A pedagogical approach to the Boltzmann factor through experiments and simulations

Abstract

The Boltzmann factor is the basis of a huge amount of thermodynamic and statistical physics, both classical and quantum. It governs the behaviour of all systems in nature that are exchanging energy with their environment. To understand why the expression has this specific form involves a deep mathematical analysis, whose flow of logic is hard to see and is not at the level of high school or college students' preparation. We here present some experiments and simulations aimed at directly deriving its mathematical expression and illustrating the fundamental concepts on which it is grounded. Experiments use easily available apparatuses, and simulations are developed in the Net-Logo environment that, besides having a user-friendly interface, allows an easy interaction with the algorithm. The approach supplies pedagogical support for the introduction of the Boltzmann factor at the undergraduate level to students without a background in statistical mechanics.

Exploring the Coherence of Student Reasoning when Responding to Questionnaires on Thermally Activated Phenomena

“…After a group discussion, students were encouraged to focus on the idea of a "two-level" system as the unifying concept behind all the situations. Some time was devoted analysing an agent-based computer model (Battaglia et al, 2009) related to the subject, built by using the NetLogo simulation environment, which can easily simulate the interactions between a large number of elements. Students discussed with the instructor a mechanical model of a twolevel system.…”

K-means Clustering to Study How Student Reasoning Lines Can Be Modified by a Learning Activity Based on Feynman’s Unifying Approach

“…It is easy to find teaching methods aimed at understanding the BF, as many have been published up to now (Feynman et al, 1963;Horne et al, 1973;Prentis, 2000). It was presented (Battaglia et al, 2009) a pedagogical approach to BF based on the comparison between the experimental data and results of a simulation based on a simple mechanical model of a two-level system. Other experiments dealing with chemical kinetics, electrodynamics and fluid dynamics have been presented (Battaglia et al, 2010;, in order to extend the basis of experimental data on physical situations that can be modelled by using the unifying approach of the BF.…”

“…After a group discussion, where similarities and differences between the functioning mechanisms of the various phenomena were discussed, the instructor encouraged students to focus on the idea of a "two-level" system. In order to better study the "two-level" system, the end of this phase was devoted to the analysis of a dynamic computer model (Battaglia et al, 2009) related to the subject, built by using the NetLogo 5 simulation environment, which can easily simulate the interactions between a large number of elements. The instructor shows how it could be possible to build a simulation of a "two-level" mechanical system by using NetLogo.…”

Teaching ideal gas in a uniform field: exploring student preferences

“…The student difficulties with the Boltzmann factor have been addressed [8,9]. For such a pedagogically challenging topic, a variety of examples and approaches might be helpful [10]. This article discusses a particular example in statistical physics and aims to offer an alternative view.…”