mersenneforum.org  

Go Back   mersenneforum.org > Great Internet Mersenne Prime Search > Math

Reply
 
Thread Tools
Old 2008-08-28, 21:14   #1
ShiningArcanine
 
ShiningArcanine's Avatar
 
Dec 2005

22×23 Posts
Default Inconsistencies on Wikipedia?

http://en.wikipedia.org/wiki/Maxwell...tion_of_speeds
http://en.wikipedia.org/wiki/Boltzmann_constant

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:

http://upload.wikimedia.org/math/c/b...84248a223c.png

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

http://upload.wikimedia.org/math/3/c...db3107f630.png
http://upload.wikimedia.org/math/2/3...172d2a6331.png

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.

Last fiddled with by ShiningArcanine on 2008-08-28 at 21:15
ShiningArcanine is offline   Reply With Quote
Old 2008-08-28, 21:40   #2
bsquared
 
bsquared's Avatar
 
"Ben"
Feb 2007

13×257 Posts
Default

Quote:
Originally Posted by ShiningArcanine View Post
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.
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:

http://www.physicsforums.com/

I can't be any more helpful at the moment, sorry.
bsquared is offline   Reply With Quote
Old 2008-08-28, 22:03   #3
michaf
 
michaf's Avatar
 
Jan 2005

1110111112 Posts
Default

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.
michaf is offline   Reply With Quote
Old 2008-08-28, 22:25   #4
ATH
Einyen
 
ATH's Avatar
 
Dec 2003
Denmark

32·331 Posts
Default

It seems ok to me. Remember that Molar mass: M = m * NA. Insert that and k=R/NA in vp 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:
http://en.wikipedia.org/wiki/Ideal_gas_law
So N = n*NA, and if you insert above:
n*NA*k = n*R or k = R/NA , which is the defenition of k.


Edit: Ops I was too slow :)

Last fiddled with by ATH on 2008-08-28 at 22:28
ATH is offline   Reply With Quote
Old 2008-09-02, 20:41   #5
ShiningArcanine
 
ShiningArcanine's Avatar
 
Dec 2005

22×23 Posts
Default

Thankyou very much for the explanation. :)
ShiningArcanine is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
yoyo@home and wikipedia Dubslow Factoring 1 2015-12-06 15:56
Mersenne Wikipedia edits? Sutton Shin mersennewiki 0 2012-09-29 08:10
Wikipedia article on SNFS fivemack Factoring 2 2007-02-15 17:52
Quadratic Sieve in wikipedia.de ThiloHarich Factoring 5 2006-07-14 09:51
promoted to administrator on Wikipedia! ixfd64 Lounge 3 2005-09-22 05:44

All times are UTC. The time now is 05:09.

Thu Nov 26 05:09:21 UTC 2020 up 77 days, 2:20, 3 users, load averages: 1.89, 1.76, 1.56

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2020, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.