Real gases are nonideal 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 points, 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 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 Vm 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) 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: 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, 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 Berthelot and modified Berthelot model The Berthelot equation (named after D. Berthelot) is very rarely used, but the modified version is somewhat more accurate Dieterici model This model (named after C. Dieterici) fell out of usage in recent years with parameters a, b, and Clausius model The Clausius equation (named after Rudolf Clausius) is a very simple three-parameter equation used to model gases. or alternatively: where where Vc is critical volume. Virial model The Virial equation derives from a