Microstates&amp;MacrostatesLect12ME501F2011

# Microstates&amp;MacrostatesLect12ME501F2011 - Purdue...

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Patterned Border Template 1 Purdue University School of Mechanical Engineering ME 501: Statistical Thermodynamics Lecture 12: Introduction to Statistical Thermodynamics, Microstates and Macrostates Prof. Robert P. Lucht Room 2204, Mechanical Engineering Building School of Mechanical Engineering Purdue University West Lafayette, Indiana [email protected] , 765-494-5623 (Phone) September 26, 2011

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Patterned Border Template 2 Purdue University School of Mechanical Engineering Lecture Topics Objective of statistical thermodynamics. Notion of a distribution. Microstates and macrostates. Most probable distribution.
Patterned Border Template 3 Purdue University School of Mechanical Engineering Fundamental Concepts: Primary Objective of Statistical Thermodynamics Primary objective of statistical mechanics: prediction of properties of an assembly in terms of the properties of the molecular constituents. • Properties of the assembly: S, H, T, U, c p , c v ..... • Properties of the molecular constituents: energies and degeneracies ( , g) of energy levels Calculation of thermodynamic properties must be done statistically. • Assembly typically contains on the order of 10 23 molecules . • Molecules continually interact via collisions. These particles may be bosons (integral spin) or fermions (half-integral spin). No two fermions can occupy the same quantum state in the assembly. • Statistical mechanics provides the means of averaging, over time, these constantly changing molecular properties to determine thermodynamic properties.

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Patterned Border Template 4 Purdue University School of Mechanical Engineering Fundamental Concepts: The Notion of a Distribution Consider a perfect gas assembly of a large number N of molecular particles. • According to quantum mechanics, these particles are indistinguishable. • These particles may be bosons (integral spin) or fermions (half-integral spin). No two fermions can occupy the same quantum state in the assembly. • The statistical models for the assembly are different for fermions and bosons, and for distinguishable and indistinguishable particles. At least in the beginning, the molecules in the assembly are assumed to be independent (weakly interacting). • A good example of this type of assembly is the ideal gas assembly. The valence (free) electrons in a metal are another good example. • The problem becomes much more complex if intermolecular forces (van der Waals forces) are considered. We will discuss this in the latter part of the course.
Patterned Border Template 5 Purdue University School of Mechanical Engineering Fundamental Concepts: The Notion of a Distribution Each molecule may assume any one of a large number of available quantum states. For a diatomic molecule: Quantum states with the same or nearly the same energy are grouped in energy levels j . The number of quantum states in each level is the degeneracy g j .

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## This note was uploaded on 12/26/2011 for the course ME 501 taught by Professor Na during the Fall '10 term at Purdue.

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Microstates&amp;MacrostatesLect12ME501F2011 - Purdue...

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