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Without using any math, can you explain to me what a rarefied gas is? And then what an ultra-rarefied gas is? I'd like to understand it from a conceptual level if you can make connections to other concepts that would be even better. I'd like to imagine the concept in my head.

I also saw this question which did give me some insight.

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    $\begingroup$ "rarefied" is the opposite of "compressed". It's gas at a low pressure, lower than atmospheric. $\endgroup$
    – Hearth
    Nov 21 '21 at 15:50
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When we are calculating the properties of a gas we usually treat it as a continuous fluid i.e. we ignore the fact it is made up from small discrete particles. For example when calculating the flow of air over aeroplane wings we use the Navier Stokes equations and these assume the gas is a continuous medium.

This only works when the gas particles (atoms or molecules) are locally in equilibrium, and this means they have to be exchanging energy with each other on a timescale and length scale much shorter than the ones used in our experiments. In a gas like air at room temperature and pressure the distance gas molecules travel in between collisions (the mean free path) is around $0.1$ microns and they collide with each other roughly every $\stackrel{1}{}\!\!\unicode{x2215}_{\!\unicode{x202f}3}$ of a nanosecond. So if we are calculating the air flow over a Boeing 747 it is fine to approximate the air as continuous.

However the mean free path is inversely proportional to the density of the gas, so if we keep decreasing the density the mean free path keeps increasing and eventually approaches the size of the aeroplane wing. Once this happens we can no longer use the continuum approximation and the Navier Stokes equations would no longer apply. We have to explicitly take into account the discreteness of the gas.

And this is what we mean by rarified. It means the mean free path, and therefore the time between collisions, of the gas particles has increased to the point where we can no longer treat the gas as a continuous fluid. To an extent this depends on the scale we are working at, the smaller the scale the higher the density at which the gas becomes rarified, so there is no single definition for when a gas becomes rarified.

I am not familiar with the term ultra-rarified but I assume it means the regime in which the mean free path of the gas particles is much longer than the length scale of the exeriment.

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