I have a question regarding the Gibbs Paradox.
Let us assume that the two partial volumes of the box are equal in size $V_1=V_2$, and that $N$ particles of a monatomic ideal gas are in each of the two chambers. All gases involved have the same particle mass and energy per particle before and after.
Now let's assume two cases:
1.both halves contain the same gas and this consists of distinguishable particles.
2.the halves contain different gases, which themselves consist of distinguishable particles.
If one calculates now the entropy change, is it not then actually the same calculation. The particles in case 1 are distinguishable, in case 2 they are different gases, but their particles among themselves are also distinguishable. In case 2, the particles cannot be more distinguishable than in case 1, can they?