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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:
Because of the definition of compressibility factor at critical condition, it is possible to reverse it to find the critical molar volume V m,c, by knowing previous found P c, T c and Z c =1/3. = => =, =>, =
where the Rackett compressibility factor , can be estimated by , A nice feature with the volume translation method of Peneloux et al. (1982) is that it does not affect the vapor–liquid equilibrium calculations. [9]
compressibility effects; variable specific heat capacity; van der Waals forces; non-equilibrium thermodynamic effects; issues with molecular dissociation and elementary reactions with variable composition; For most applications, such a detailed analysis is unnecessary, and the ideal gas approximation can be used with reasonable accuracy.
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]
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]
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]