Each one of the assumptions listed below adds to the complexity of the problems solution. As the density of a gas increases with rising pressure, the intermolecular forces play a more substantial role in gas behavior which results in the ideal gas law no longer providing "reasonable" results. At the upper end of the engine temperature ranges (e.g. combustor sections – 1300 K), the complex fuel particles absorb internal energy by means of rotations and vibrations that cause their specific heats to vary from those of diatomic molecules and noble gases. At more than double that temperature, electronic excitation and dissociation of the gas particles begins to occur causing the pressure to adjust to a greater number of particles (transition from gas to plasma). Finally, all of the thermodynamic processes were presumed to describe uniform gases whose velocities varied according to a fixed distribution. Using a non-equilibrium situation implies the flow field must be characterized in some manner to enable a solution. One of the first attempts to expand the boundaries of the ideal gas law was to include coverage for different thermodynamic processes by adjusting the equation to read pV = constant and then varying the n through different values such as the specific heat ratio, γ'.
Real gas effects include those adjustments made to account for a greater range of gas behavior:
*Compressibility effects (Z allowed to vary from 1.0)
*Variable heat capacity (specific heats vary with temperature)
*Van der Waals forces (related to compressibility, can substitute other equations of state)
*Non-equilibrium thermodynamic effects
*Issues with molecular dissociation and elementary reactions with variable composition.
For most applications, such a detailed analysis is excessive. Examples where real gas effects would have a significant impact would be on the Space Shuttle re-entry where extremely high temperatures and pressures were present or the gases produced during geological events as in the image of the 1990 eruption of Mount Redoubt.