l18 - Quantum statistics(again Entropy Temperature...

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Unformatted text preview: Quantum statistics (again) Entropy Temperature Maxwell-Boltzmann Maxwell velocity distribution Helium Partition and Gibbs Quantum statistics: the basics (again) Chemical potential Distribution I: Maxell-Boltzmann Fermi-Dirac Bose-Einstein Blackbody revisited Quantum statistics Bose A few things • Exam: since I just got back last night, I suspect I won’t have graded all of the exams until Nov. 17. • Today’s New York Times had an article on solar sailing. I sent an email link. • Where we are in the course: • We’ve done special relativity. • We’ve done some basics of quantum theory: Planck, Bohr, Rutherford, de Broglie, Schrödinger equation, and application to the hydrogen atom. • We’re 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 Maxwell-Boltzmann Maxwell velocity distribution Helium Partition and Gibbs Quantum statistics: the basics (again) Chemical potential Distribution I: Maxell-Boltzmann Fermi-Dirac Bose-Einstein 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 Planck’s 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 (Avogadro’s number of N A = 6 . 02 × 10 23 atoms/mole is large), let’s work with the logarithm g R ( E ) , or σ 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 Maxwell-Boltzmann Maxwell velocity distribution Helium Partition and Gibbs Quantum statistics: the basics (again) Chemical potential Distribution I: Maxell-Boltzmann Fermi-Dirac Bose-Einstein Blackbody revisited Quantum statistics Bose Entropy and probability • System S is in a state 1 with energy ǫ 1 , or a state 2 with energy ǫ 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 ( ǫ 1 ) P ( ǫ 2 ) = g R ( U − ǫ 1 ) g R ( U − ǫ 2 ) = exp bracketleftbig σ R ( U − ǫ 1 ) bracketrightbig exp bracketleftbig σ R ( U − ǫ 2 )...
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l18 - Quantum statistics(again Entropy Temperature...

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