Derivation of the Boltzmann entropy equation in a toy model

The concept of entropy is mostly recognized as one of the most difficult for the students to comprehend. This makes entropy also a subject hard to teach. In this paper, we discuss the employment of a simplified version of the solid Einstein model, largely employed to illustrate multiplicity, to construct the concept of entropy and to obtain the Boltzmann entropy equation. In this constructive process, STEM students can gain intuition on that entropy is a statistical quantity and on what it represents. The process is carried out in a close way to the Clausius definition, allowing the connection of the result of the model to other thermodynamic quantities.