In the natural sciences, an intensive quantity (also 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.

Combined intensive quantities

If a set of parameters, $\backslash \{a\_i\backslash \}$, are intensive quantities and another set, $\backslash \{A\_j\backslash \}$, are extensive quantities, then the function $F(\backslash \{a\_i\backslash \},\backslash \{A\_j\backslash \})$ is an intensive quantity if for all $\backslash alpha$,

$F(\backslash \{a\_i\backslash \},\backslash \{\backslash alpha\; A\_j\backslash \})=\backslash alpha\; F(\backslash \{a\_i\backslash \},\backslash \{A\_j\backslash \})\backslash ,$.

It follows, for example, that the ratio of two extensive quantities is an intensive quantity - density (intensive) is equal to mass (extensive) divided by volume (extensive).

Joining systems

Let there be a system or piece of substance a of amount m_a and another piece of substance b of amount m_b. Let V be an intensive variable. The value of variable V corresponding to the first substance is V_a, and the value of V corresponding to the second substance is V_b. If the two pieces a and b are put together, forming a piece of substance "a+b" of amount m_a+b = m_a+m_b, then the value of their intensive variable V is:

$V\_\{a+b\}\; =\; \backslash frac\{m\_a\; V\_a\; +\; m\_b\; V\_b\}\{m\_a\; +\; m\_b\}$ ,

which is a weighted mean. Further, if V_a = V_b then V_{a + b} = V_a = V_b, 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 constant.

In a thermodynamic system composed of two monatomic ideal gases, a and b, if the two gases are mixed, the final temperature T is

$T\; =\; \backslash frac\{N\_aT\_a+N\_bT\_b\}\{N\_a+N\_b\}$,

where $N\_i$ is the number of particles in gas i, and $T\_i$ is the corresponding temperature.

Examples of intensive quantities

• Density
• Pressure
• Specific heat
• Speed
• Temperature
• Voltage (Electric potential)

See also

• Extensive quantity
• Physical quantity

Physical quantity

intensive Größe | Intensieve grootheid | Zmienna intensywna | Intenzivna količina