- #1
pines-demon
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I have a not-so-well based intuition about this one, I think that in general odors travel farther in winter than in summer. I can smell the close-by bakery more intensively when is cold than when is hot. This might be a variety of reasons (like there being more smells to sense in summer) but I was thinking that molecules travelled father without colliding.
I have two ways to think about this that give me the opposite of my original intuition.
1) Brownian motion: per the usual formula the distance travelled of a particle in random field is ##\langle x^2\rangle=2Dt## where ##D## is the diffusion constant (proportional to temperature ##T##). So this results says that in hotter environment a particle travels farther than in cold environment in a time ##t##. However this is not the same that I wanted to calculate as it consider a single particle and it implies that there are many collisions moving the particle, I wanted to know how much a packet of particles can travel before collisions so:
2) Mean free path: the mean free path of a gas is proportional to temperature and inversely proportional to pressure. Meaning again that the hotter the environment, the father the particle travels. However I do not know how to account for pressure here as pressure lowers in colder environments.
So which is it? Do smells travel faster in cold environments or is it the opposite?
Note: I am not talking about volatility (how easily something emits some molecule), this clearly increases with temperature as things get rotten or evaporate more easily. I am talking of travel distance as a noticeable chemical signature before diffusing into the background.
I have two ways to think about this that give me the opposite of my original intuition.
1) Brownian motion: per the usual formula the distance travelled of a particle in random field is ##\langle x^2\rangle=2Dt## where ##D## is the diffusion constant (proportional to temperature ##T##). So this results says that in hotter environment a particle travels farther than in cold environment in a time ##t##. However this is not the same that I wanted to calculate as it consider a single particle and it implies that there are many collisions moving the particle, I wanted to know how much a packet of particles can travel before collisions so:
2) Mean free path: the mean free path of a gas is proportional to temperature and inversely proportional to pressure. Meaning again that the hotter the environment, the father the particle travels. However I do not know how to account for pressure here as pressure lowers in colder environments.
So which is it? Do smells travel faster in cold environments or is it the opposite?
Note: I am not talking about volatility (how easily something emits some molecule), this clearly increases with temperature as things get rotten or evaporate more easily. I am talking of travel distance as a noticeable chemical signature before diffusing into the background.
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