lecture_11_04_13_2011

lecture_11_04_13_2011 - Connecting statistics and entropy...

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Unformatted text preview: Connecting statistics and entropy Thermal expansion and contraction Lecture 11 S = k B ln ln ln ln (w) Processes that are idealized as reversible include: • Frictionless movement • Restrained compression or expansion • Energy transfer as heat due to infinitesimal temperature gradients • Electric current flowing through a zero resistance • Restrained chemical reaction • Mixing of two samples of the same substance in the Review: A reversible process does NOT produce entropy same state Processes that are irreversible include: • Movement with friction • Unrestrained expansion • Energy transfer as heat due to large temperature gradients • Electric current flowing through a non zero resistance • Spontaneous chemical reaction • Mixing of matter of different composition or state There is a strong connection between the 2 nd Law of Thermodynamics, Probability and Statistics You can devise countless simple experiments to illustrate that “movement toward more disorder” is a law that nature follows. Highly ordered systems become improbable as the number of objects in a system increases. Essentially, every observed configuration of a large number of objects is highly disordered. This leads to the conclusion that nature has a strong tendency to move toward maximum multiplicity (and maximum entropy). Equal number of red & green A simple example of states and multiplicities (pulling 4 marbles out of a hat) Multiplicity or number of microstates (w) Large number of marbles Macro States , , , , , , , , , , 4R 1G,3R 2G,2R 3G,1R 4G 1 4 6 4 1 16 N=1 1 2 1 3 3 1 1 1 N=2 =3 2 4 The multiplicity of possible states when pulling N marbles from a jar Total Microstates Multiplicity w 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 N=3 N=4 N=5 N=6 8 16 32 64 etc....
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This note was uploaded on 04/23/2011 for the course PHYS 242 taught by Professor Staff during the Spring '08 term at Purdue University.

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lecture_11_04_13_2011 - Connecting statistics and entropy...

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