|MadSci Network: Physics|
Patrick, Okay bear with me for a little while, because first I'm going to give brief explanations of what heat and entropy are. I think that by the time I get done with those explanations you will probably be able to answer your question yourself. Heat is just another name for thermal energy; that is, energy that is associated with the motion of particles. There are many other forms of energy out there though, and even the definition I just gave is a bit misleading since most thermodynamicists you talk to will also group infrared radiation (which is technically electromagnetic energy) in with "heat" since it is a well-known way for heat to be transferred through space (even empty space). Why does it matter if infrared radiation is considered heat? In your question, you imagine a large cube that prevents the transmission of heat, and what I think you really wanted to say was that it prevents the transmission of *all* energy (and mass, naturally). If you limit the cube to just being able to block heat, there is still the possibility that electromagnetic energy would flow in or out and that would mess things up. The concept of entropy is a difficult one to grasp. You hear people talk about entropy as a measure of the "disorder" of a system or a relation of the number of possible states of a system, but neither of those descriptions is particularly helpful to most people. I typically think of entropy as it relates to "usable" energy in a system. Specifically, whenever entropy is created, some energy is "lost" and cannot be used to do work. The normal explanation given for this "lost" energy is that it is turned into heat, and that is true, but it's not really the whole story. Some of that heat could be collected and transformed into other kinds of energy (for example, it could heat air that is then run through a turbine to generate electrical power). But because of the entropy rise that occurred, you could never reclaim all of the energy that was initially present. The larger the entropy rise, the less energy you could reclaim. Is there a simple explanation for why this is true? Unfortunately, there isn't, but there are parallels that can help you understand the consequences of entropy generation. For example, say you have an aquarium that is divided in half, and you fill one half with water. Let's say we let it sit long enough for the temperature to be even and all motion to stop. We now have a system with a certain amount of potential energy, and if we removed the separator, some of that potential energy would be transformed to kinetic energy and cause the water to move. As soon as the water starts to move, friction begins turning the kinetic energy to heat, and eventually all the motion stops again after the water settles out at its new level. At this point, we have absolutely no way of restoring the original state (with all the water on one side of the aquarium) unless we add more energy. This example illustrates what nature is all about: it tries to even things out (or if you want to be technical, it tries to eliminate gradients). The only way to restore a gradient once it is gone is to add more energy. Eventually, if you have no energy added to the system, all of the gradients will disappear. All of the energy would still be accounted for, but it would be evenly spread out and there would be no way to group the energy together or use it to do work. So let's go back to your question. If you put the earth in a box that did not let mass or energy flow in or out, and that box didn't also contain the sun, we could not get light from the sun. Even if you make the box big enough to contain the sun (or perhaps the whole solar system), eventually the earth would not be able to support life. Eventually the entropy would increase so much that none of the energy in the box could be used to do any kind of work. Everything in the box would be inert and energy would be spread evenly throughout the box. There would probably be quite a bit of heat in the box, but the energy could take other forms as well (radiation comes to mind). The part that would be the real killer is that no chemical reactions would be taking place, and that's obviously a requirement for life as we know it. So I think the answer to your question is definitely "yes," although I should probably point out that it would take so long to generate this much entropy that it's more likely the sun would run out of fuel, turn into a red giant, and engulf the inner planets (including earth) before we had to worry about entropy. Well there it is, and I think I got a little carried away, but I hope this is more helpful than a simple "yes." David Coit
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