- #1
gsingh2011
- 115
- 1
Why is there a logarithm in the entropy formula? Why is it S=kln(N) where k is the Boltzmann constant and N is the number of microstates? Why isn't it S=N?
The reason that I know of, is that we require entropy to be an extensive property.
Suppose that we have two systems, with N_{1} and N_{2} microstates, respectively, and we join them. From basic statistics it follows that the new system has N = N_{1}N_{2} microstates.
However, to be an extensive quantity, the entropy should scale as
S = S_{1} + S_{2}.
But is ln the only function for which f(xy) = f(x)+f(y)?