12

Is this something that we observe that always happens or is there some fundamental reason for two extensive quantities to give an intensive when divided?

David Z
  • 77,804

1 Answers1

19

It is mainly a mathematical reason. Extensive quantities grow with system size. If two quantities scale in the same way with a variable (in this case system size), it cancels out in the division.

Mini-example: $A$ and $B$ are extensive physical quantities both dependent on $n$. Their ratio is called $C = A / B$. If you scale the system up, $A$ and $B$ grow by a factor of $n$. What happens to $C$?

$\frac{A \cdot n}{B \cdot n} = \frac{A}{B}$

$C$ stays the same, irrespective of $n$. Hence, $C$ is intensive. The most common physical example is mass and volume, which scale with system size and still exhibit the same ratio, the density.

EDIT including the comment of probably_someone: The argumentation is particularly true since by definition an extensive quantity grows linearly with system size. This justifies the proportionality that I presented in the mini-example.

lmr
  • 1,334