![]() How can we understand this irreversibility in light of the 2 nd Law's statement about entropy? Revisiting thought experiment 2: The sliding chairĬonsider now the case of the chair sliding across a floor with friction and coming to a stop, an example of a process that exhibits a uni-directionality not explained using just the 1 st Law of Thermodynamics. (For the slow molecule to speed up the fast one it would have to be in just the right place to catch the fast one from behind - possible, but very unlikely.) The result, therefore, is the same as what one would obtain using probabilistic considerations of entropy alone: the two objects move toward an equilibrium temperature lying somewhere between the two extreme temperatures. ![]() In such a collision, the hot molecule is much more likely to transfer some of its kinetic energy to the cold molecule, thereby producing two molecules whose temperatures (energies) are more similar to each other than they were prior to the collision. Instead of considering probabilities, think for a moment about what happens when a hot molecule comes in contact with a cold molecule via a collision. There is another, more mechanistic way of understanding what happens when a hot object is placed in contact with a cold object. This calculation is worked out in more explicit detail in the follow-on examples We've just described this with a simple one-step model to see how it works. As the temperature difference between the objects gets greater, the Second Law says that the direction of heat flow becomes almost solely toward the colder object. We see, then, that in this simple case of a hot object placed next to a cold object, the probabilistic statement of the Second Law of Thermodynamics correctly tells us the direction in which heat is likely to transfer. In this case, the system's entropy has gone UP, since the 7/3 distribution is consistent with more arrangements than is the 8/2 distribution. Now consider, instead, that the hot object transfers one "unit" of heat to the cold object. What does such a process do to the entropy of the system? Clearly, the entropy of the system has gone down! There are fewer arrangements consistent with the 9/1 energy distribution than there are arrangements consistent with 8/2 energy distribution, just like 9 H/1T is less likely in flipping a coin 10 times than is 8H/2T. It's not "just" the energy itself.) The result is that the hot object now has 9 "units" of energy and the cold object is left with just 1 block. (Remember: "Heat" refers to blocks of energy transferred by thermal contact. ![]() Let's say that the cold object starts with 2 blocks of energy and the hot object starts with 8 blocks of energy, and let's assume that one block of heat is transferred from the cold object toward the hot one. So our model is a simple one: Two isolated identical objects that can share a set of energy blocks between them, but that have no exchange of energy or matter with anything else in the universe. This is much easier to think about, and, in fact, the key reasoning is identical to the more formally correct reasoning using limits. But the sense of the process can be seen by modeling the energy as coming in finite-sized blocks that can be shared between the two objects in different ways. It requires breaking the energy up into tiny pieces, creating sums, taking limits as the pieces go to zero, and changing the sums to integrals. To "count" the number of ways energy can be distributed is very tricky. With the subtleties of density vs total energy and energy translated into temperature suppressed by our choice of example, we can just look at how much energy is transferred between our two identical objects.Īnother complexity is that energy is a continuous variable. And remember, each kind of material translates heat into temperature in its own way. Remember, it's temperature - the density of thermal energy, not the total - that tells us which way energy flows. We do this so we can talk about total amount of energy and not worry about the important but complicating factors of density of energy and specific heat. Let's consider the case of a system composed of a hot object placed in contact with a cold object made of the same material and of the same mass. Revisiting thought experiment 1: A hot object and a cold object How does the very general statement about probabilities and states that we developed in our discussion of the second law explain why cold objects don't spontaneously transfer heat to hot objects, or why resting chairs don't spontaneously pick up heat from the floor and start moving? Let's go through our examples on our motivating page ( The 2nd Law of Thermodynamics) and see how adding the concept of micro and macrostates and the idea of entropy helps to explain why things run spontaneously in the direction observed. ![]()
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