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:

• 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. On the other hand, real-gas models have to be used near the condensation point of gases, near critical pointss, at very high pressures, to explain the Joule–Thomson effect, and in other less usual cases. The deviation from ideality can be described by the compressibility factor Z.

Models

Van der Waals model

Where p is pressure, T is temperature, R is the ideal gas constant, and Vm is the molar volume. a and b are parameters that are determined empirically for each gas, but are sometimes estimated from their critical temperature (Tc) and critical pressure (pc

The constants at the critical point

With the reduced properties the equation can be written in the reduced form

Redlich–Kwong model

The Redlich–Kwong 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

where a and b are two empirical parameters that are not

The constants at critical point can be expressed as functions of the parameters a, b

Berthelot and modified Berthelot model

The Berthelot equation (named after D. Berthelot)

Dieterici model

This model (named after C. Dieterici

with parameters a, b. These can be normalized by dividing with the critical point statewhich casts the equation into the reduced form:

Clausius model

The Clausius equation (named after Rudolf Clausius

where Vc is critical volume.

Virial model

The Virial equation derives from a perturbative treatment

where A, B, C, A, B, and C are temperature dependent constants.

Peng–Robinson model

Peng–Robinson equation of state (named after D.-Y. Peng and D. B. Robinson

Wohl model

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

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

Beattie–Bridgeman model

This equation is known to be reasonably accurate for densities up to about 0.8ρcr, where ρcr 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, Vm, T

Benedict–Webb–Rubin model

where d is the molar density and where a, b, c, A, B, C, α, and γ are empirical constants. Note that the γ constant is a derivative of constant α and therefore almost identical to 1.

Thermodynamic expansion work

.

See also

• Compressibility factor

• Equation of state

• Ideal gas law: Boyle's law and Gay-Lussac's law

References

Further reading

External links

• http://www.ccl.net/cca/documents/dyoung/topics-orig/eq_state.html