Lab 9 - Entropy1

Lab 9 - Entropy1 - Lab 9: Entropy Performed On: Due On:...

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Lab 9: Entropy Performed On: 03/09/2012 Due On: 03/30/2012 Names: Brian Wilhelm Andy Gutting Weston Wands Brian Cosey David Bonsaver Contributions: See Appendix B
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In this lab analysis was applied to the results of a chance situation involving 18 two sided, wiggle-eyes which had a total of 19 possible macrostates and 262,144 microstates. The dispersal of microstates in a meta-analysis of data from six experiments was observed to show that the most likely macrostate was the one with the highest number of possible microstates (and highest entropy); this was determined to be the macrostate with 9 “up” wiggly eyes and 9 “down” wiggly eyes. ΔE was determined to be 2.384x10 -22 , which is negligibly close to zero and demonstrates a solid and accurate representation of actual statistical probability and entropy by the experiments completed. Introduction: There are two methods through which one can approach entropy: the thermodynamic definition and the statistical definition. In this case the statistical definition was used to evaluate the entropy of the experimental system. Basic information that was necessary to begin this analysis included finding the number of macrostates and microstates. Although wiggly eyes were used in this lab, each was essentially equivalent to a coin flip (two sides and two possible outcomes). Determining macrostates can then be done using the following equation: (1) Here N is the number of wiggly eyes present. Determining microstates also involves N as well as the number of possible states for each wiggly eye. Since there are two possible states for each wiggly eye (up or down), the total number of microstates will be determined by: (2) If we let n equal the number of wiggly eyes that are facing up in a particular macrostate (and therefore N-n will be the number of wiggly eyes facing down), we can arrive at the probability of that particular macrostate: (3) Here u is the simply the probability of a wiggly eye being face up and d the probability of a wiggly eye being face down. Thermodynamics states that the probability of each microstate is technically equal. However, the energy of that microstate can vary and this energy determines the actual probability of the occurrence of that microstate. 22
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This note was uploaded on 04/03/2012 for the course PHY 252 taught by Professor Treacy during the Spring '08 term at ASU.

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Lab 9 - Entropy1 - Lab 9: Entropy Performed On: Due On:...

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