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Unformatted text preview: Quantum statistics (again) Entropy Temperature MaxwellBoltzmann Maxwell velocity distribution Helium Partition and Gibbs Quantum statistics: the basics (again) Chemical potential Distribution I: MaxellBoltzmann FermiDirac BoseEinstein Blackbody revisited Quantum statistics Bose A few things Exam: since I just got back last night, I suspect I wont have graded all of the exams until Nov. 17. Todays New York Times had an article on solar sailing. I sent an email link. Where we are in the course: Weve done special relativity. Weve done some basics of quantum theory: Planck, Bohr, Rutherford, de Broglie, Schrdinger equation, and application to the hydrogen atom. Were now going to touch on quantum statistics and some solid state physics before we end the course with nuclear physics. Quantum statistics (again) Entropy Temperature MaxwellBoltzmann Maxwell velocity distribution Helium Partition and Gibbs Quantum statistics: the basics (again) Chemical potential Distribution I: MaxellBoltzmann FermiDirac BoseEinstein Blackbody revisited Quantum statistics Bose A return to quantum statistics We are now jumping to Chapter 10 of Serway, where we will talk about quantum statistics. We will find this involves associating the occupancy of states with temperature, so we want to review the discussion we had of this back with Plancks blackbody radiation theory. Notation used here is of Thermal Physics by Charles Kittel and Herbert Kroemer (W. H. Freeman and Company, 1980). A system S has g R ( E ) states accessible for total energy E . Put this system S into thermal contact with a reservoir R which originally had a total energy U . The reservoir is so large that the system S has a weak effect on the reservoir R . Since we usually deal with huge numbers of atoms (Avogadros number of N A = 6 . 02 10 23 atoms/mole is large), lets work with the logarithm g R ( E ) , or R ( E ) = log g R ( E ) , (1) The logarithm of the number of available states is known by a particular name in statistical mechanics: it is the entropy of a system. Quantum statistics (again) Entropy Temperature MaxwellBoltzmann Maxwell velocity distribution Helium Partition and Gibbs Quantum statistics: the basics (again) Chemical potential Distribution I: MaxellBoltzmann FermiDirac BoseEinstein Blackbody revisited Quantum statistics Bose Entropy and probability System S is in a state 1 with energy 1 , or a state 2 with energy 2 . What happens to the reservoir R as a consequence of these two choices? Fundamental assumption: equal likelihood for all available energy= U states. Therefore probability P that the reservoir is in state 1 versus state 2 is simply given by the ratio of states g R ( E ) accessible to the reservoir at the two energies, or P ( 1 ) P ( 2 ) = g R ( U 1 ) g R ( U 2 ) = exp bracketleftbig R ( U 1 ) bracketrightbig exp bracketleftbig R ( U 2 )...
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This note was uploaded on 05/28/2011 for the course PHY 251 taught by Professor Rijssenbeek during the Fall '01 term at SUNY Stony Brook.
 Fall '01
 Rijssenbeek
 Physics, Entropy

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