Intensive and Extensive Variables

Consider two bodies each with the same volume $V_1$ and the same pressure. Bring the bodies together, what is the result?

$$\input{equations/ext-int-examp}$$ (03-2)

Variables that are additive like $V$ are called extensive variables, they depend on the size or the extent of the system.

Variables that do no add, but combine like $P$ are called intensive variables, they are intrinsic to the system and can vary from point to point. Fields and potentials are intensive variables.

Another example: Temperature:²

Question: Is $T$ an extensive or intensive variable?

Can you design a small device that would measure the temperature at a point? (what does it resist changes in?)

This is a difficult question because we haven't defined temperature.

Leads to difficult argument found in thermodyanamics books (e.g., Denbigh §1.4) which can be extended to an even more difficult argument that defines the absolute zero of temperature.