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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. Alternatively, the compressibility factor for specific gases can be read from generalized compressibility charts [ 1 ] that plot Z {\displaystyle Z} as a function of pressure at ...
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Z can, in general, be either greater or less than unity for a real gas. The deviation from ideal gas behavior tends to become particularly significant (or, equivalently, the compressibility factor strays far from unity) near the critical point, or in the case of high pressure or low temperature.
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 largest and the lowest solution are the gas and liquid reduced volume. In this situation, the Maxwell construction is sometimes used to model the pressure as a function of molar volume. The compressibility factor = / is often used to characterize non-ideal behavior. For the van der Waals equation in reduced form, this becomes
Where p is the pressure, T is the temperature, R the ideal gas constant, and V m the molar volume. a and b are parameters that are determined empirically for each gas, but are sometimes estimated from their critical temperature (T c) and critical pressure (p c) using these relations:
The low compressibility of non-gasses, and of water in particular, leads to their often being assumed as incompressible. The low compressibility of water means that even in the deep oceans at 4 kilometres (2.5 mi) depth, where pressures are 40 MPa, there is only a 1.8% decrease in volume. [43]