Re, "distinction between Liquid and Gas is an artificial one." Imagine a mountain ridge. At the western end, there is a tall cliff, but as you walk toward the east, the height of the cliff gradually decreases until you reach the place where the top meets the bottom, and there is no cliff at all. Does the fact that there is a path you can follow from the bottom to the top without climbing the face mean that the so-called "cliff" actually is just an artificial construct? Or would you really get hurt if you stepped off the top at the western end?

I had to downvote. This is just a more wordy version of knzhou's non-answer. — Another (unimportant) matter: you put so much emphasis-markup into your answer that it becomes hard to even read. In particular, please don't use math mode as “super-italic” emphasis.

@leftaroundabout : You may be unhappy with knzhou's answer, but everything he says is correct and, as far as I can tell, fully answers the OP. So, to call this a non-answer is quite unfair and, frankly, borderline dishonest.

@SolomonSlow : your analogy does not explain why you believe that this (and knzhou's) answer is incorrect. He does not deny the fact that there is a phase transition. In fact, you would even have coexistence of the 2 phases along the phase coexistence line. But this has nothing to do with the fact that one cannot provide a general rule to distinguish between gaseous and liquid phases. All such characterizations involve vague dichotomies such as small/large, high/low, strong/weak, etc. Notice that all the latter are merely quantitative, not qualitative.

@YvanVelenik I did not downvote knzhou's answer, because it is a valid point that the liquid/gas transition can be circumvented around the critical point. That just doesn't answer the question about the very real phase transition that we do encounter in so many situations. — The reason I downvote this answer is because introduces a whole lot of additional terms without actually bringing anything relevant new to the discussion.

@leftaroundabout But you still called it a non-answer, which it is not. The fact that you can locally (close to the coexistence line) recognize (and thus differentiate) the two phases is true. But whether, given a "picture" of a fluid, you can provide a general answer to the question "is this a liquid or a gas?" is a totally different question (whose answer is no, you can't, as knzhou explains in his answer).

@YvanVelenik so, how about you post an answer elaborating properly how to differentiate the two phases (close to the coexistence line, or whereever).

@leftaroundabout I might have, if I thought my answer would bring something not mentioned in the answers already given. Actually, it is not even clear what you expect: at the transition, one has two phases with different densities; it is then customary to call the dense one "liquid" and the dilute one "gas". By extension, as long as you keep close to the coexistence line, you call "gas" and "liquid" the two phases located on each side of the coexistence line. But this does not work anymore once you get too far away (in particular, once you start going around the critical point).

(Nikita's answer seem to be quite close to what I say, although the emphasis on symmetry in that answer seem to me to be misleading. The gist of the answer if fine, however, and just another variation around knzhou's one.)

@YvanVelenik, I did not say that this (or anybody's) answer is incorrect. I only disagree with the language in one paragraph. There may be no clear distinction between a liquid and a super-critical fluid, and there may be no clear distinction between a super-critical fluid and a gas, but IMO that does not make the phase transition between liquid and gas in some restricted realms of temperature and pressure "artificial." It's a real phenomenon, that can be observed in experiments that can be independently replicated by anyone.

@SolomonSlow But nobody said that the phase transition is artificial. Of course, it's a real phenomenon, but this has nothing to do with the question.

What he said is "the distinction between Liquid and Gas is an artificial one", not that the phase transition is artificial. The phase transition is between two phases with different densities, and it does not care what you call these two phases. As I said in a previous comment, you can define the low density phase as gaseous and the high density phase as liquid. This makes sense. It still makes sense in part of the phase diagram. But it does not make sense in general. The question is about a general criterion and the only correct answer is that such a criterion does not exist.

It may look like a rant to you, but it makes an important point regarding the culture here. We (at least I) come here to do physics. This is important. So let it be. Also, as a general rule, CENSORSHIP is not healthy for democracy. Just saying.

Also @ doesn't work in the answers.

@insomniac This very much is not a democracy. It's a privately owned website run for profit (albeit based on the contributions of volunteers). I don't see how making points about the culture on this website is relevant to a question of physics. If you come here to do physics... your answers should focus on the physics and any rants about culture should be removed so that it is clear that it is actually the focus.

@JMac : thank you. I am sick of pretences of democracy in this country. But if this privately owned website is to have any value, then this cultural point needs to be understood. This is in the best interest of whichever private entity owns this website. There is a strong strain of anti-intellectualism running around here that needs to be addressed. Just answering questions about Physics won't cure that.

@insomniac We have a whole meta website where we can discuss issues with the site moderation, culture, etc. The main physics site is for physics questions and answers, not for addressing the issues you have with the SE system or a site in particular at the bottom of your answers.

As suggested, I'll try to make a meta post out of this. But let me re-iterate. Physics and the culture of the room where we do the physics are not so easily separable,

But please. Do not make major edits to my posts without checking first. Unlike many answerers on this site, I actually am spending a lot of time writing them up,

thanks.

@insomniac Well I meant that you should use comment for such purpose. Doing such things in your answer only reduces it's quality.

@insomniac That's not really how this works either. SE allows you to edit other peoples content because the site is a community effort, and when something doesn't belong in the answer, it's actually appropriate for other community members to fix that.

Now see a moderator has edited your post. If you do a rollback then your post might get locked.