Entropy and disorder

Entropy is sometimes referred to as a measure of the amount of "disorder" in a system. Lots of disorder = high entropy, while order = low entropy. It's not too hard to see why this association came about. If water molecules are confined to a drop of water, that may seem more orderly than if they are scattered all over the room in the form of water vapor. And if the water molecules in that drop are arranged in a hexagonal array (ice!), that's even more orderly. And indeed, the entropy in ice is lower than in the same amount of water; and the entropy in water is lower than in the same amount of water vapor.

If all the air in your room is gathered into the same side of the room, that can seem more "orderly" than if they're scattered all over the place. If the energy in your kitchen is concentrated in your bowl of soup, that may seem more orderly than if the energy is scattered evenly throughout the room so that your soup is at room temperature. And again, the more orderly states are the states with the lower entropy.

Similarly, a room with socks strewn all over the floor has more entropy than a room in which socks are paired up, neatly folded, and placed in one side of your sock and underwear drawer.*

So there's some justification to associating entropy with disorder. (This is why I never clean my apartment. I could decrease the entropy in my apartment, but according to the second law of thermodynamics I'd only be increasing it somewhere else.) (That's a little physics humor there.) (Physicists are funny guys, eh?)

But entropy is more than this, as we've seen. We know that on a cold day, water freezes. It's clear that the water molecules become more ordered. Its entropy decreases. This means there must be an increase in entropy somewhere else. This increase is in the atmosphere (where the heat from the water goes). But the air doesn't really become more "disordered".

Thinking of entropy as "disorder" can be misleading, mainly because while order and disorder are important to entropy, they don't take into account heat, which we've seen is also very important. Occasionally one hears creationists argue that evolution violates the second law of thermodynamics. This is a misunderstanding that arises from thinking of entropy as a measure of disorder. The claim is that the incredible precision with which the human body is arranged could not have evolved from less complex organisms without violating the second law of thermodynamics. But the same argument could be used just as effectively to disprove ice! The problem with the argument is that it doesn't recognize the increase in entropy in the chemical processes that take place in assembling a human being, because there's no visible increase in disorder. If we only think of entropy as disorder, we miss much of what is going on, and we make the wrong conclusion.

But you wouldn't do this, because now you know all about entropy! (Well, not all about entropy. There are still a few details, such as all the mathematics behind this.) I hope this gives you a new outlook on life. Or at least gives you some useful cocktail party banter with which to impress members of the opposite sex. Well, okay, I hope you learned something.



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* Well, applying these principles to collections of large objects, such as socks, is usually not a good idea. One unspoken assumption that's made in thermodynamics is that all the microstates we consider can actually be reached from each other. For example, in the box of gas all the molecules are in motion, so the system can easily move from one microstate to another. On the other hand, if your socks are folded in your drawer, you know that (barring some kind of intervention) they're going to stay folded in your drawer. They simply lack the kinetic energy (motion) to make a transition to other microstates. I threw the socks in this discussion more for amusement than for education.

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