corresponding states) indicates that all fluids, when compared at the same reduced temperature and reduced pressure, have approximately the same compressibility factor and all deviate from ideal gas behavior to about the same degree. [1] [2]
Figure 7: Generalized compressibility chart for a van der Waals gas. Real gases are characterized by their difference from ideal by writing p v = Z R T {\displaystyle pv=ZRT} . Here Z {\displaystyle Z} , called the compressibility factor, is expressed either as Z ( p , T ) {\displaystyle Z(p,T)} or Z ( ρ , T ) {\displaystyle Z(\rho ,T)} .
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]
In physics and thermodynamics, the Redlich–Kwong equation of state is an empirical, algebraic equation that relates temperature, pressure, and volume of gases. It is generally more accurate than the van der Waals equation and the ideal gas equation at temperatures above the critical temperature.
For an ideal gas, the ideal gas law applies without restrictions on the specific heat. An ideal gas is a simplified "real gas" with the assumption that the compressibility factor Z is set to 1 meaning that this pneumatic ratio remains constant. A compressibility factor of one also requires the four state variables to follow the ideal gas law.
To calculate the third state property, it is necessary to know three constants for the species at hand: the critical temperature T c, critical pressure P c, and the acentric factor ω. But once these constants are known, it is possible to evaluate all of the above expressions and hence determine the enthalpy and entropy departures.