13. How To Measure Disorder   Previous PageNext Page

The man who gave entropy a molecular meaning was Ludwig Boltzmann, a mathematician and physicist who worked during the last half of the nineteenth century. Boltzmann first suggested that entropy was a measure of disorder and gave this suggestion a concrete form. He proposed that entropy, S, was related to the number of different microscopic ways of obtaining a macroscopically definable and observable situation. If the number of ways of constructing a situation is W, then the entropy is proportional to the logarithm of W:

S = k ln W

The proportionality constant, k, is the gas constant per molecule, or

k = R/Nin

which R is the gas constant and N is Avogadro's number. The constant k was chosen by Boltzmann such that his statistical entropy would have the same units, and be on the same scale, as thermodynamic entropy. It is called, appropriately enough, the Boltzmann constant.


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