I’m looking for a demonstration that volume is not a conserved quantity.
Here’s what I have come up with.
Mark the height of water in an open-topped container. Define the system to
be the volume occupied by the liquid water, the container up to the mark.
Put the container in the freezer. Upon freezing, the water/ice expands
upwards past the mark. There has been a (non-zero) flow of water/ice volume
out of the system, upward past the mark. However, the system, the container
up to the mark, is still full of ice. The change in water/ice volume in the
system is zero. The flow does not equal the change so volume is not a
conserved quantity.
This can be run in reverse as well. Start with ice, and mark the height of
the ice. The container up to the mark is our system. Put the container
somewhere at room temperature. The ice melts, and the level of the
water/ice falls below the original mark. There is now empty space in the
system. The volume of water/ice in the system has changed. However, there
has been no flow of water/ice volume out of the system, so the flow is
zero. Once again, the flow does not equal the change so volume is not a
conserved quantity.
What do you think? Is this a legitimate demonstration of non-conservation?