compressibility factor formula |
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\( Z \;=\; \dfrac{ p \cdot V }{ n \cdot R \cdot T }\) (Compressibility Factor) \( p \;=\; \dfrac{ z \cdot n \cdot R \cdot T }{ V }\) \( V \;=\; \dfrac{ z \cdot n \cdot R \cdot T }{ P }\) \( n \;=\; \dfrac{ p \cdot V }{ z \cdot R \cdot T }\) \( R \;=\; \dfrac{ p \cdot V }{ z \cdot n \cdot T }\) \( T \;=\; \dfrac{ p \cdot V }{ z \cdot n \cdot R }\) |
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| Symbol | English | Metric |
| \( Z \) = Compressibility Factor | \( dimensionless \) | \( dimensionless \) |
| \( p \) = Pressure | \(lbf\;/\;in^2\) | \(Pa\) |
| \( V \) = Volume | \(ft^3\) | \(m^3\) |
| \( n \) = Number of Moles | \( dimensionless \) | \( dimensionless \) |
| \( R \) = Specific Gas Constant | \(lbf-ft\;/\;lbm-R\) | \(J\;/\;kg-K\) |
| \(\large T \) = Temperature | \(F\) | \(K\) |
Compressibility factor, abbreviated as Z, a dimensionless number, also called compression factor, gas compression factor, gas compressibility factor, or gas deviation factor, corrects for deviation from the ideal gas law to account for the real gases behavior. It is defined as the ratio of the actual molar volume of a gas to the molar volume predicted by the ideal gas law at the same temperature and pressure.
The ideal gas law describes the behavior of ideal gases under most conditions. However, real gases deviate from this ideal behavior, especially at high pressures and low temperatures. The compressibility factor is introduced to correct for these deviations. The compressibility factor is defined as the ratio of the actual volume of the gas to the volume predicted by the ideal gas law at the same conditions.
For an ideal gas, the compressibility factor is always equal to 1, indicating that the gas follows the ideal gas law exactly. However, real gases can deviate from ideal behavior due to intermolecular forces, molecular size, and other factors. As a result, the compressibility factor for real gases can be greater or less than 1. At low pressures and high temperatures, most gases tend to behave more ideally, and their compressibility factors approach 1. At high pressures and low temperatures, gases can exhibit significant deviations from ideal behavior, and their compressibility factors can deviate substantially from 1.
The compressibility factor is an essential parameter for accurately modeling and predicting the behavior of real gases in various thermodynamic processes and calculations, such as determining the fugacity, calculating compressibility and density, and analyzing phase equilibria.
Various equations of state, such as the Peng-Robinson Equation of State, Redlich-Kwong Equation of State, and Van der Waals Equation are used to model the behavior of real gases and calculate their compressibility factors under different conditions.
- Less Compressibility Factor (Z < 1) - The gas is more compressible than an ideal gas. Indicates attractive intermolecular forces dominate, reducing the pressure or volume compared to an ideal gas. It is common at low to intermediate temperatures near or below the critical temperature Tr≈1. Moderate pressures where molecules are close enough for attractions to matter.
- Compressibility Factor Ideal Gas Behavior (Z = 1) - The gas behaves ideally, following the ideal gas law (PV=nRT). Occurs at low pressures and high temperatures, where intermolecular forces are negligible, and molecular volume is insignificant compared to the container volume.
- More Compressibility Factor (Z > 1) - The gas is less compressible than an ideal gas. Indicates repulsive intermolecular forces or the finite volume of molecules dominate, increasing the pressure or volume compared to an ideal gas. It is common at high pressures where molecules are crowded, and their volume becomes significant. High temperatures where kinetic energy overcomes attractions, but crowding increases repulsion.
