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A Summary of Statistical Thermodynamic Calculations

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Abstract

In this document students can explore the full set of statistical thermodynamic calculations leading to the prediction of the heat capacity at constant volume from the translational, rotational, vibrational, and electronic partition functions. The document is heavily annotated to permit independent study or review of the concepts. Some questions in the document help students to focus on the chemical concepts while others focus on the mathematical methods. The document demonstrates using the symbolic derivation feature of Mathcad by a derivation of the vibrational contribution to the heat capacity of a molecule. An extension of the calculation of the thermodynamic properties of a molecule is made to predict the equilibrium constant of the dissociation of N₂. The document concludes with the study of the NO molecule which has a low lying electronic energy level. A mastery exercise is included for students to use to extend their understanding. This document was completed during the 1997 "Workshop for Integration of Numerical Methods into the Undergraduate Physical Chemistry Curriculum Using the Mathcad Software" at the University of South Alabama, Mobile Alabama.

Figure 1. Heat capacity at constant volume for NO as a function of T ( as i K). Cv(i K) is the total heat capacity (solid line); Cvv(i K) is the vibrational component of the heat capacity (dotted line); Cve is the electronic heat capacity component (dot-dash line).

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Mathcad 12	stat_thermo.mcd

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Mathcad 12	stat_thermo.pdf

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Keywords

Audience: Upper-Division Undergraduate;

Domain: Physical Chemistry;

Pedagogy: Computer-Based Learning;

Topics: Mathematics / Symbolic Mathematics; Statistical Mechanics; Thermodynamics;

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