Alright, so now I understand that entropy is a state function and we can easily calculate it by devising a reversible path between the two states of an irreversible path. For calculating the entropy of mixing of two different gases, the professor in this video at 35:02 states that we can achieve such a reversible process by using pistons permeable only to each individual gas, but, how is this physically possible? Does there really exist such pistons permeable only to one kind of gas or is this whole procedure just a mathematical construct?

When I say mathematical construct, I mean that it is just a mathematical piston that we could use to drive the process backward and calculate entropy i.e: does not exist in reality.

I discussed this problem with a friend of mine, and he told to me that we could achieve this if we had a hypothetical porous wall that had intermediate pore size between the molecule size of two gases. So, the gas with a lower pore size could simply pass through the porous wall.

So, is this experimentally feasible? If they do exist, then I'd appreciate some videos demonstrating it.

  • $\begingroup$ You are aware of semipermeable membranes being used to do gas separations, correct? How does using ideal semipermeable membranes to evaluate entropy change differ from using ideal gases to evaluate entropy change? These are just approximations to actual behavior that can be corrected later to account for non-idealities. $\endgroup$ – Chet Miller Sep 10 at 22:28
  • $\begingroup$ No, I mean the process seems quite ideal but if we do it mathematically, we get the equations and everything out alright. Now, does this entropy change reflect the entropy change or is this ideal reversible process just an upper limit? $\endgroup$ – Buraian Sep 11 at 8:23
  • $\begingroup$ I don't quite understand the question. The entropy change determined in this way (i.e., the entropy of mixing) agrees with the results obtained for the entropy of mixing for ideal gases determined from statistical thermodynamics. And they also agree with the entropy change for mixing an "ideal liquid solution" from statistical thermo. $\endgroup$ – Chet Miller Sep 11 at 11:39
  • $\begingroup$ A true reversible path doesn't exist in reality, and hence, it should be impossible to create such calculations using direct physical methods. However if we were to create mathematical constructions of these perfect semi permeable membranes, then everything does work out. $\endgroup$ – Buraian Sep 11 at 11:52
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    $\begingroup$ We can approach a true reversible path as closely as we desire. I think you are overthinking this. $\endgroup$ – Chet Miller Sep 11 at 13:21

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