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When the smell in my room seems to be full of flatulence(it wasn't me), what happens with the gases when I open a window? Detail: It is winter and the air outside is cold whereas the air in the room is warm. When I close the window the smell of flatulence comes back nearly right away. What does the process of diffusion look like here?

And would the smell be dispersed faster if I sprayed another odor into the room?

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When you open the window the air closest to the window is quickly pushed out the top of the window by cold air pushing in at the bottom. That’s convection, which is a fast way to mix fluids. But far from the window the air is more stagnant and the only way for the smell to disperse is by diffusion which is a slow process. When you go back to the part of the room far from the window the smell is still there.

Adding a new odor to the room would not speed up diffusion but it might overwhelm your odor receptors enough to prevent you from smelling what’s there. Some deodorizing sprays actually contain oxiders that chemically alter smelly molecules into non-smelly ones.

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