High School Why are the relative fluctuations of intensive properties so small?

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The discussion addresses the small relative fluctuations of intensive properties in thermodynamics, explaining that these properties are derived from extensive properties, which exhibit tiny fluctuations. The central limit theorem applies, suggesting that averaging across a large system leads to stable intensive property values. Additionally, for an intensive property to be reliable, it must represent the limit as the population approaches infinity, resulting in reduced variation due to the combination of two peaked distributions. This understanding clarifies why intensive properties maintain small fluctuations despite their dependence on extensive properties. Overall, the relationship between extensive and intensive properties is key to understanding their stability in thermodynamic systems.
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I get that the relative fluctuations of extensive properties (in thermodynamics) are tiny because you can divide the whole system in many subsystems and apply the central limit theorem, but I just dont get it with intensive properties. Could someone explain?
 
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Intensive properties are are often calculated by dividing one extensive property by another. So if the extensive properties have small fluctuations, so will the associated intensive ones.
You can think of an intensive property of a large system as an average across the whole system of intensive properties of component parts. So the same central limit tendencies will apply.
 
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andrewkirk said:
So if the extensive properties have small fluctuations, so will the associated intensive ones.
In addition to that, in order to be relied upon, the quoted value of an intensive property needs to be the limit as the population goes to infinity. That implies a smaller variation because it would be the product of two peaked distributions of huge populations.
 
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