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Boltzman's entropy


sanctus

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Just a question: does anybody know why Botlzman's entropy S=k*log(W) (with k the boltzman constant and W proportionnel of the number of ways one can arrange the sytem) isn't extensive? Ie. why lim (1/N)*k*log(W) diverges?

 

Thanks very much to those who know (and answer as well :) ).

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entropy.. where does the energy go?

 

its like the universe is self metabolizing. which would imply the big crunch, but thats contrary to popular expansionist theory...

 

is dark matter simply simple particles resulting from entropy of normal matter? once the fire goes out you're left with soot?

 

tormod ain't gonna like this post i'm sure. ..

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well here i am again... and i'm affraid i don't know....but i can guess of course :(

and my guess is that th e N particles have to be destributed over at least N energy states. This can be done in N! different ways, so W~>N! (~>="at least proportional to")

and 1/N log(N!) diverges. (by the golden rule that anything with a !-sign diverges...)

 

and no i dn't like statistical mechanics :()

 

Bo

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Like Bo says, if log(W) diverges, total would diverge. I found a couple of websites that

might help....

 

http://members.tripod.com/~boltzmann/ludwig.html

http://www.draaisma.net/rudi/compex/appendix.html

http://facweb.eths.k12.il.us/chemphys/Word/Chem-Phys%20ENTROPY%20-%20Student.htm

 

I found these from a Google search. :D

 

Maddog

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I found these from a Google search. :cup:

 

Maddog

 

 

I know, but usually I prefer to hear explications from people I somehow know a bit and so I preferred to ask here. Actually it didn't even come to my mind to search in the net, so thanks for remining me of that option :hihi:

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