# S = k ln W : ln : From Both Multiplicity and Integral ?

1. Jan 17, 2012

### morrobay

Can the natural logarithm in the statistical mechanics formulation of entropy , S = k ln W be based on both multiplicity and an integral ? The extensive property and multiplicity explanation : That for any given macrostate , the total entropy of two interacting
systems is the sum of their individual entropies:
Stotal = k ln( WA WB)
= k ln WA + k ln WB = SA + SB
For the natural logarithm to be based on the integral : x1 to x2 1/x dx = ln x2/x1
That the thermodynamic entropy is based on : delta Q /T = n R ln v2/v1
http://www.eoht.info/page/S+=+k+ln+W on page 2 of this link
W2/W1 = v2/v1 are equated. In a physical chemistry text delta S = k ln W2/W1
So is this term , ln W2/W1, the property of the integral : from W1 to W2 dw/1/W ?

Last edited: Jan 18, 2012
2. Jan 20, 2012