Given the scenario you just laid out it seems no work can be extracted just by letting mix two substances that are at the same temperature and pressure. But there is something about it that doesn't quite add up to my intuition of symmetry and conservation laws. Could you please elaborate more on that?
[0]: https://en.wikipedia.org/wiki/Semipermeable_membrane [1]: https://en.wikipedia.org/wiki/Osmosis
The former scenario is famously the setting for Maxwell's daemon. I was assuming this scenario is something else.
I'm confused because on one hand I can see that it requires work to reorder the particles once they have been shuffled around. On the other hand I don't see how one could extract work while they get shuffled around if they all have the same momenta.
Perhaps the answer is that we cannot have a system where the microscopic entities are at the same indistinguishable but also distinguishable. Perhaps if they had different "colours' it means they do interact differently with the environment? I'm still confused frankly
That is irrelevant, we don't need to be able to tell them apart, the membrane needs to be able to. Besides that, they can be completely identical.
> I'm confused because on one hand I can see that it requires work to reorder the particles once they have been shuffled around. On the other hand I don't see how one could extract work while they get shuffled around if they all have the same momenta.
In the illustration with the cylinder from Wikipedia you can see that the level of the one fluid (which the other fluid is selected into) rises. It performs work against gravity and builds up potential energy / increases the pressure. You can harvest that.
> The former scenario is famously the setting for Maxwell's daemon. I was assuming this scenario is something else.
In Maxwell's daemon you start with a substance which is already mixed and separate it into its components. That requires work and is the exact opposite of what is happening here. In fact it is called reverse Osmosis [0]. Osmosis gives you pressure which you can harvest, so reverse osmosis needs pressure back to operate. That completes the cycle.
Nope. The work comes from the system coming from ordered state into unordered. Why the problem above is good for intuition because you can work out how to reverse the state. You invent semi-magical barrier which is fully transparent for particles A and reflects particles B, then you start to push such barrier from left to right up to the middle, compressing gas B (and making work!) and leave left part with gas A only, then repeat similar exercise on the right side.
>Given the scenario you just laid out it seems no work can be extracted just by letting mix two substances that are at the same temperature and pressure. But there is something about it that doesn't quite add up to my intuition of symmetry and conservation laws. Could you please elaborate more on that?
As far as I understand this asymmetry was the exact reason why entropy was introduced. Then later explained by Boltzmann via a measure of number of microscopic states.
Naturally second law of thermodynamics forbids perpetual engines.
