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As far as I know, for all substances other than helium, if you extrapolate the solid-gas line on the phase diagram, it passes through the origin. That is, no matter how low the temperature is, you can still vaporize the substance by lowering the pressure, and no matter how low the pressure is, you can still freeze the substance by lowering the temperature.

This makes sense to me on thermodynamic grounds. If we keep lowering the pressure at a given temperature, the entropy of vaporization increases without bound (although only logarithmically) and at some point the gas phase is favoured, whereas if we keep lowering the temperature at a given pressure, then the entropy term in free energy becomes negligible and the solid phase is favoured by enthalpy.

The phase diagrams I've found online for helium-4, however, don't follow this rule. They seem to show that helium-4 is exclusively a liquid in a neighbourhood of the origin. Example here: http://ltl.tkk.fi/research/theory/helium.html

(Edit: The linked web page seems to be unavailable. A cached version of the referenced image is available here.)

I wonder whether this is true, and if so, how it can be possible. How can it be that no matter how low the pressure is, helium-4 will not boil? I understand that superfluidity is a quantum phenomenon but I can't see how my previous reasoning could not apply.

Edit since some people think this is a duplicate: Again, my question is whether helium-4 will not boil at zero pressure, and if so, how that can be; it concerns the liquid-gas transition and not the solid-liquid one.

Brian
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  • possible duplicate of Why can't helium be solidified at 'ordinary' pressures? –  May 23 '15 at 04:10
  • @santiago I don't think this is a duplicate. My question asks why helium-4 will not boil at zero pressure, whereas every other liquid apparently will. Not why it will not freeze. – Brian May 23 '15 at 04:36
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    Interesting question and preamble. I'd never considered the content in your second paragraph. – Nicolau Saker Neto May 23 '15 at 11:01
  • https://en.wikipedia.org/wiki/Lambda_point – Mithoron May 23 '15 at 12:07
  • It will boil all right. – Ivan Neretin Jul 02 '17 at 06:49
  • You wrote: "no matter how low the temperature is, you can still vaporize the substance by lowering the pressure, and no matter how low the pressure is, you can still freeze the substance by lowering the temperature." These are contradictory. The former says that, even at 0K, you can vaporize it by lowering p (=> phase at 0K & 0 bar is gas), while the latter says that, even at 0 bar, you can freeze it by lowering T (=> phase at 0K & 0 bar is solid). – theorist Apr 25 '22 at 23:39
  • @theorist It's only a contradiction if you assume that zero temperature and zero pressure are achievable, which of course they are not. – Brian Apr 25 '22 at 23:43
  • Except that you're asking specifically about what would happen at 0K and 0 bar. Even though those conditions aren't physically achievable, we can make physical statements about them, and the statements you're making are contradictory: In the first case you're saying that, in the limit of 0 bars, everything is a gas, even in the limit of 0K. And in the second case you're saying that, in the limit of 0K, everything is a solid, even in the limit of 0 bars. – theorist Apr 25 '22 at 23:52
  • @theorist No, what I'm saying is this: for every T > 0, there exists a P > 0 that is sufficiently low that you can vaporize the substance; and for every P > 0, there exists a T > 0 that is sufficiently low that you can freeze the substance. But helium-4 seems to violate this rule. – Brian Apr 25 '22 at 23:53
  • Your presentation is confusing, because in your comment you say you're referring to finite temperatures and pressures, but in your title you are referring to zero temperature and pressure. And when your title refers to zero T and p, the most reasonable interpretation of, e.g., "no matter how low the temperature is" would be "in the limit of 0K". – theorist Apr 25 '22 at 23:58
  • See He vapor pressure calculator for T=0.65 K .. 5.1 K. – Poutnik Apr 26 '22 at 12:53
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    To make a gas, He atoms must have translational kinetic energy, what they would not have at T 0K. Additionally, you cannot make any gas at p=0, as then p<>0. – Poutnik Apr 26 '22 at 12:59

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It could be that the liquid-vapor line does not exactly hit zero pressure at any temperature above absolute zero, the pressure just becomes too small to distinguish on the graph. You might see the same thing, for instance, with water if you tried to plot the solid/vapor equilibrium line all the way down from the triple point to 100 Kelvins using a reasonable plotting scale. The zero pressure line, if we could achieve it exactly, would then be in vapor phase at all positive temperatures.

Oscar Lanzi
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