Self Assembly and Entropy ```Name: Azmath Status: student Grade: 9-12 Location: N/A ``` Question: How are small and large scale systems formed when the universe favours entropy? It seems that the probability of forming them are very low. --------- Replies: Your question is the result of a common misunderstanding of the Second Law of Thermodynamics. This misunderstanding has several origins. The first misunderstanding is that processes that result in a decrease in entropy cannot occur. This is an incorrect statement of the Second Law. Every time water freezes the entropy of the transition of water to ice decreases. The same can be said of many other processes. The Second Law states the following: "Some things happen -- other things do not." It is a succinct statement of many billions of empirical observations. It is an empirical observation that processes that can occur are accompanied by an increase in the total change in entropy. That means not only the entropy change of some parts of the total system (the Universe if you want to be grandiose about it) but in practice the "system" is usually some small sub-set of the Universe. There are many alternative, but equivalent, statements of this observation. One alternative statement is that Nature left to itself does not create gradients. A simple example is that a bar of metal at a constant temperature does not, left to itself, evolve into a condition where one end of the bar is hotter / colder than the other. Another is that a balloon, pricked by a pin, does not "unpop". It always "pops". Because the Second Law is a statistical rule, there is a remote, a very very remote possibility that it could "unpop", but the probability (which can actually be computed) is older than the age of the Universe, so betting on "unpoping" is not a very good bet. Saying that the "Universe favors entropy" is misleading because the niverse does not have a choice in the matter. A clearer, more correct statement of the Second Law is this: "Some things (events) happen; some things do not." Those events which happen are associated with an increase in the TOTAL entropy change calculated according to a set of very specific set of rules. That does not mean that there cannot be "local" decreases in entropy, sometimes very large decreases. Every event that has ever been observed to occur, always has associated with it a positive increase in the TOTAL entropy. Repeating -- this does not mean that there cannot be "local" decreases in entropy -- it means that the TOTAL entropy is positive. Historically, "the Universe" got involved in statements of the Second Law, which is unfortunate because in the translation from German to English the term "Universe" takes on a philosophical context that in not intended in the original language. There is nothing mysterious about the Second Law if you keep in mind the empirical statement that, "Some things happen. Some things do not." And also remember that the ultimate "happening" or "not happening" has nothing to do with the speed of it happening. It only refers to the ultimate "possibility" or ultimate "impossibility" of the event occurring. Vince Calder Entropy is not just a matter of how matter is distributed in space. The other factor to consider is the distribution of energy. Just as entropy is maximized by the dispersion of matter, it is also maximized by the dispersion of energy. In many processes, these two tendencies work in opposite directions. A classic example of this interplay is the formation of a star by the gravitational collapse of a cloud of gas. Clearly, such a process causes matter to become more localized rather than more dispersed. How can this be consistent with the fact that all processes that actually occur act to increase entropy? The answer is the distribution of energy. The dispersed gas cloud has fairly high potential energy, since all the molecules of gas, which attract each other gravitationally, are far apart. As they move together under the force of their mutual gravitational attraction, they speed up. So, as their potential energy decreases, their kinetic energy increases by the same amount. In fact, if that were all there was to the story, the gas cloud never could actually collapse. The molecules would be moving so fast when they are close together that they would never stay close: they would simply zoom back out just as separated as they were at the beginning. The key is that their kinetic energy is sapped by another process: radiation. As the molecules move faster, they become hotter (temperature basically IS molecular kinetic energy). Hot things emit more electromagnetic radiation than cold things, and some of this radiation escapes the collapsing cloud entirely. Thus, the cloud can continue to collapse, and the molecules come closer together, even while getting hotter. Matter becomes more localized, but energy is radiating out into space, beyond the dimensions of the original gas cloud. When you take energy into account, you see that the entropy of the universe is increasing. All other spontaneous processes that cause matter to become localized involve a compensating delocalization of energy, typically as the production of heat or elecrtromagnetic radiation. Richard Barrans Department of Physics and Astronomy University of Wyoming Click here to return to the Material Science Archives

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