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<p>Chemical potential is one of the most elusive concepts students encounter in thermodynamics partly owing to its polymorphism. To help students dissect this concept, we introduce various expressions of chemical potential and their applications in this paper. Furthermore, the chemical potential under constant <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40828_2025_205_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="28" /> </InlineMediaObject> <EquationSource Format="TEX">\(TP\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="italic">TP</mi> </mrow> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40828_2025_205_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="27" /> </InlineMediaObject> <EquationSource Format="TEX">\(TV\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="italic">TV</mi> </mrow> </math></EquationSource> </InlineEquation>, or <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40828_2025_205_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="31" /> </InlineMediaObject> <EquationSource Format="TEX">\(HP\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="italic">HP</mi> </mrow> </math></EquationSource> </InlineEquation> conditions is analyzed via numerical calculations and analytical derivations for an ideal gas in a mixture. As either in-class or after-class activities, these numerical calculations and analytical derivations would make the abstract and elusive chemical potential more concrete and tangible for the students to grasp. Finally, teaching and learning practices are proposed to help the students develop a solid understanding of this concept in three hours.</p> Graphical abstract <p></p>

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Dissecting the polymorphism of chemical potential numerically and analytically

  • 期刊论文

  • 发表日期：

    2025年4月28日

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  • Yingbin Ge

摘要

Chemical potential is one of the most elusive concepts students encounter in thermodynamics partly owing to its polymorphism. To help students dissect this concept, we introduce various expressions of chemical potential and their applications in this paper. Furthermore, the chemical potential under constant \(TP\) TP , \(TV\) TV , or \(HP\) HP conditions is analyzed via numerical calculations and analytical derivations for an ideal gas in a mixture. As either in-class or after-class activities, these numerical calculations and analytical derivations would make the abstract and elusive chemical potential more concrete and tangible for the students to grasp. Finally, teaching and learning practices are proposed to help the students develop a solid understanding of this concept in three hours.

Graphical abstract