Real gases are non-ideal gases whose molecules occupy space and have interactions; consequently, they do not adhere to the ideal gas law. To understand the behaviour of real gases, the following must be taken into account:
For most applications, such a detailed analysis is unnecessary, and the ideal gas approximation can be used with reasonable accuracy. On the other hand, real-gas models have to be used near the condensation point of gases, near critical points, at very high pressures, to explain the JouleâÂÂThomson effect, and in other less usual cases. The deviation from ideality can be described by the compressibility factor Z.
Real gases are often modeled by taking into account their molar weight and molar volume
or alternatively:
Where p is the pressure, T is the temperature, R the ideal gas constant, and V<sub>m</sub> the molar volume. a and b are parameters that are determined empirically for each gas, but are sometimes estimated from their critical temperature (T<sub>c</sub>) and critical pressure (p<sub>c</sub>) using these relations:
The constants at critical point can be expressed as functions of the parameters a, b:
With the reduced properties , , the equation can be written in the reduced form:
The RedlichâÂÂKwong equation is another two-parameter equation that is used to model real gases. It is almost always more accurate than the van der Waals equation, and often more accurate than some equations with more than two parameters. The equation is
or alternatively:
where a and b are two empirical parameters that are not the same parameters as in the van der Waals equation. These parameters can be determined:
The constants at critical point can be expressed as functions of the parameters a, b:
Using , , the equation of state can be written in the reduced form: with
The Berthelot equation (named after D. Berthelot) is very rarely used,
but the modified version is somewhat more accurate
This model (named after C. Dieterici) fell out of usage in recent years
with parameters a, b. These can be normalized by dividing with the critical point state:which casts the equation into the reduced form:
The Clausius equation (named after Rudolf Clausius) is a very simple three-parameter equation used to model gases.
or alternatively:
where
where V<sub>c</sub> is critical volume.
The Virial equation derives from a perturbative treatment of statistical mechanics.
or alternatively
where A, B, C, A′, B′, and C′ are temperature dependent constants.
PengâÂÂRobinson equation of state (named after D.-Y. Peng and D. B. Robinson) has the interesting property being useful in modeling some liquids as well as real gases.
The Wohl equation (named after A. Wohl) is formulated in terms of critical values, making it useful when real gas constants are not available, but it cannot be used for high densities, as for example the critical isotherm shows a drastic decrease of pressure when the volume is contracted beyond the critical volume.
or:
or, alternatively:
where where , , are (respectively) the molar volume, the pressure and the temperature at the critical point.
And with the reduced properties , , one can write the first equation in the reduced form:
This equation is based on five experimentally determined constants. It is expressed as
where
This equation is known to be reasonably accurate for densities up to about 0.8 ÃÂ<sub>cr</sub>, where ÃÂ<sub>cr</sub> is the density of the substance at its critical point. The constants appearing in the above equation are available in the following table when p is in kPa, V<sub>m</sub> is in , T is in K and
The BWR equation,
where d is the molar density and where a, b, c, A, B, C, ñ, and ó are empirical constants. Note that the ó constant is a derivative of constant ñ and therefore almost identical to 1.
The expansion work of the real gas is different than that of the ideal gas by the quantity .