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We know that $T_c$ is the temperature above which no amount of pressure could force a gas to liquefy.

But why is this? Somehow I don't buy the point that the gas molecules exert too much pressure back to get close and turn into a liquid. If we had tens of thousands of atmosphere pressure (such as on the inside of hot planets), we should be able to liquefy any gas at any temperature.

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    $\begingroup$ This is analogous to other abstractions in physics. For example, at high enough energies, the electro-magnetic force becomes indistinguishable from the weak force. It's just our abstractions failing us, not reality - when you go above "critical temperature / pressure", neither "liquid" nor "gas" adequately describes the "stuff" you're dealing with, and you have a supercritical fluid instead - just like EM+W "becomes" a single combined electroweak force, which behaves in its own way. But again, it's just our models - the simplifications are what breaks down, not reality. $\endgroup$
    – Luaan
    Mar 31, 2016 at 13:13
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    $\begingroup$ Possible duplicates: physics.stackexchange.com/q/19815/2451 and links therein. $\endgroup$
    – Qmechanic ♦
    Jul 19, 2016 at 16:03

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Your description of critical temperature isn't quite right.

If you increase the temperature of a liquid beyond the critical point, the atoms are moving so quickly that persistent structure fails to form and so you have something that behaves a lot like a very dense gas.

Similarly, if you increase the pressure of a gas beyond the critical point, it becomes very dense so that it's like a liquid but without persistent structure.

In other words, it's not so much that the liquid phase does not form, but rather the liquid and gas phases become indistinguishable (rather intuitively) and you end up with what's called a supercritical fluid.

Here's the phase diagram of CO$_2$ for clarity:

enter image description here

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    $\begingroup$ In other words, the liquid and gas phase become indistinguishable (rather intuitively) and you end up with what's called a supercritical fluid. Like deep in Jupiter's atmosphere? $\endgroup$
    – cst1992
    Mar 31, 2016 at 10:47
  • $\begingroup$ @cst1992 Yes, and also Venus. $\endgroup$
    – lemon
    Mar 31, 2016 at 10:50
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    $\begingroup$ @cst1992 or at your neighborhood dry cleaners. $\endgroup$
    – Dan Is Fiddling By Firelight
    Mar 31, 2016 at 20:41
  • $\begingroup$ What do you mean by a persistent structure? $\endgroup$
    – oshhh
    Sep 3, 2016 at 4:18
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    $\begingroup$ @OsheenSachdev liquid molecules stick together to form slightly rigid structures - not dissimilar to a crystal. The difference is that the molecules that form these structures will frequently break away (typically on the pico- to nano-second timescale) and move to some other position. You can partially observe this structure experimentally by measuring the radial distribution function, or study it computationally using molecular simulation. $\endgroup$
    – lemon
    Sep 3, 2016 at 8:12

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