Extensive variable

An extensive variable is a variable whose value is proportional to the quantity of substance under study, for instance: total mass, volume, number of particles, energy content, etc.

The opposite is an intensive variable.

Suppose there is one piece of substance whose mass is n and another piece whose mass is m. Let V be an extensive variable. Let the first piece have a value V(n) of the extensive variable. Let the second piece have a value V(m) of the extensive variable. Then, if the two pieces are put together to form a piece with mass n + m, then their corresponding variable is

$V(n+m)=V(n)+V(m)$.

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