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Unit 2: explaining thermal expansion Compilation. Unit 2: explaining thermal expansion Date: Thu, 2 Mar 2006 From: Glen M. Carter, Broward Schools, Florida Subject: Re: Internal Energy Just about to complete Unit 2 and need an explanation on why the height (volume) in a thermometer column rises. The kids have more or less figured that as energy is applied to a liquid that affects a temperature change, that applied energy increases the speed of particles (KE account). If the heat applied creates a phase change, e.g. boiling, then that applied energy reduces the attraction between particles (IE account) and ultimately creates a volume increase. The question presented by a few kids is, "if the increased energy (temperature increase) only affects the particles’ speed and not the attraction to one another, should the particles not be the same distance from each other and ultimately not affect a volume change?" I realize the volume change is extremely small, hence the reason for a capillary tube to see the change. So how do you relate the increased energy that affects the speed of the particles to this small volume increase? -------------------Date: Fri, 3 Mar 2006 From: Darrell Rahn, a Department of Defense Education Agency high school. My students raised the same question. Here is what I did. I threw a ball up in the air and talked about the gravitational and potential energy account changes. Is there ever a time when one is changing and the other isn't? No. In the case of the particles both accounts are changing all of the time but not as uniformly. During phase changes the interaction energy changes dwarf the KE changes, and during warming the KE changes are much more noticeable than the IE changes. One student’s interpretation: "it's a sig figs issue." Talking about a possible mechanism seemed to help, too. Something like: During warming the particles are moving around a lot more but because of the attractions between particles they are not getting much further away; therefore the IE changes are small. During phase changes the particles are initially gaining KE but now have enough speed to overcome the attractive forces and move large distances from neighboring particles. As they move away the forces attracting them slow them just as the gravitational force slowed the ball. The net effect is a transfer of KE to IE and the overall KE account has changed little while the IE account has changed a lot. -------------------Date: Sun, 5 Mar 2006 From: Larry Dukerich, Dobson HS, Arizona State University To me, this is yet another argument for why one should do physics before chemistry. The physics people are lucky because in their initial studies they can reduce almost every situation to one or two point particles in the system. The simple phenomena we chemists try to explain are much more complicated because there are so many particles interacting with one another. For years I have struggled with how to tell a manageable story about energy storage and transfer in such simple situations like phase change. I looked at the heating curves and wondered why we have to go through such great pains in the real laboratory to obtain data that yield such perfect graphs. Well, this is just another example of modeling: these representations are idealized. We need to remind our students that the real world is so messy that it is difficult to explain. So, in order to make sense of it, we make all sorts of simplifying assumptions. If we don't keep reminding ourselves that we are describing a model of the situation (and not the situation itself) we can end up with statements that are incredible. Take for example, our description that the energy supplied to the system is stored as Ei (and not Ek) during phase change. Of course 1 Unit 2: explaining thermal expansion that's a simplification; as anyone who has heated a sample of icy water knows, it's easy to have an ice-water mixture in which a thermometer shows a temperature above 0. We should be careful not to imply that the energy supplied to our system of a myriad of particles somehow "knows where to go." Students should see that in certain groups of particles in the system the Ek CAN increase, but then, as energy is transferred through collisions of particles, the Ek of that particular set of particles decreases as the Ei of another collection increases. The reason we heat gently and stir frequently is to allow these transfers to even things out during phase change so that we can see more than one energy storage account. If you want a silly $$ analogy, you can have two kids representing the energy accounts in the system: Bob represents Ek and Bill is Ei. Someone else (the surroundings) passes dollar bills to Bob who promptly hands them to Bill. The net effect is that Bill has a greater balance than before, but at a number of instants in the process, Bob was temporarily richer, too. I think that both Darrell (and Andy after him) have provided credible explanations of the phenomenon of thermal expansion of a solid or liquid that should satisfy one who wants to probe more deeply. I think we tell the kids that we sometimes pretend that only one step is occurring at a time because that way it's easier to represent simpler changes with such tools as energy bar graphs. -------------------Date: Mon, 6 Mar 2006 From: Carmela Minaya, Hanalani School, Hawaii Also another thought, every book has those fraction of particles storing kinetic energy vs. kinetic energy of system graphs for students to get an idea of the big picture. Reading those graphs and interpreting physical meaning is a feat in and of itself. I think that with particle diagrams and energy bar graphs should help to fill in the picture at different levels. -------------------Date: Tue, 7 Mar 2006 From: John Barrere, Fresno, CA I'm presently taking Bruce Sherwood's online course Matter & Interactions. It is a great course and I highly recommend it. Lots of emphasis on basic principles and connecting the macro & micro worlds. Modeling matter at the micro level as balls and springs allows good prediction of many macro properties. In this regard, energy inputs are stored as KE of the balls or PE in the springs with shifting back and forth. Adding more energy increases both the average KE and the average PE (and therefore the average disps of the balls). 2