# 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