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I'm trying to relate the concept of entropy to keeping my room clean as suggested by my high school teacher ~1993...

Comparing the two scenarios:

  1. Every day I come home and throw an empty can on the floor and every night before bed I pick it up and throw it in the trash.

  2. Every day I come home and throw an empty can on the floor and every six months I bag them all up at once.

So to me it's obviously more efficient to let entropy run its course and then undo it in a "batch" as opposed to constantly undoing it.

Is that right though? I'm thinking since entropy is related to energy, then is has to be conserved and the same amount of effort should be required to keep a room clean than to clean it after its become horribly messy.

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I was told to think of it as a measure of disorder or randomness. That sounds like an orderly mess you have there. – Magpie Nov 19 '12 at 6:47
up vote 1 down vote accepted

I agree with @PaulJGans on that order/disorder is not a good analogy. Moreover, the thermodynamic entropy of your room is the same when the room is ordered that when is not. In a first approximation the entropy of your room is $S = U/T$ with $U$ internal energy and $T$ temperature. Entropy will change as $dS = dU/T$ if you heat up your room from 15 ºC to 21 ºC. In a more general model you will be considering other changes in entropy due to flows of mass, chemical reactions, diffusion...

Yes, entropy is related to energy, but entropy is not a conserved quantity and its nonconservation is guided by the second law, which says that entropy production is non-negative.

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this answer works for me, although I'd be happy to see what others might have to say as well I'm going to mark it – Aaron Anodide Nov 19 '12 at 22:42
Thank you! You can find several resources explaining why entropy is not disorder and why its use in some textbooks has caused lots of confusion. E.g. check this online article by Prof Lambert. Check also references 5 to 13 here Most are online and for free. – juanrga Nov 20 '12 at 16:05

I think it dangerous to use room order/disorder as an example. For instance if you carefully place each empty can on a grid on the floor as opposed to just tossing the cans into a garbage bag, the gridded can system will have lower entropy but civilians might not think it more ordered.

Besides, all those comparisons are set up for systems in which there is no interaction energy, the so-called microcanonical systems. There you can make a kind of order argument of the sort we might consider order. But in systems where total energy is not fixed, those order arguments fall apart.

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Civilians is a nice alternative name for non-physicists! – Virgo Nov 19 '12 at 8:11

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