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lecture_11_04_13_2011

# lecture_11_04_13_2011 - Connecting statistics and entropy...

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Connecting statistics and entropy Thermal expansion and contraction Lecture 11 S = k B ln (w)

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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 same state Review: A reversible process does NOT produce entropy 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).

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Equal number of red & green A simple example of states and multiplicities (pulling 4 marbles out of a hat) , , , 4R 1 Multiplicity or number of microstates (w) Large number of marbles Macro States , , , , , , , 1G,3R 2G,2R 3G,1R 4G 4 6 4 1 16
N=1 1 2 1 1 3 3 1 1 1 N=2 N=3 2 4 8 The multiplicity of possible states when pulling N marbles from a jar Total Microstates Multiplicity w 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 N=4 N=5 N=6 16 32 64 etc.

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