If Avogadro's number is a fundamental constant in physics and chemistry, it's because it links the microscopic and macroscopic scales not only for weight quantities, but also for electrical and thermal quantities. Avogadro's number is also a bridge between quantum and classical statistical descriptions of matter.
In experiments where a certain quantity of matter is measured and deposited by a quantity of electricity, Avogadro's constant links the elementary charge e to a macroscopically measurable quantity of electricity via Faraday's constant :
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(1) - AVOGADRO (A.) -
Essai d'une manière de déterminer les masses relatives des molécules élémentaires des corps, et les proportions selon lesquelles elles entrent dans ces combinaisons.
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Journal de Physique, 73, p. 58-76 (1811).
(2) - KASTLER (A.) -
Le concept...
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