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24&30- Intro to Entropy, entropy of polymer chains.docx

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CHEM 204
Christopher Barrett

CHEM 204 03/13/2013 Lecture 24&30 Martin M. PHGY Tutor Introduction to Ever-Increasing Entropy Review: Energy is conserved like mass, and it is neither created nor destroyed. In an isolated system, the internal energy remains constant, and thus . st st The 1 law determines what permitted to happen. Only a small subset of the 1 law can actually happen, though, with respect to the second law. Every possible outcome has a possibility associated with it, and the second law determines the most probable outcomes.  For example, as a ball bounces it loses its potential energy and kinetic energy as heat into the surface and comes to a stop. How come the table doesn't randomly give off enough heat to the ball to make it fly off? Technically this still obeys the conservation of energy, but because of entropy - it's not a possible outcome  As any outcome is possible! A process is spontaneous if it produces the most probably outcome, and vice versa. Entropy is a whole number of ALL the possible states a system can assume. For example, if there are 2 balls in a room divided in 2, there are 4 possible outcomes but 2 of them are indistinguishable from each other. This indistinguishability is predicted by Pascal's Triangle. Continuing the 2 molecules in a room analogy: Amount of molecules Amount of time until it is probable that they all appear on one side 8 2 min 15 4.6 h 25 194days 35 544years! Thus at high "n", Pascal's triangle morphs into gaussian probability function. But once you get to a mole of a substance, the probability distribution looks like a single spike and that's why it seems to assume only one state. Essentially the gaussian is ( ) centered on the most probable outcome (x )0and stretched by . The full equation just for fun is ( ) ( ) ( √ ) CHEM 204 03/13/2013 Lecture 24&30 Martin M. PHGY Tutor Entropy of Real Polymer Chains Overal
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