Dissecting the polymorphism of chemical potential numerically and analytically

Chemical potential is one of the most elusive concepts students encounter in thermodynamics partly due to its polymorphism. To help students dissect this concept, we introduce in this paper various definitions of chemical potential and their applications. Furthermore, the chemical potential under constant TP and constant TV conditions are analyzed via numerical calculations and analytical derivations for an ideal gas in a mixture. These numerical calculations and analytical derivations, either illustrated by instructors or practiced by students, would make the abstract and elusive chemical potential more concrete and tangible for the students in thermodynamics.