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Well thought out and well written.
You might want to reexamine your definition of the 2nd Law, however. You got the concept right, but your definition for entropy is leading you down the wrong path. German scientist Rudolf Clausius invented the term in 1865 to describe the ratio of heat exchanged to the absolute temperature in an ideal or reversible heat cycle. Or put another way, entropy describes the amount of thermal energy put into a system that cannot be extracted as mechanical work. Ideally, entropy is a conserved value, a “constant.” In the real world, however, within a closed system entropy always increases.
Following 1865, entropy came to be associated with energy that is irreversibly lost and with disorder. But the word disorder has a very narrow definition, which has resulted in widespread misunderstanding of the 2nd Law. Here, disorder means the number of ways that you can rearrange a system so that it looks exactly the same. For example, when an ice sculpture melts, the water molecules go from a fixed arrangement to a relatively free arrangement. Because there are far more ways to rearrange water molecules in a puddle (so that it looks like a puddle) than there are ways to rearrange water molecules in an ice statue (so that it looks like the same ice statue), the entropy of the puddle is greater than the entropy of the ice statue. The disorder of the ice statue has increased through melting—thanks to Ludwig Boltzman for this 1896 explanation.
If you think of the 2nd Law in terms of disorder, without qualifying that term, you are misunderstanding the Law. It is far better to think of the 2nd Law in terms of irreversibly lost energy. Even better is to develop an intellectual understanding of the term entropy(think in terms of the ice statue example).
Thus the 2nd Law can be expressed either as:
In a closed system, entropy either remains constant or increases.
Or as
In a closed system in the real world, entropy always increases.
posted by
arGee
on October 26, 2003 at 9:36 AM
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