From my experience, volume, surface and length are extensive properties. Indeed :
- the reunion of two cubes of 1 $m^3$ leads to a cube of 2 $m^3$
- the reunion of two tiles of 1 $m^2$ leads to a tile of 2 $m^2$
- the reunion of two spaghetti of 1 $m$ leads to a spaghetti of 2 $m$
But I also read that the ratio of two extensive properties should lead to an intensive property. This is indeed the case for molar volume (ratio of a volume over a mole number) or pressure (ratio of a force over a surface). But if I do the ratio of a volume over a surface I get a length that is not an intensive property.
So should I consider that length is an intesive quantity or that the ratio of two extensive properties does not necessarily leads to an intensive property?
I did some sketches and it seems fairly true that only volume is an extensive property and that their is not absolute result for length and surface. I observed that a pavement of volume $V = S \times L$, with $S$ its caracteristic surface and $L$ its caracteristic length, it is possible to create two subsystems in many different ways. For exemple
- either splitting the pavement into two pavements of caracteristic surface $S/2$ and caracteristic length $L$ ($S$ is extensive while $L$ is intensive)
- either splitting the pavement into two pavements of caracteristic surface $S$ and caracteristic length $L/2$ ($S$ is intensive while $L$ is extensive)
- either splitting the pavement into two pavements of caracteristic surface $S$ and caracteristic length $L$ ($S$ and $L$ are intensive)
So I guess it is a question of context whether these quantites should be considered extensive or intensive. Are there some classical exemples where surface or length are alternatively considered as extensive or intensive?