Two experiments to approach the Boltzmann factor: chemical reaction and viscous flow

Abstract

In this paper we discuss a pedagogical approach aimed at pointing out the role played by the Boltzmann factor in describing phenomena usually perceived as regulated by different mechanisms of functioning. Experimental results regarding some aspects of a chemical reaction and of the viscous flow of some liquids are analysed and described in terms of macroscopic variables whose temperature dependence is proportional to the Boltzmann factor. A description of a workshop implementing the approach in the framework of an undergraduate course for engineering education and some preliminary results about its pedagogical relevance are then reported.

Revisiting the Saha–Basu equation of state

“…Let N ˜be the number of molecules per cm 3 near the wall of the container and N 0 ˜be the same in the interior. Then, according to the Boltzmann distribution [9][10][11],…”

Color controllable smart white lighting based on various device architectures of electrically driven quantum-dot light-emitting diodes

“…5e (ESI †). 40 As a result, the R QD layer exhibits the highest radiative recombination rate regardless of the voltage changes as shown in Fig. 5f.…”

Reductionist approach to chemical rate constants using conditional energy probabilities

“…The classical form of the Arrhenius law was published in 1889 [2] and anticipated by van't Hoff in 1884 [3], but van't Hoff acknowledged that he did not enter into theoretical considerations [3]. The exponential term of this equation related to temperature through the Boltzmann factor has proved very effective, as illustrated by pedagogical and convincing laboratory experiments such as those on the formaldehyde clock chemical reaction [4], potential barrier crossing by electrons in a transistor [5], and a mechanical simulator allowing one to count the passages of a randomly propelled ping-pong ball between two different levels of a plateau [6]. Given its efficacy for modeling chemical reactions, several attempts at formalization have been developed a posteriori, based on thermodynamics, statistical mechanics and quantum mechanics, including theories on diffusion from an energy well [7], reactive flux [8] and transition paths [9].…”