- #1

- 46

- 1

## Main Question or Discussion Point

Hi guys, I have a question regarding the Gibbs paradox. Let's say we take a container A of helium gas and place it next to another container B also containing helium gas at the same temperature and pressure. When we remove the partition (wall) between them, what happens?

If we use classical physics, then the entropy increases by 2Nk ln(2), since we treat every atom as distinguishable. The mixing causes an increase in entropy.

If we use quantum physics, however, the atoms are indistinguishable. So, if we take our partition function and divide it by N!, then after using Stirling's approximation we get a new value for S, where S(container A) + S(container B) = S(complete container after partition removed). According to the math, the entropy does not increase.

But I cannot believe this: before the partition is removed, there is a definite amount of atoms in the left half of the complete container and a definite amount of atoms in the right half of the complete container. After, there is no longer a definite amount of atoms in each half, and so I believe that even in a quantum mechanical description, the entropy should increase.

So, does it increase or does it not? If yes, then where is the math that gives us the corrected value for S incorrect? If no, then where did I go wrong conceptually?

Thanks.

If we use classical physics, then the entropy increases by 2Nk ln(2), since we treat every atom as distinguishable. The mixing causes an increase in entropy.

If we use quantum physics, however, the atoms are indistinguishable. So, if we take our partition function and divide it by N!, then after using Stirling's approximation we get a new value for S, where S(container A) + S(container B) = S(complete container after partition removed). According to the math, the entropy does not increase.

But I cannot believe this: before the partition is removed, there is a definite amount of atoms in the left half of the complete container and a definite amount of atoms in the right half of the complete container. After, there is no longer a definite amount of atoms in each half, and so I believe that even in a quantum mechanical description, the entropy should increase.

So, does it increase or does it not? If yes, then where is the math that gives us the corrected value for S incorrect? If no, then where did I go wrong conceptually?

Thanks.