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 ShiningArcanine 2008-08-28 21:14

Inconsistencies on Wikipedia?

[url]http://en.wikipedia.org/wiki/Maxwell-Boltzmann_distribution#Distribution_of_speeds[/url]
[url]http://en.wikipedia.org/wiki/Boltzmann_constant[/url]

Wikipedia says that the Boltzman constant k, is k = R/N(a), where R is the ideal gas constant and N(a) is Avogadro's number, yet whenever this is substituted into equations on wikipedia, terms seem to vanish.

For example, in the following, m, the molar mass, seems to disappear from the equation:

In the case of the ideal gas law, n, the number of moles, also seems to disappear from the equation:

Is this some error or is there some implicit thing that I fail to see?

I apologize if asking here is inappropriate, but this is the only place that I know where I can ask math/math-related questions and expect to receive some sort of answer, so I thought I would ask here.

By the way, I had not seen that the equation for the mean speed of molecules in a gas had already been derived for me on Wikipedia, so I took it upon myself to derive it. While working on that problem, I found a problem in my old Calculus textbook that asked for a derivation of the very same thing, wondered why there was a discrepancy between the usage of R and k in the equation the textbook had (it used R) and the equation Wikipedia had (it used k) and solved the textbook problem anyway. I would not have noticed this if it had not been for that. I am very curious as to what the reason is for the discrepancies I have found.

 bsquared 2008-08-28 21:40

[quote=ShiningArcanine;140224]
I apologize if asking here is inappropriate, but this is the only place that I know where I can ask math/math-related questions and expect to receive some sort of answer, so I thought I would ask here.
[/quote]

I'm not trying to tell you to go away, but here is another possible venue for this question, which also seems to have lively participation by knowledgable people:

[URL]http://www.physicsforums.com/[/URL]

I can't be any more helpful at the moment, sorry.

 michaf 2008-08-28 22:03

With (1) pV=nRT (n is given in moles)
and (2) pV=NkT (n is given in number of molecules)

it implies that nRT=NkT --> nR=Nk --> k=R*n/N

Given that k=R/N_a (N_a is the number of Avogadro, # molecules per mole)
this gives that N_a equals N/n

I think you got disoriented by the different kinds of n's.

 ATH 2008-08-28 22:25

It seems ok to me. Remember that Molar mass: M = m * N[sub]A[/sub]. Insert that and k=R/N[sub]A[/sub] in v[sub]p[/sub] and the 2 equations are the same.

The last two equations implies that N*k = n*R which at first glance looks wrong. But N is not Advogadros constant it is the actual number of molecules:
[URL="http://en.wikipedia.org/wiki/Ideal_gas_law"]http://en.wikipedia.org/wiki/Ideal_gas_law[/URL]
So N = n*N[sub]A[/sub], and if you insert above:
n*N[sub]A[/sub]*k = n*R or k = R/N[sub]A[/sub] , which is the defenition of k.

Edit: Ops I was too slow :)

 ShiningArcanine 2008-09-02 20:41

Thankyou very much for the explanation. :)

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