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The Boltzmann Distribution
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Abstract
It is demonstrated that the Boltzmann Distribution may be derived in a straightforward manner by using a combination of the Boltzmann formula for entropy and the requirement of minimum Helmholtz energy for equilibrium in a closed system of constant volume. This approach avoids the use of unfamiliar mathematical techniques such as Lagrange's Method of Undetermined Multipliers.
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Statistical MechanicsCiting Articles
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This article has been cited by 5 ACS Journal articles (5 most recent appear below).
Energy Distributions in Small Populations: Pascal versus Boltzmann
Roger W. Kugel, Paul A. WeinerJournal of Chemical Education2010 87 (11), 1200-1205Energy Distributions in Small Populations: Pascal versus Boltzmann
Roger W. Kugel, Paul A. WeinerJournal of Chemical Education2010 87 (11), 1200-1205The theoretical distributions of a limited amount of energy among small numbers of particles with discrete, evenly-spaced quantum levels are examined systematically. The average populations of energy states reveal the pattern of Pascal’s triangle. An ...
Enhanced Intensity Distribution Analysis of the Rotational–Vibrational Spectrum of HCl
Monty L. FetterolfJournal of Chemical Education2007 84 (6), 1062Enhanced Intensity Distribution Analysis of the Rotational–Vibrational Spectrum of HCl
Monty L. FetterolfJournal of Chemical Education2007 84 (6), 1062Data are presented that indicates the best fit of intensity of the HCl vibrational–rotational FTIR spectrum, which includes a Boltzmann population profile, is accomplished by accounting for factors from the full transition moment integral and by relaxing ...
Boltzmann without Lagrange
Carl W. DavidJournal of Chemical Education2006 83 (11), 1695Boltzmann without Lagrange
Carl W. DavidJournal of Chemical Education2006 83 (11), 1695A derivation of the Maxwell Boltzmann distribution without using the Lagrange method of undetermined multipliers is represented.
The Microscopic Statement of the Second Law of Thermodynamics
Igor NovakJournal of Chemical Education2003 80 (12), 1428The Microscopic Statement of the Second Law of Thermodynamics
Igor NovakJournal of Chemical Education2003 80 (12), 1428The teaching of basic concepts in thermodynamics is described from the microscopic point of view, that is, using only particle energies and level populations as descriptors.
A Simple Derivation of the Boltzmann Distribution
Sean A. C. McDowellJournal of Chemical Education1999 76 (10), 1393A Simple Derivation of the Boltzmann Distribution
Sean A. C. McDowellJournal of Chemical Education1999 76 (10), 1393The Boltzmann distribution is a central concept in chemistry and its derivation is usually a key component of introductory statistical mechanics courses. However, the derivation, as outlined in most standard physical chemistry textbooks, can be a ...
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History
- Received: August 03, 2009
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