I still cannot fully comprehend the essence of a critical point on phase diagrams.
It is usually said in textbooks that the difference between liquid and gaseous state of a substance is quantitative rather than qualitative. While it is easy to understand for a liquid-solid transition (symmetry breaking is a qualitative change), it is unclear to me what meaning does it have for a liquid and it's gas: there is always a quantitative difference between a gas at 300 $K$ and at 400 $K$.
Is it correct to say just "this substance is in gaseous state"? Shouldn't we also specify the path on the phase diagram by which the substance got in it's current state? Did it cross the boiling curve or went over the critical point and never boiled?
Why does a critical point even exist? Blindly, I would assume that either there is no boiling curve at all - since the difference is quantitative, the density of a substance smoothly decreases with temperatures and increases with pressure; or that the boiling curve goes on to "infinity" (to as high pressures and temperatures as would remain molecules intact). Why does it stop?
