1. Thermodynamics & Gibbs Paradox

2. The Mixing of Non-Identical Gases
Before

3. Shows obvious increase in entropy (disorder)
After
Shows obvious increase in entropy (disorder)

4. The Mixing of Identical Gases
Before

5. Shows zero increase in entropy as action is reversible
After
Shows zero increase in entropy as action is reversible

6. There is a CONTRADICTION!!!
Compare the two scenarios of mixing and we realize that……
There is a CONTRADICTION!!!

7. Gibbs’ Resolution to the Paradox
When 2 non-identical gases mix and entropy increases, we imply that the gases can be separated and returned to their original state
When 2 identical gases mix, it is impossible to separate the two gases into their original state as there is no recognizable difference between the gases

8. Thus, these two cases stand on different footings and should not be compared directly with each other.
The mixing of gases of different kinds that results in an entropy change was independent of the nature of the gases.
Hence it is independent of the degree of similarity between them

9. The Mixing of Identical Gases (Revisited)
Before

10. After