I Experimental test of the Mixing Paradox

[Philip Koeck]

TL;DR Summary

Is there an experimental test of the mixing paradox?

Can anybody point to an experiment that shows that the total entropy increases if two different gas mix at constant pressure and temperature, whereas if two volumes of identical gases mix the total entropy doesn't change?

 

[Vanadium 50]

How do you build an entropy meter?

And without one, how do you say it's "experimental" and not "theoretical"?

 

[Dale]

That is kind of a problem, isn’t it. I guess entropy is, in that sense, a little like the wavefunction.

 

[bob012345]

That is kind of a problem, isn’t it. I guess entropy is, in that sense, a little like the wavefunction.

Or like potential energy since you can always measure the difference of potential energy but never an absolute value?

 

[Chestermiller]

If they are identical, how can you identify that anything has even happened?

 

[Philip Koeck]

Or like potential energy since you can always measure the difference of potential energy but never an absolute value?

The experiment I'm looking for would only need to show an entropy change, not an absolute value.

 

[Philip Koeck]

In principle I would say you can measure entropy change using a calorimeter for processes that are approximately reversible. For example for the melting of an ice cube at (just above) zero Celsius it should be easy to measure Q and from that calculate the entropy change.
Obviously this is approximate, but acceptable, I would say.

I'm looking for something similar for the mixing of different/identical gases (or liquids).

 

[Philip Koeck]

If they are identical, how can you identify that anything has even happened?

That's exactly how the mixing paradox is resolved in most textbooks (I believe): Identical particles are indistinguishable and therefore you cannot tell that they've mixed. By simply replacing the partition wall you're back to the original state. This means the process of mixing must have been reversible and the entropy change must have been zero.

I'm looking for a more direct confirmation of this conclusion.

 

[DrStupid]

In principle I would say you can measure entropy change using a calorimeter for processes that are approximately reversible.

Is the mixing process of two gases reversible?

By simply replacing the partition wall you're back to the original state. This means the process of mixing must have been reversible and the entropy change must have been zero.

No, that means that from the thermodynamic point of view there is no process at all. The macro state doesn't change.

 

[Philip Koeck]

Is the mixing process of two gases reversible?
No, that means that from the thermodynamic point of view there is no process at all. The macro state doesn't change.

If I understand the textbooks correctly the mixing of identical gases is reversible, whereas the mixing of different gases is not.
I'm simply looking for an experimental test of this statement.

 

[DrStupid]

If I understand the textbooks correctly the mixing of identical gases is reversible

What does "reversible" means in this case? If nothing changes than there is nothing to be reversed.

 

[Philip Koeck]

What does "reversible" means in this case? If nothing changes than there is nothing to be reversed.

Good point!

The question still stands though:
If there is no process, as in the case of identical gases, then entropy doesn't change.
In the case of two different gases the mixing is an irreversible process and entropy changes.
Has this been shown experimentally?

 

[DrStupid]

If there is no process, as in the case of identical gases, then entropy doesn't change.
In the case of two different gases the mixing is an irreversible process and entropy changes.
Has this been shown experimentally?

I don't know what kind of experiment you are expecting. You can even have both cases with the same experiment at once - depending on what you are able to measure or what you are interested in. If you for example don't care about isotopes then it makes no difference for you if you have two separated volumes of pure ²³⁵UF₆ and pure ²³⁸UF₆ or a single volume with a mixture of them. But it makes a huge difference if you care.

PS: There is a parallel thread about the same topic. The link in #2 should explain it.

 

[vanhees71]

https://doi.org/10.1021/ed049p212