Give Them Money: The Boltzmann Game, a Classroom or Laboratory Activity Modeling Entropy Changes and the Distribution of Energy in Chemical Systems

Michalek, Bridget; Hanson, Robert M.

doi:10.1021/ed083p581

Cited by 12 publications

(6 citation statements)

References 17 publications

(23 reference statements)

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“…Having students represent particles themselves is another way to model particles. The Boltzmann game 57 is an effective role play for simulating energy distributions leading to a Boltzmann distribution (Box 1, LO 5.2). Each student begins the role play with five pieces of play money ("Joule bucks") and then plays multiple rounds of rock-paper-scissors with other students with the winner receiving a Joule buck from the loser of each round.…”

Section: Particulate Role Playmentioning

confidence: 99%

Integrating Particulate Representations into AP Chemistry and Introductory Chemistry Courses

Prilliman

2014

J. Chem. Educ.

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The College Board’s recently revised curriculum for advanced placement (AP) chemistry places a strong emphasis on conceptual understanding, including representations of particle phenomena. This change in emphasis is informed by years of research showing that students could perform algorithmic calculations but not explain those calculations using particulate representations. This article provides a discussion of particulate representations in chemistry and specific examples of ways to introduce particulate representations to students and to integrate them throughout the AP chemistry or any introductory chemistry course. This contribution is part of a special issue on teaching introductory chemistry in the context of the advanced placement chemistry course redesign.

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Section: Particulate Role Playmentioning

confidence: 99%

Integrating Particulate Representations into AP Chemistry and Introductory Chemistry Courses

Prilliman

2014

J. Chem. Educ.

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“…42 The findings also indicate that higher-order thinking skills, including problem-solving, group collaboration, and critical thinking, have gained greater prominence in research during recent years. 43 Educators worldwide have published 14 academic papers exploring educational games in thermodynamics, 44−47 chemical kinetics, 48−53 and chemical equilibrium. 54−57 However, none of these games simultaneously cover the three subjects or are digital.…”

Section: ■ Introductionmentioning

confidence: 99%

Space Race Game: A Web-Based Board Game for Aiding Students in Reviewing Thermochemistry, Chemical Equilibrium, and Chemical Kinetics

da Silva Júnior,

Ribeiro,

Melo Leite Junior

et al. 2024

J. Chem. Educ.

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This work provides information about the design, implementation, and assessment of the instructional role of a bilingual (English and Portuguese) web-based board game designed to assist Brazilian Mechanical Engineering undergraduate students in reviewing the content related to thermodynamics, chemical equilibrium, and chemical kinetics. The game can be an alternative instrument to traditional problem-solving classes. Sixty-four mechanical engineering undergraduate students played the game using the Portuguese version and evaluated it positively. Also, learning assessments revealed that the game effectively promotes learning like conventional problem-solving classes.

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“…In contrast, the onset of the Boltzmann distribution in the simple game where N ≫ 1 players exchange a fixed amount of money in a random direction can be understood using simple arguments. In this game, which is known in econophysics as the Bennati-Dregulescu-Yakovenko game [3,4], and which is also used by physical chemistry teachers to illustrate various concepts of statistical mechanics [28], a randomly selected pair of players exchange a single money unit in a random direction. A physical counterpart of this game corresponds to N 'molecules' with (quantum) harmonic oscillator energy spectra, and with pairs of oscillators exchanging one quantum of energy at random such that the total energy is conserved.…”

Section: Introductionmentioning

confidence: 99%

Nonequilibrium statistical mechanics of money/energy exchange models

Miao,

Makarov,

Blom

2024

J. Phys. A: Math. Theor.

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Many-body dynamical models in which Boltzmann statistics can be derived directly from the underlying dynamical laws without invoking the fundamental postulates of statistical mechanics are scarce. Interestingly, one such model is found in econophysics and in chemistry classrooms: the money game, in which players exchange money randomly in a process that resembles elastic intermolecular collisions in a gas, giving rise to the Boltzmann distribution of money owned by each player. Although this model offers a pedagogical example that demonstrates the origins of Boltzmann statistics, such demonstrations usually rely on computer simulations -- a proof of the exponential steady-state distribution in this model has only become available in recent years. Here, we study this random money/energy exchange model, and its extensions, using a simple mean-field-type approach that examines the properties of the one-dimensional random walk performed by one of its participants. We give a simple derivation of the Boltzmann steady-state distribution in this model. Breaking the time-reversal symmetry of the game by modifying its rules results in non-Boltzmann steady-state statistics. In particular, introducing “unfair” exchange rules in which a poorer player is more likely to give money to a richer player than to receive money from that richer player, results in an analytically provable Pareto-type power-law distribution of the money in the limit where the number of players is infinite, with a finite fraction of players in the ``ground state'' (i.e., with zero money). For a finite number of players, however, the game may give rise to a bimodal distribution of money and to bistable dynamics, in which a participant's wealth jumps between poor and rich states. The latter corresponds to a scenario where the player accumulates nearly all the available money in the game.

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Give Them Money: The Boltzmann Game, a Classroom or Laboratory Activity Modeling Entropy Changes and the Distribution of Energy in Chemical Systems

Cited by 12 publications

References 17 publications

Integrating Particulate Representations into AP Chemistry and Introductory Chemistry Courses

Integrating Particulate Representations into AP Chemistry and Introductory Chemistry Courses

Space Race Game: A Web-Based Board Game for Aiding Students in Reviewing Thermochemistry, Chemical Equilibrium, and Chemical Kinetics

Nonequilibrium statistical mechanics of money/energy exchange models

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