ext n intensive - A method to illustrate the extensive and...

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A method to illustrate the extensive and intensive properties of thermodynamic variables Stephen R. Addison Department of Physics and Astronomy University of Central Arkansas Conway, AR 72035 saddison@mail.uca.edu
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2 INTRODUCTION Over the last ten years, unified courses in thermal physics, including both macroscopic thermodynamics and microscopic statistical mechanics, have become increasingly common, particularly at the undergraduate level. This reflects a change from traditional curricula, where entire courses are devoted to classical thermodynamics and statistical physics is briefly introduced in survey courses in modern physics, with serious study delayed until graduate school. A thorough understanding of statistical and probabilistic is becoming increasingly important to chemists and physicists. This understanding is often developed by a serious study of statistical mechanics. Undergraduate thermal physics provides an ideal foundation for such study. Undergraduate courses in thermal physics do not afford us the time follow the languid, historical, phenomenological development of the laws of thermodynamics as exemplified in the classic text by Zemansky (1981). The study of thermodynamics can be abbreviated by using the axiomatic method. The most widely accepted axioms are those proposed by Callen (1960). A thorough discussion of these axioms is provided in Callen’s Thermodynamics and in the more recent book by Tien and Lienhard (1985). In the axiomatic approach, the extensive or intensive nature of thermodynamic variables is emphasized and the relationship to the theory of homogeneous functions is presented. However, this relationship is not often exploited, and an opportunity to provide a foundation for the later study of critical point phenomena is lost. In the following sections the relationship between homogeneous function theory and thermodynamics is developed, and, as an illustration, a method for calculating the thermodynamic properties of N moles of a material if an equation is known for a fixed amount of that material. The author first became familiar with some of these methods in a course based on Callen’s text, and began to use them some years later after having developed a course in thermal physics. An extended literature search has failed to find a description of the methods described herein. HOMOGENEOUS FUNCTIONS As the properties of homogeneous functions are not well known, they are reviewed here. As is well known, a polynomial of the form AA x A x A x n n 01 2 2 ++ + + ... (1) is of degree n, if A n is not equal to zero. Thus, the degree of a polynomial is equal to the largest exponent in the polynomial. A polynomial in more than one
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3 variable is said to be homogeneous if all of its terms are of the same degree. For example, the polynomial in variables x and y fxy x x y y (,) =+ + 22 2 (2) is homogeneous of degree 2 . This much is familiar.
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This note was uploaded on 01/06/2011 for the course CHE 6272 taught by Professor Dr.ladd during the Fall '10 term at University of Florida.

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ext n intensive - A method to illustrate the extensive and...

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