You have a balloon that contains 1 kg of helium that occupies a volume of 4 m sometime later, the balloon still holds 1 kg of helium, but it now occupies a volume of 2m'. your friend suggests that the helium can be considered an isolated system in this case. can they be correct?

Yes! They can be correct

Explanation:

An isolated system is a system where its total energy and mass stay constant.

In this case, even though the volume changed, the mass remains constant (m = 1 kg), so there is no mass exchange, and we must think that the globe is completely closed.

Now, we don't know exactly what happens with energy, but I can give you an example where the total energy of the globe remains constant.

Imagine that the balloon of volume is at a certain height , under some pressure, . If you lower the balloon to a height , the pressure increases, and from the Boyle's law,

,

, where ,

, just like the case you state, and there was no exchange of mass or energy related to the inner gas of the balloon, so yes, They can be correct.