Compressibility coefficient of gas with temprature
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The compressibility factor (Z) is a useful thermodynamic property for modifying the ideal gas law to account for behavior of real gases.[1][2][3][4][5] It is a measure of how much the thermodynamic properties of a real gas deviate from those expected of an ideal gas. It may be thought of as the ratio of the actual volume of a real gas to the volume predicted by the ideal gas at the same temperature and pressure as the actual volume.
For an ideal gas, Z always has a value of 1. For real gases, the value may deviate positively or negatively, depending on the effect of the intermolecular forces of the gas. The closer a real gas is to its critical point or to its saturation point, the larger are the deviations of the gas from ideal behavior.
The upper graph in Figure 1 illustrates how the compressibility factor varies for different gases at the same temperature and pressure. The lower graph illustrates how the compressibility factor of a gas (for example, methane) at a given pressure varies with temperature.[1]
This article deals only with the compressibility factor of gases and does not delve into the compressibility of liquids or vapor-liquid mixtures.
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[show]
Determination of gas compressibility values
The ideal gas law is defined as:

and the ideal gas law corrected for non-ideality is defined is:
where: = pressure= molar volume of the gas= compressibility factor= Universal gas constant= temperature
and thus:

which is the simplest and most widely used real gas equation of state (EOS). The major limitation of this equation of state is that the gas compressibility factor, Z, is not a constant but varies from one gas to another as well as with the temperature and pressure of the gas under consideration. It must be determined experimentally.
Where experimental data is available for specific gases, that data may be used to produce graphs (such as in Figure 1) of Z versus pressure at a constant temperature or of Z versus pressure for various temperatures for those specific gases. Such graphs are useful for readily obtaining interpolated values of Z between the experimentally determined values.
The compressibility factor, as mentioned earlier, may also be expressed as:

For an ideal gas, Z always has a value of 1. For real gases, the value may deviate positively or negatively, depending on the effect of the intermolecular forces of the gas. The closer a real gas is to its critical point or to its saturation point, the larger are the deviations of the gas from ideal behavior.
The upper graph in Figure 1 illustrates how the compressibility factor varies for different gases at the same temperature and pressure. The lower graph illustrates how the compressibility factor of a gas (for example, methane) at a given pressure varies with temperature.[1]
This article deals only with the compressibility factor of gases and does not delve into the compressibility of liquids or vapor-liquid mixtures.
Contents
[show]
Determination of gas compressibility values
The ideal gas law is defined as:

and the ideal gas law corrected for non-ideality is defined is:
where: = pressure= molar volume of the gas= compressibility factor= Universal gas constant= temperature
and thus:

which is the simplest and most widely used real gas equation of state (EOS). The major limitation of this equation of state is that the gas compressibility factor, Z, is not a constant but varies from one gas to another as well as with the temperature and pressure of the gas under consideration. It must be determined experimentally.
Where experimental data is available for specific gases, that data may be used to produce graphs (such as in Figure 1) of Z versus pressure at a constant temperature or of Z versus pressure for various temperatures for those specific gases. Such graphs are useful for readily obtaining interpolated values of Z between the experimentally determined values.
The compressibility factor, as mentioned earlier, may also be expressed as:

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