Every time I've heard someone describe entropy, they always use the analogy of a clean room, and say that the natural tendency is for the room to become messy. Now, I'm just starting to learn about entropy, so I don't see any DIRECT connection between the entropy of mixing gases, say, and the "entropy" of a pile of clothes on the floor. Is there some over-arching connection between entropy and all possible systems of things in the universe (e.g. the clothes on the floor), or is it merely an analogy?
Thank you
2006-12-30
17:51:57
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4 answers
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asked by
Anonymous
in
Science & Mathematics
➔ Physics
For a room with things in it that can be moved around, entropy is a measure of how many different ways the things could be arranged in the room. For example, if the room is empty except for one sock, the entropy isn't very large, as compared to a room full of things. Whether or not those things are arranged nicely or messily is irrelevant.
It's critical to note that the different accessible states of the system need to be in circulation, which is why using a static room, messy or not, is a misleading way to describe thermodynamic entropy. Look for information theory and Shannon Entropy for the static room analogy.
And, like you, I hate cute and enormously misleading analogies of rooms getting messy as an explanation of what entorpy is. That seems so popular.
And, finally, entropy is NOT energy! It is a DIMENSIONLESS quantity.
Addendum: To salvage the idea of connecting entropy with rooms getting messy, what we can do is to denote group of sets of the room in varying arrangements of the things in it. The group of "cleanest room" would have things in the right places with little variability, so that configuration space is relatively small. The next group "not so clean room" would have things in some wrong places, so that the configuration space is a bit larger, etc.., until we have the set of maximum chaos, which in fact will have the largest configuration space because many more ways of arranging things in the room is possible and still belong in the set of maximum chaos. Entropy, then, is a measure of the size of those configuration spaces, and if the state of the room is a point in the entire configuration space, which is the sum of the set configuration spaces, then assuming a random walk, the state of the room will probabilitistically tend towards the largest configuration space, or messiest condition. But this is using a freelance interpretation of entropy, and is not the strict thermodynamic or Boltzman interpretation of entropy, created for the benefit of curious laymen.
2006-12-30 17:56:28
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answer #1
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answered by Scythian1950 7
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One of the ways of grasping the concept of entropy, I find, is to highlight the distinction between macroscopic and microscopic measurements, which is crucial in thermodynamics and statistical mechanics. Let's have an example.
You know that the temperature of a gas somehow measures the average speed of the molecules in the gas. The macroscopic state of the gas is its temperature; the microscopic state is the specific speed and position of each particle at one given moment. (Another example would be the pressure of the gas (macroscopic) and the momentum of the particles (microscopic).)
Now notice what's happening when you go from the microscopic point of view to the macroscopic one. One specific microscopic state of your gas entirely determines the temperature (macroscopic). BUT the converse is not true: in general, there are lots and lots of microscopic states of your gas that would give you the same overall temperature.
If you were to cool down your gas enormously (it might even become liquid or solid), you would gradually be limiting the number of microscopic states that would result in such a temperature. At the limit, by the time you reach (near) absolute zero, you know that all the molecules are virtually stopped, and the number of possible microscopic states is reduced as much as it could be.
This is where entropy comes in. You could say that the entropy of a given macroscopic state is a measure of HOW MANY different microscopic states would yield that macroscopic state. Lots of microscopic states? High entropy. Few microscopic states? Low entropy.
Let's come back to the room analogy. We are assuming that there is ONLY ONE microscopic state which your mother's eyes will consider as "in order" (her macroscopic point of view), namely when each object is in its own appointed place; entropy is at its lowest. On the other hand, there are millions of ways of scattering your room's content, which all will result in the lapidary judgment: "messy room". Very high entropy!
Having one star and eight planets (with a scattering of other bits) is a very organized system: there are relatively few ways of rearranging the matter in the solar system to produce the same macroscopic result, therefore entropy is relatively low. At the other end of the cosmic spectrum, consider a system in the shape of a huge blob of gas: most random rearrangements of the molecules won't change the macroscopic state, therefore lots of microscopic states describe that macroscopic state, therefore very high entropy.
2006-12-30 18:55:04
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answer #2
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answered by Christine F 2
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Another way to look at this is to consider that keeping a room clean takes energy. If you don't put the energy into keeping the room clean, the room will tend to get disorganized and dirty with time.
The same could be said for keeping the dye from mixing. The dye would mix without energy causing it to stay in one place. If we apply this energy, it will always take more energy to hold the dye in place than the energy the dye has in wanting to spread out. Does this help?
2006-12-30 18:02:30
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answer #3
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answered by christopher_az 2
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What they are talking about is the way things tend to become chaotic from order.
Nature wants to mix things up to a point that all things are spread equally throughout all other things.
A drop of dyed water dropped into plain water will eventually be mixed throughout the entire vessel even without stirring.
Your room, no matter how clean it is, even if you stopped living in it, would become dirty over time.
2006-12-30 17:58:10
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answer #4
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answered by James F 4
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