PartitionFunctionLect15ME501F2011

# PartitionFunctionLect15ME501F2011 - Purdue University ME...

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Patterned Border Template 1 Purdue University School of Mechanical Engineering ME 501: Statistical Thermodynamics Lecture 15: Equilibrium Distribution and The Partition Function Prof. Robert P. Lucht Room 2204, Mechanical Engineering Building School of Mechanical Engineering Purdue University West Lafayette, Indiana [email protected] , 765-494-5623 (Phone) October 5, 2011

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Patterned Border Template 2 Purdue University School of Mechanical Engineering Lecture Topics • Partition function and its significance. • Calculation of thermodynamic properties.
Patterned Border Template 3 Purdue University School of Mechanical Engineering The Partition Function • Recall the Maxwell-Boltzmann distribution law • The partition function is defined as: • Using energy states (instead of energy levels):    exp / exp / jj B j B j g kT N N g   exp / B j Z gk T      exp / exp / ii B i B Z T k T 

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Patterned Border Template 4 Purdue University School of Mechanical Engineering The Partition Function • Z (zustandssumme = sum over states) • The thermodynamic probability that system occupies a particular energy level is then given by: This is also commonly known as the Boltzmann fraction   exp / jj B j Z gk T    exp / B j T P Z
Patterned Border Template 5 Purdue University School of Mechanical Engineering

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PartitionFunctionLect15ME501F2011 - Purdue University ME...

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