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In physics and chemistry, an intensive quantity (also referred to as an intensive variable) is a physical quantity whose value does not depend on the amount of the substance for which it is measured. It is the counterpart of an extensive quantity.
Properties
Let there be one piece of substance of amount n and another piece of substance of amount m. Let V be an intensive variable. The value of variable V corresponding to the first substance is V(n), and the value of V corresponding to the second substance is V(m). If the two pieces are put together, forming a substance of amount n+m, then the value of their intensive variable should be
- <math> V(n+m) = \frac{n V(n) + m V(m)}{n + m}<math> ,
which is a weighted mean. Further, if <math>V(n)=V(m)<math> then <math> V(n+m) = V(n) = V(m)<math>, i.e. the intensive variable is independent of the amount. Note that this property holds only as long as other variables on which the intensive variable depends stay the same.
The ratio of two extensive quantities is an intensive quantity. For instance, density (intensive) is equal to mass (extensive) divided by volume (extensive). For a more subtle example, consider the following: Pressure is force divided by area. But neither force nor area are either extensive or intensive. However, force multiplied by length is work, which is extensive, and area multiplied by length is volume, which is extensive. Therefore, pressure actually is a ratio of two extensive variables—work/volume—and so it is intensive.
The reciprocal of an intensive quantity is itself intensive.
Examples
Examples of intensive physical quantities are
The following variables are neither extensive nor intensive: length, time, area, force, angular momentum.
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