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This theory has bugged me ever since my first physics class on the subject. If this ( is true, it leads me to a few weird conclusions.

Opening the rear window in a pickup truck at 10 m/s doesn't empty the cabin of all its air. This means that gas molecules can catch up with us from behind so we can conclude that gases move much faster than 10 m/s at normal temperatures.

Then, shouldn't gases mix almost instantaneously? For example, shouldn't a fart's smell reach us faster than a car on an highway and then dissapear almost immediately into such a large area that the concentration is too low for our noses to detect?

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This question is gold hahahahaah – Dylan Sabulsky Dec 5 '12 at 6:29
up vote 5 down vote accepted

The kinetic theory of gases does in fact say that molecules in a gas move very rapidly (although some move quite slow, and others even faster).

However, there is another crucial component to the theory. The idea of Mean Free Path. Here, a molecule is moving very fast but doesn't get very far before hitting another molecule. This is why things like odors travel relatively slow and why gases don't "mix instantaneously." A given molecule may only move 1e-6 meters before bouncing off of another molecule, and the direction it bounces is random. This slows down the progress of mixing.

Additionally, in your example of opening the rear window of a truck, it's important to look at the macroscopic effects of the flow, which kinetic theory doesn't really explain. The truck cabin generates a wake with a recirculation zone behind it. This means that the air immediately behind the window is relatively stagnant, which is also why the air in the cabin doesn't leave as fast as it could.

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This makes a lot of sense. I always thought the size of the molecules and the number of impacts was negligible in a gas. Thanks! – Kevin Coulombe Dec 5 '12 at 6:44
Collisions between molecules drive everything. Energy transfer, chemical reactions, momentum transfer, all of it. Viscosity and drag wouldn't exist without the collisions! The only real exception is radiative transfer of energy. – tpg2114 Dec 5 '12 at 6:45
@tpg2114 The size of the molecules and the number of impacts was negligible in a gas are assumptions in kinetic theory :) Just sayin' – namehere Dec 5 '12 at 10:03
@namehere I didn't say anything about the size of molecules and the number of their collisions. Just that they do in fact collide and the average distance they travel is the MFP. Which is explained by kinetic theory and explains why the processes of mixing aren't instantaneous. – tpg2114 Dec 5 '12 at 10:43
@tpg2114 Yeah I know. Just sayin' there – namehere Dec 5 '12 at 11:02

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