Is helium liquid at 0 K?

Question

I just saw in the dynamic periodic table that He is liquid at $-273.15\ ^\circ \rm C$. Is that true?

How is that even possible? Can someone explain?

Answer 1

The thermodynamic phase of a material is never a function of temperature only. The correct statement is that helium remains in a liquid state at whatever small temperature achievable in a laboratory at normal pressure. It is well known that $^4$He freezes into a crystalline solid at about 25 bar.

Such peculiar behavior (helium is the only element remaining liquid at normal pressure close to $0$K) is partly due to its weak interatomic attraction (it is a closed shell noble gas) and partly to its low mass, which makes quantum effects dominant. A signal of the latter is the well-known transition to a superfluid phase at about $2$ K.

A theoretical explanation of the avoided freezing at normal pressure could be done at different levels of sophistication. No classical argument can be used, since a classical system would stop moving at zero temperature. A hand-waving argument is related to the zero-point motion of the system, which is large for light particles. A theoretically more robust approach is based on the density functional theory of freezing (DFT).

The qualitative explanation of the freezing process based on DFT is that the difference of free energy between the solid and the liquid is controlled by the competition between the contribution of the change of density (favoring the liquid), and the contribution of the correlations of the liquid phase in reciprocal space, in particular at wavelengths close to the first reciprocal vector of the crystalline structure (favoring the solid). It turns out that the latter contribution is particularly weak in liquid $^4$He.

Answer 2

Temperature is interesting in a logarithmic way. There is as much potential for interesting physics between $1\rm\,K$ and $10^{-6}\rm\,K$ as there is between $1\rm\,K$ and $10^{+6}\rm\,K$. The difference is that we live in the upper interval, so we have lots of experience and a finely-honed intuition which we call "classical thermodynamics." To explore the sub-kelvin temperature regime, we have to build complicated cryostats and understand quantum mechanics.

Note that $\rm -273\,^\circ C = 0.15\,K$ is a positively balmy temperature if you're interested in microkelvin phenomena.

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Here's a phase diagram for helium-3 that shows both the pressure and the temperature on logarithmic scales, going down to $\rm10\,\mu K$. (Dear Britannica-from-twenty-years-ago: using a different colored font to represent a unit change is bad design.) For helium-4 the diagram is similar, but the temperatures and pressures of the phase transitions are different: helium-4 and helium-3 have very different masses. The number of distinct phases for helium-4 versus helium-3 is also different, because helium-3 has a different nuclear spin than helium-4 and therefore different statistical properties. There are a number of features on this diagram that we hide from students who are new to thermodynamics, like the critical point on the curve between the normal liquid and the vapor phase.

You can see from this diagram that helium (or at least helium-3) does have a low-temperature solid phase, but not at one atmosphere of pressure. Furthermore, the minimum pressure to support the solid phase appears to be temperature-independent, even at the little triangle of superfluid-A phase. I bet there's an interesting explanation about why the solidification pressure doesn't depend on temperature, but I don't know it.

Helium isn't alone in having a low-density, low-temperature phase which is not solid but is fundamentally quantum-mechanical. It's just that helium's mass is so low that these quantum-mechanical effects happen in a relatively accessible part of the phase space. Superfluidity in helium-4 is closely related to the phenomenon of Bose-Einstein condensation, which happens in rubidium vapor at around $\rm 10^{-7}\,K$. Likewise, superfluid helium-3 is a kind of Fermi-Dirac condensate, which has been observed in nanokelvin (!) potassium vapor. Both rubidium and potassium are solids at "normal" pressures, all the way up beyond room temperature, but their low-pressure, low-temperature quantum-mechanical behaviors have a lot in common with superfluid helium.

Answer 3

From the Wikipedia article on helium:

Unlike any other element, helium will remain liquid down to absolute zero at normal pressures. This is a direct effect of quantum mechanics: specifically, the zero point energy of the system is too high to allow freezing. Solid helium requires a temperature of 1–1.5 K (about −272 °C or −457 °F) at about 25 bar (2.5 MPa) of pressure.

So yes, helium is liquid down to absolute zero (unless the pressure is high enough to cause it to solidify), and the reason is because of quantum effects - in particular, the "zero point energy", or the lowest possible energy a system can have while still obeying the Heisenberg uncertainty principle.

Answer 4

Yes, it is true.

If you cool off a gas, you can make it condense into a liquid. For some gases, this is easy because the temperature at which they turn into liquids is fairly high. For example, for water vapor (steam) this happens at +100 C. But for helium gas, it does not turn into a liquid until it has been chilled down to -269 degrees C. Wikipedia has a pretty good article about this.

Answer 5

Other answers have highlighted the remarkable properties of super-cold helium. The apparent conflict between liquid (implying motion) and absolute zero (implying no motion) might still be troubling, though, so I'll add some basic points that apply to all substances, not just to helium.

Other answers have already pointed out that quantum physics is essential at such low temperatures. Instead of saying that all motion stops, we can say it in a more quantumy way like this: absolute zero ($T=0$ Kelvin) has been attained if the system is in the state of lowest total energy. Lowest total energy implies zero momentum... but if the momentum is zero, then how can the substance flow? The apparent conflict dissolves when we remember these basic points:

• Even if all of the atoms in a sample of helium could have zero momentum in one reference frame, they wouldn't have zero momentum in other reference frames. Clearly, no matter how cold the sample might be, its coldness cannot prevent it from being in relative motion compared to something else in the universe (like, say, the laboratory), because motion is relative. The conceptual significance of this is highlighted in another answer by knzhou.

• What if we try to ignore that issue by working in the sample's "rest frame"? The quotation marks are a warning! In quantum physics, the (badly named) uncertainty principle implies that zero momentum and localized in a finite region of space are mutually contradictory conditions. Absolute zero is not compatible with being contained in a laboratory of finite size. The same is true for any specific nonzero momentum, so the reference-frame issue highlighted in the previous paragraph doesn't make this go away — not for liquids or solids or anything-else-ids. Absolute zero is absolutely unattainable.