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I know that modeling gases as ideal gases includes two approximations:

  • approximating Particles as points regarding the collisions with macroscopic objects
  • neglecting inter-particle interactions

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?

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  • $\begingroup$ What flow regime are you asking about? There's a world of difference between subsonic flows which are essentially perfectly continuous and hypersonic flows with occasional molecules striking surfaces. $\endgroup$
    – D. Halsey
    Oct 1, 2022 at 12:16
  • $\begingroup$ Broadly, we can say that the ideal gas assumption is suitable if the compressibility factor is sufficiently close to 1 for one’s purposes for the relevant pressure and temperature. $\endgroup$ Oct 1, 2022 at 14:11

1 Answer 1

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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:

enter image description here

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.

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