Intensive and Extensive Properties - Counterexamples

Counterexamples

There are measured physical properties which are neither intensive nor extensive. For example the electrical resistance of two resistors is the sum of their two resistances only if the resistors are connected in series, but not if they are connected in parallel (if they are placed in parallel, it is instead the electrical conductance – the inverse of the resistance – of the two resistors that is the sum of their two conductances). The electrical resistance of independent noninteracting resistors (subsystems) is therefore not additive in general, and electrical resistance is not an extensive property. Nor is it intensive because the resistance of the two resistors is not equal in general, even if they consist of the same material at the same temperature and pressure.

Another counterexample is invariant mass in special relativity, which is not additive for subsystems in motion relative to each other. Invariant mass is therefore not an extensive quantity, nor it is an intensive quantity.

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