Unraveling the Principles of Boltzmann's Law

[benedwards2020]

Write down the 3 principles underpinning Boltzmanns law and indicate which of these is incompatible with the quantum theory of gases

The Attempt at a Solution

Well I know two...

1. The conservation of energy
2. Equal probabilities of allowed configurations

But I'm a bit stuck with the third. Can anyone help me out here?

I know that Boltzmann said that it matters which molecule is in which state and that there is no restriction on the number of molecules that can occupy a given state, but I wasn't aware that this is an underpinning principle. If it is, then I would say that this is the one that isn't compatible with the quantum theory of gases due to the indistinguishability issue.

 

[genneth]

Which Boltzmann law? I think you're thinking of $$S = k \ln W$$ but they could mean the statistical Boltzmann law, i.e. the distribution of energies of molecules in a gas.

 

[benedwards2020]

Well, I'm assuming that its the principles of statistical mechanics that they're after. As I said, I only know of two 'principles'. I am working on quantum theory though and don't know of any separate principles from Boltzmann for this.