Boltzmann's version of 2nd Law -log relationship

1. Sep 5, 2004

celal777

Hello List,

I understand Boltzmann defined entropy as log W where W is the number of microstates in the system time a constant "k" ; hence S= k Log W.

Can someone explain to me where the logarithmic relationship comes from please ?

Celal Berker
London, England

2. Sep 5, 2004

kuengb

You want the Entropy to be a quantum that adds up when you're looking at more than one system: E. g. if you have two containers filled with gas, you want the relationship S(container A & container B) = S(container A) + S(container B).

But if the system A has $W_a$ states and the system B has $W_b$ states, the combined system has $W_a W_b$ states: a product, not a sum. So youo have to take the logarithm of this number to get the relation above.

3. Sep 6, 2004

celal777

Many Thanks Bruno (is that your name?)

So how did Planck, by what thought or reasoning processes did he go from the relation S= k log W to E=Hf ?

--Celal