# What is supercooled liquid helium

## Liquid helium (4.2 K) sealed and then raised to a temperature below LOX (~ 70 K) - what is the new pressure?

### asdfex

We don't have to look at the phase diagram here, as it doesn't matter which way we get to a particular endpoint. We can assume that we heat the helium at constant pressure and then reduce its volume again.

The density of the liquid helium boiling at 1 atm pressure is 0.125 g / cm3. The density of gaseous helium at 273 K is 0.18 mg / cm3. Therefore it has 700 times the volume or, if the volume is limited, a pressure of 700 bar. At a temperature of LOX, ie 70 K, we can treat helium as a perfect gas which, as a first approximation, behaves according to the ideal gas law. That is, pV./T.=const. So pressure will be a factor T.Lox / 273K = 0.26 lower. A volume of liquid helium that is sealed and heated to 70 K has a pressure of 180 bar.

This only applies if we can assume that helium still behaves like an ideal gas even at a pressure of 18 MPa. This deviation can be found in the compressibility factor and was measured (see e.g. SW Van Sciver, Helium Cryogenics, Appendix 1). This factor is around 1.2 to 1.3 under our conditions, so the actual pressure is around 230 bar.

### uhoh

Hmm ... The whole reason I asked the question here is that I was convinced that with such a high density of numbers and when the condition was more accurate than supercritical fluid as a ideal gas is described That the assumptions behind the ideal gas law would be incorrect any longer Can you provide some supportive information to suggest that it is known to be valid here? Many Thanks!

### asdfex

You are right, we are close to where the deviation from an ideal gas becomes important. I will add a paragraph

### uhoh

Many Thanks! OK, so the pressure seems to be within reach of a realistic, well-designed and manufactured tank. I got this question in physics, but not even a nibble so far.