### Statistical Mechanics Lecture 20 of 29

July 6, 2012 by Matteo Marsili

M. Marsili, ICTP

In this lesson continues with the study of the canonical ensemble for this type of ensembles the macrostate is specified by the number of particles N, the volume V and the temperature T. The probability distribution is then calculated by considering that each microstate as a system with a given energy and that the macrostate is composed by N systems and nR is the number of system with energy ER. Then the probability of finding a system with energy ER is PR=<nR>/N. To solve this problem first it was calculated the number nR* that maximized PR.

A trick to compute <nR> was to introduce the Generating functions, then <nR> can be calculated as a first derivative of this Generating function. After long and tedious mathematics it is obtained that <nR> = nR*. Then it was shown that PR fallows a Boltzmann distribution PR=Exp[-?ER]/Z where is called the partition function (Z = ? Exp[-?En]).

As a complementary tool you can also see some lessons on Statistical Mechanics given in the <span class="yt-user-name author">Stanford</span> University.

Lecture 5 | Modern Physics: Statistical Mechanics April 27, 2009 - Leonard Susskind discusses the basic physics of the diatomic molecule and why you don't have to worry about its structure at low temperature. Susskind later explores a black hole thermodynamics.

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