Experimental test of the Mixing Paradox

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Discussion Overview

The discussion revolves around the experimental verification of the Mixing Paradox in thermodynamics, specifically addressing the entropy changes that occur when different gases mix compared to when identical gases mix. Participants explore the theoretical implications and seek experimental evidence for these concepts.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • Some participants inquire about experiments that demonstrate total entropy increases when different gases mix at constant pressure and temperature, while entropy remains unchanged for identical gases.
  • Questions are raised regarding the feasibility of measuring entropy changes experimentally without a dedicated entropy meter.
  • There is a comparison made between entropy and other physical concepts, such as the wavefunction and potential energy, highlighting the challenges in measuring absolute values versus changes.
  • Some participants argue that if gases are identical, it is difficult to identify any changes that occur during mixing, suggesting that the mixing process may be reversible and thus have zero entropy change.
  • Others propose that entropy change can be measured using calorimetry for approximately reversible processes, seeking similar methods for the mixing of gases.
  • There is a contention about whether the mixing of gases is a reversible process, with some asserting that mixing identical gases is reversible while mixing different gases is not, and questioning the implications of these definitions.
  • Participants express uncertainty about what constitutes a "process" in the context of mixing identical gases, with some suggesting that if no observable change occurs, then the entropy does not change.
  • One participant mentions the possibility of conducting an experiment that could simultaneously demonstrate both cases of gas mixing, depending on the measurements taken.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the experimental verification of the Mixing Paradox. There are multiple competing views regarding the nature of mixing processes, the definition of reversibility, and the implications for entropy changes.

Contextual Notes

Participants note limitations in measuring entropy changes and the dependence on definitions of processes and states. The discussion highlights the complexity of distinguishing between reversible and irreversible processes in the context of identical versus different gases.

Philip Koeck
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TL;DR
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?
 
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How do you build an entropy meter?

And without one, how do you say it's "experimental" and not "theoretical"?
 
That is kind of a problem, isn’t it. I guess entropy is, in that sense, a little like the wavefunction.
 
Dale said:
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?
 
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If they are identical, how can you identify that anything has even happened?
 
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bob012345 said:
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.
 
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).
 
Chestermiller said:
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.
 
Philip Koeck said:
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?

Philip Koeck said:
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.
 
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  • #10
DrStupid said:
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.
 
  • #11
Philip Koeck said:
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.
 
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  • #12
DrStupid said:
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?
 
  • #13
Philip Koeck said:
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.
 
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