Lecture
Intensive and extensive quantities — two opposite kinds of physical quantities. A quantity is called intensive if its value does not depend on the size of the system — for example, temperature or density. Extensive quantities, on the other hand, such as energy and electric charge, usually possess the property of additivity (with respect to mass or volume), that is, the value of the quantity corresponding to the whole object equals the sum of the values of the quantities corresponding to its parts.
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Intensive quantities
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Extensive quantities
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Establishing a numerical ratio between two values of an intensive quantity is meaningless. Measurement of an intensive quantity can only be considered by using the objective relationship between changes in the intensive quantity, on the one hand, and changes in an extensive quantity, on the other hand .
For example, density is an intensive quantity, that is, if a system in a state of thermodynamic equilibrium is divided into several subsystems, the density of each of the subsystems will be the same as the density of the whole system.
According to Hegel, an intensive quantity is defined as a «degree», that is, a quantity that is not quantitative .
The property of extensiveness for certain, often vector, physical quantities is called the superposition (additivity) principle:
Often the term superposition principle implies the additivity of fields created by sources that are themselves additive, and is applied to theories whose fundamental equations are linear.
In metrology, the additivity of a quantity is understood as the applicability and meaningfulness of operations such as addition, division, and multiplication of values by a constant coefficient.
Some quantities, such as mass, velocity (relative motion), or time (successive intervals), allow addition in classical physics, but not in the theory of relativity.
In general, in the case of high or ultrahigh energies, additivity, as a rule, is sooner or later lost, since the equations cease to be linear (and only their low-energy approximations are linear); however, the superposition principle is nearly always useful in the limit of weak perturbations, and sometimes turns out to be valid for the whole or almost the whole practically accessible range of values. In this case the theory is greatly simplified and can be developed more easily and better.
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