1.14.4: Extensive and Intensive Variables

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Michael J Blandamer & Joao Carlos R Reis
University of Leicester & Faculdade de Ciencias

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The terms, variables and properties are synonymous. Nevertheless a given thermodynamic property of a system can be classified as either intensive or extensive.

Intensive Properties. The magnitude of an intensive variable does NOT depend on the amount of chemical substance in a given closed system; e.g. density.

Extensive Properties. The magnitude of an extensive variable depends on the amount of chemical substances in a closed system; e.g. volume. Let us ask – is temperature an intensive or extensive variable? Consider two conical flasks. Flask A contains \(10 \mathrm{~cm}^{3}\) of water(\(\ell\)) at \(298 \mathrm{~K}\). Flask B contains \(5 \mathrm{~cm}^{3}\) of water(\(\ell\)) at \(298 \mathrm{~K}\). The contents of Flask are poured into Flask B.

What is the volume of liquid in flask B? The answer is clearly \(15 \mathrm{~cm}^{3}\).
What is the temperature of the liquid in flask B? Based on the answer to the previous question, we might answer \(596 \mathrm{~K}\), being the sum \(298 + 298\). This is clearly wrong. We have not distinguished between extensive variable variable and the intensive variable temperature. Temperature is an intensive variable as, for example, is the density of liquids.
A quick test to decide whether a given variable is either extensive or intensive is to ask what happens to the number value if the amount of chemical substance in a system increases by a factor of two. If the variable (e.g. volume) also increases by a factor of two, the variable is extensive. If the variable ( e.g. temperature, equilibrium constant…) remains unchanged , the variable is intensive. Otherwise the variable is neither extensive nor intensive (e.g. the inverse of volume).

Footnote

[1] O. Redlich ( J. Chem.Educ.,1970,42,154) presents a provocative discussion of the distinction between intensive and extensive variables.