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Unformatted text preview: The elusive chemical potential Ralph Baierlein Department of Physics and Astronomy, Northern Arizona University, Flagstaff, Arizona 86011-6010 ~ Received 12 April 2000; accepted 10 October 2000 ! This paper offers some qualitative understanding of the chemical potential, a topic that students invariably find difficult. Three meanings for the chemical potential are stated and then supported by analytical development. Two substantial applicationsdepression of the melting point and batteriesillustrate the chemical potential in action. The origin of the term chemical potential has its surprises, and a sketch of the history concludes the paper. 2001 American Association of Physics Teachers. @ DOI: 10.1119/1.1336839 # I. INTRODUCTION It was the semesters end in spring 1997, and I had just finished teaching a course in thermal physics. One of my students said to me, Now I really understand temperature, but what is the meaning of the chemical potential? Clearly, a topic needed greater emphasis, both in class and in the draft text. I vowed to do better the next year, andaltogetherI spent several years looking into responses to the question. The present article first describes three meanings of the chemical potential, next develops them analytically, and fi- nally gives two substantial examples of how the chemical potential is used. Some observations are interleaved, and the paper concludes with a short history. For whom is this paper intended? I wrote primarily for someoneinstructor or studentwho already knows about the chemical potential but would like to understand it better. Some portions of the paper are original, but much of it con- sists of material that is common knowledge among textbook writers. I have gathered together interpretations, insights, and examples to construct a kind of tutorial or review article on the chemical potential. II. MEANINGS Any response to the question, What is the meaning of the chemical potential?, is necessarily subjective. What satis- fies one person may be wholly inadequate for another. Here I offer three characterizations of the chemical potential ~ de- noted by m ! that capture diverse aspects of its manifold na- ture. ~ 1 ! Tendency to diffuse . As a function of position, the chemical potential measures the tendency of particles to diffuse. ~ 2 ! Rate of change . When a reaction may occur, an extre- mum of some thermodynamic function determines equi- librium. The chemical potential measures the contribu- tion ~ per particle and for an individual species ! to the functions rate of change. ~ 3 ! Characteristic energy . The chemical potential provides a characteristic energy: ( ] E / ] N ) S , V , that is, the change in energy when one particle is added to the system at con- stant entropy ~ and constant volume ! ....
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This note was uploaded on 12/05/2010 for the course CHBE 251 taught by Professor Scotty during the Winter '09 term at The University of British Columbia.
- Winter '09