Numbers if molecules for differnt velocities in gas

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SUMMARY

The forum discussion centers on the interpretation of the velocity distribution function f(u) for gas molecules, specifically how f(u) du represents the fraction of molecules with speeds between u and u + du. Users express confusion regarding the concept of infinitesimal quantities and their implications for calculating fractions of molecules. A key clarification provided is that while du is infinitesimal, integrating f(u) du over an interval yields the fraction of molecules within that velocity range, resolving the initial misunderstanding.

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georg gill
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http://bildr.no/view/1099870

The distribution of velocities of particles in this text is given by f(u) later in the text (the final part) they say that f(u) du gives fraction of gas molecules with speed between u and du+u. I thought that would only give a infinite small number since du is infinite small and not a fraction of the molecules?

And I also wonder about that in the next sentence they refer to a function that is drawn in figure 5.15 and 5.16. Is this f(u)du? I would have thought it would have to be only f(u) but it does not get through in the text for me which function they mean

The text is also here in page 162-163 in the link to the whole book:

http://bildr.no/view/1099870

(sometimes some pages does not load but if one open it in different readers for the internet one get different pages unavailable each time. But the part of the book with the text that I wonder about is in the link in the beginning anyway)
 
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georg gill said:
http://bildr.no/view/1099870

The distribution of velocities of particles in this text is given by f(u) later in the text (the final part) they say that f(u) du gives fraction of gas molecules with speed between u and du+u. I thought that would only give a infinite small number since du is infinite small and not a fraction of the molecules?

And I also wonder about that in the next sentence they refer to a function that is drawn in figure 5.15 and 5.16. Is this f(u)du? I would have thought it would have to be only f(u) but it does not get through in the text for me which function they mean

The text is also here in page 162-163 in the link to the whole book:

http://bildr.no/view/1099870

(sometimes some pages does not load but if one open it in different readers for the internet one get different pages unavailable each time. But the part of the book with the text that I wonder about is in the link in the beginning anyway)

sorry wrong second link don't think it is that important the question is given in the first anyway

http://books.google.no/books?id=2Ox...Q-oGrDg&ved=0CEQQ6AEwBDgK#v=onepage&q&f=false
 
georg gill said:
http://bildr.no/view/1099870

The distribution of velocities of particles in this text is given by f(u) later in the text (the final part) they say that f(u) du gives fraction of gas molecules with speed between u and du+u. I thought that would only give a infinite small number since du is infinite small and not a fraction of the molecules?

An infinitely small fraction is still a fraction of the molecules. More importantly, integrating f(u) du from a to b gives you the fraction of molecules with velocities between a and b.
 

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