I've been thinking again. The formula for the Maxwell Speed Distribution for a non-ideal gas is [itex]\displaystyle f(v) = 4\pi \left(\frac{M}{2\pi RT}\right)^{\frac{3}{2}} v^2 e^{\frac{-Mv^2}{2RT}}[/itex].(adsbygoogle = window.adsbygoogle || []).push({});

My derivation follows as such:

[itex]\displaystyle f(v) = 4\pi \left(\frac{m}{2\pi nRT}\right)^{\frac{3}{2}} v^2 e^{\frac{-mv^2}{2nRT}}[/itex], where m is the mass of the gas and n is the number of moles.

[itex]\displaystyle f(v) = 4\pi \left(\frac{m}{2\pi P_{ideal}V_{ideal}}\right)^{\frac{3}{2}} v^2 e^{\frac{-mv^2}{2P_{ideal}V_{ideal}}}[/itex], by the ideal gas law.

[itex]\displaystyle f(v) = 4\pi \left(\frac{m}{2\pi (P + \frac{an^2}{V^2})(V-nb)}\right)^{\frac{3}{2}} v^2 e^{\frac{-mv^2}{2(P + \frac{an^2}{V^2})(V-nb)}}[/itex], through the Van der Waals equation.

Factoring, we get [itex]\displaystyle f(v) = 4\pi \left(\frac{mV^2}{2\pi (PV^3-nbPV^2+an^2V-abn^3)}\right)^{\frac{3}{2}} v^2 e^{\frac{-mv^2}{2(PV^3-nbPV^2+an^2V-abn^3)}}[/itex].

As ridiculous as it looks, it probably isn't ridiculous enough. Would this work for modeling a non-ideal gas?

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# MSD for non-ideal gas?

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