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

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.

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.