We ask: how large is the probability of the last-mentioned state relative to the original state? Or, what is the probability that at some point in time all n independently moving points in a volume v0 have by chance ended up in the volume v?
For this probability, which is a "statistical probability" one obtains the value:
one derives from this, applying Boltzmann's principle:
It's noteworthy that for this derivation, from which the Boyle-Gay-Lussac law and the identical law of osmotic pressure can be easily derived thermodynamically , there is no need to make any assumption regarding the way the molecules move.
Interpretation of the Volume Dependence of the Entropy of Monochromatic Radiation using Boltzmann's Principle
In paragraph 4 we found for the dependence of Entropy of the monochromatic radiation on volume the expression:
This formula can be recast as follows:
- If E is the energy of the system, then one obtains: