How much helium will there eventualy be in the insulating vacuum space of a helium dewar

Question

If we were to start with a good vacuum in a dewar that was used to hold helium and the helium diffused in slowly and out to the atmosphere from the outer container wall.

1. What would the equilibrium 'pressure' of helium be in the vacuum space?

2. How long would it take to reach this equilibrium?

3. Later if the dewar was stored empty would the amount of helium decrease further and how long might that process take?

Just curious if the vacuum gets soft when used with helium and then gets better if used later for other more massive gas molecules and would this cause increased thermal losses and are special materials used to mitigate this in helium service.

Answer 1

The helium will diffuse through the barrier until the partial pressure of helium is the same on both sides. So the pressure on the inside will $P(t) = P_\text{eq} + (P_0-P_\text{eq})e^{ -t/\tau}$, where the initial pressure $P_0$ evolves towards the equilibrium pressure $P_\text{eq}$ with some time constant $\tau$ which depends on the area and permeability of the barrier.

For a dewar exposed to air, this gives you eventually about five millibar. The time constant, judging by the passive dewars I've used, seems to be decades.

Important practical safety note: one of the differences between a liquid nitrogen dewar and a much more expensive liquid helium dewar is the permeability of the dewar's vacuum space to helium. A nitrogen dewar that is filled with liquid helium, loosely capped with a styrofoam plug, and carried down the hall to another experiment will usually be found to be empty. This is a conspiracy among several factors: the much larger temperature difference between the warm part of the dewar (at 300K) and the nitrogen (at 77K) compared to to helium (at 4K); the much lower enthalpy of vaporization, by a factor of twenty, for helium than for nitrogen; and some of the unusual properties of liquid helium.

Relevant to your question, exposure to liquid helium, enormously more dense than gaseous helium, impregnates ("wets") the material of the dewar with helium very rapidly. The helium in the solid is equally likely to leave the solid on the air/liquid side of the dewar or on the vacuum side of the dewar. Helium which enters the dewar vacuum will leave the dewar with same time constant as above: decades. A nitrogen dewar which has been exposed to liquid helium, even briefly, must be considered to have a spoiled vacuum and should be destroyed for safety reasons.

I think (it's been a while) that most of the helium dewars I have used have had gauges for monitoring the dewar vacuum, and a relatively easy way to pump the dewar out again (perhaps designed to be serviced by the helium vendor, rather than the user). Nitrogen dewars, like coffee thermoses, tend to be entirely passive devices.