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Chapter 20 Lecture 2

# Chapter 20 Lecture 2 - Microstates and Statistical...

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Microstates and S tatistical Probability, W Microstates and W increases 20-11

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Entropy and 2 nd Law of Thermodynamics A system with relatively few equivalent ways to arrange its components (smaller W ) has relatively less disorder and low entropy. A system with many equivalent ways to arrange its components (larger W ) has relatively more disorder and high entropy. S universe = S system + S surroundings > 0 2 nd Law: A spontaneous process occurs in the direction that increases the entropy of the universe (system + surroundings) There are no restrictions on the signs of S sys and S surr as long as the sum of the two is greater than zero 20-12
Spontaneous Expansion of a Gas in Vacuum During the expansion the total energy E system =0 no heat is exchanged and no work is done since P = 0 no heat is exchanged and no work is done since ext The volume increases so the number of possible positions available to the particles increases ֜ W Th i d i b i i th iti l di d d th The process is driven by increase in the positional disorder and thus increase in the entropy 20-13

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The entropy increase due to the expansion of a gas More number of particle locations, more translational energy levels At constant temperature, the total energy of the particles remains constant but their energy has more ways to be distributed 20-14 constant, but their energy has more ways to be distributed.
Expansion of a gas and the increase in number of microstates W final =2 N A W initial Boltzman equation: S = k ln W S = S final - S initial = k ln W final -kln W initial W = k ln = R ln2 = 5.76 J/mol K final W initial 20-15

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Entropy Change through a “Reversible” Process S q rev For a reversible process: sys = T T : the temperature q
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Chapter 20 Lecture 2 - Microstates and Statistical...

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