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Session:
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PICUP: Reports on the Growing Computational Physics Education Revolution
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Paper Type:
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Contributed
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Title:
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Simplified Analysis of Phase Transitions in Thermodynamics
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Meeting:
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2019 Summer Meeting: Provo, UT |
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Location:
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N/A |
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Date:
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Time:
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3:10PM
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Author:
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Jay J. Wang, UMass Dartmouth
5089999136, jwang@umassd.edu
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Co-Author(s):
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Nick J. Moniz
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Abstract:
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Understanding critical phenomena in physical systems such as thermodynamic phase transitions is important in the study of physics, but often such topics pose challenges including advanced mathematics hindering the discussion of them at earlier stages of the curriculum. In this presentation we discuss simplified analysis of two problems in thermodynamics in terms of the Lambert W function, including the mean field approximation of the Ising model and Bose-Einstein condensation (BEC). Utilizing appropriate simplifying approximations, we find a closed-form mean-field solution to the Ising model, and an approximate but quantitative dependence of the chemical potential on temperature in BEC in terms of the special W function. This analytic approach illuminates the essential physics in a clear and direct manner, allows for visualization with VPython (see http://www.faculty.umassd.edu/j.wang/), complements but does not require full numerical computation in the standard treatment of these problems, and highlights the use of special functions as a powerful toolkit in the physicist's arsenal.
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Footnotes:
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None
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Presentation:
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AAPT-2019-Summer-Presentation-BK07-Jay.Wang.pdf
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