I know that modeling gases as ideal gases includes two approximations:
The first approximation seems pretty "harmless", it is the quality of the second approximation im interested in.
Under what circumstances can inter-particle interaction be neglected?
Especially: Can aerodynamic calculations be done reliably using the ideal gas approximation?
Real gases behave as ideal gases at low pressures and high temperatures. The quantitative test is $$Z = \frac{P V}{RT} \approx 1$$ where $Z$ is the comprehensibility factor. To a good approximation $Z$ can be represented in the form of a universal graph for all gases as a function of reduced pressure ($P_r=P/P_c$) and reduced temperature ($T_r=T/Tc$), where $P_c$, $T_c$ are the critical pressure and temperature of the gas:
The gas is essentially ideal if $Z$ is close enough to 1.
To determine whether the ideal gas is applicable to aerodynamics, suppose the gas to be nitrogen ($T_c=126.2$ K, $P_c=33.98$ bar). Then use a typical $P$ and $T$ in your problem and determine $Z$. For example, with at $T=300$ K we have $T_r=2.4$. As we see from the graph, the isotherm $T_r=2.4$ is pretty close to 1 up to fairly high pressures. So, nitrogen at 25 C is pretty close to ideal gas at least up to $P_r\approx 2$ or $P=2 P_c\approx 70$ bar.
