Visualizing the Kinetic Theory of Gases by Student-created Computer Programs

Guenter Bischof; Christian J. Steinmann

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Conference: 2017 ASEE Annual Conference & Exposition
Location: Columbus, Ohio
Publication Date: June 24, 2017
Start Date: June 24, 2017
End Date: June 28, 2017
Conference Session: Engineering Physics & Physics Division Technical Session 4
Tagged Division: Engineering Physics & Physics
Page Count: 12
DOI: 10.18260/1-2--29109
Permanent URL: https://peer.asee.org/29109
Download Count: 1831

Paper Authors

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Guenter Bischof Joanneum University of Applied Sciences

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Throughout his career, Dr. Günter Bischof has combined his interest in science and engineering application. He studied physics at the University of Vienna, Austria, and acquired industry experience as development engineer at Siemens Corporation. Currently he teaches Engineering Mathematics at Joanneum University of Applied Sciences. His research interests focus on automotive engineering, materials physics, and on engineering education.

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Christian J. Steinmann HM&S IT-Consulting

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Christian Steinmann has an engineer degree in mathematics from the Technical University Graz, where he focused on software quality and software development process assessment and improvement. He is manager of HM&S IT-Consulting and provides services for SPiCE/ISO 15504 and CMMI for development as a SEI-certified instructor. He performed more than 100 process assessments in software development departments for different companies in the finance, insurance, research, automotive, and automation sector. Currently, his main occupation is a consulting project for process improvement for safety related embedded software development for an automobile manufacturer. On Fridays, he is teaching computer science introductory and programming courses at Joanneum University of Applied Sciences in Graz, Austria.

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Abstract

Most introductory thermodynamics courses use the historical derivation of thermodynamics that relies on macroscopic properties of substances. Classical thermodynamics is a phenomenological theory; it studies the properties of a thermodynamic system without going into the mechanism of the observed phenomena. The thermodynamic state of a system is given by a limited number of thermodynamic variables, like the volume of the system and its temperature, and studies the dependence of quantities like pressure, energy, and entropy on these variables.

On the other hand, the kinetic theory of gases attempts to describe the macroscopic properties in terms of a microscopic picture of the gas as a collection of a large number of particles in motion. The particles collide elastically with each other and with the walls of the container, and the pressure exerted by the gas is due to the elastic collisions of the particles with the walls. In equilibrium, this pressure is equal throughout the gas, and the kinetic theory predicts that the pressure is proportional to the number of particles per unit volume and to their average kinetic energy. By identifying the absolute temperature as the average kinetic energy of the particles, Boyle’s pressure-volume law and Amontons' pressure-temperature law can be derived. Thus, the application of the laws of mechanics to the microscopic constituents of a macroscopic system predicts, with the aid of statistical techniques, the behavior of the system in agreement with experimental observation.

Computer programs that simulate and visualize the kinetic theory of gases within the hard sphere model have been developed within the framework of undergraduate student projects. The C# simulations use a freely selectable number of particles to simulate the molecules of an ideal gas in a two-dimensional container. The particles are considered as small hard spheres and collide with each other and with the walls of the container. At impact, they exchange momentum and energy according to the rules of elastic collision. One wall is replaced by a piston that is loaded either by gravity or by a spring force. This piston moves when the velocity of the particles is changed and increases or decreases the volume in the simulation. In this way, the ideal gas law can be tested. In addition, the distribution of molecular speeds is plotted as a function of time, thus depicting the gradual transformation of an initially uniform particle speed distribution into a two-dimensional Maxwell-Boltzmann distribution.

In this paper the theoretical approach to the problem and the outcome of the student projects will be presented. The dynamic visual output of the program can increase and enhance understanding of various thermodynamic phenomena and is therefore well suited as a teaching aid.

Citation
Format

Bischof, G., & Steinmann, C. J. (2017, June), Visualizing the Kinetic Theory of Gases by Student-created Computer Programs Paper presented at 2017 ASEE Annual Conference & Exposition, Columbus, Ohio. 10.18260/1-2--29109

TY - CPAPER
AB - Most introductory thermodynamics courses use the historical derivation of thermodynamics that relies on macroscopic properties of substances. Classical thermodynamics is a phenomenological theory; it studies the properties of a thermodynamic system without going into the mechanism of the observed phenomena. The thermodynamic state of a system is given by a limited number of thermodynamic variables, like the volume of the system and its temperature, and studies the dependence of quantities like pressure, energy, and entropy on these variables.

On the other hand, the kinetic theory of gases attempts to describe the macroscopic properties in terms of a microscopic picture of the gas as a collection of a large number of particles in motion. The particles collide elastically with each other and with the walls of the container, and the pressure exerted by the gas is due to the elastic collisions of the particles with the walls. In equilibrium, this pressure is equal throughout the gas, and the kinetic theory predicts that the pressure is proportional to the number of particles per unit volume and to their average kinetic energy. By identifying the absolute temperature as the average kinetic energy of the particles, Boyle’s pressure-volume law and Amontons&#39; pressure-temperature law can be derived. Thus, the application of the laws of mechanics to the microscopic constituents of a macroscopic system predicts, with the aid of statistical techniques, the behavior of the system in agreement with experimental observation.

Computer programs that simulate and visualize the kinetic theory of gases within the hard sphere model have been developed within the framework of undergraduate student projects. The C# simulations use a freely selectable number of particles to simulate the molecules of an ideal gas in a two-dimensional container. The particles are considered as small hard spheres and collide with each other and with the walls of the container. At impact, they exchange momentum and energy according to the rules of elastic collision. One wall is replaced by a piston that is loaded either by gravity or by a spring force. This piston moves when the velocity of the particles is changed and increases or decreases the volume in the simulation. In this way, the ideal gas law can be tested. In addition, the distribution of molecular speeds is plotted as a function of time, thus depicting the gradual transformation of an initially uniform particle speed distribution into a two-dimensional Maxwell-Boltzmann distribution.

In this paper the theoretical approach to the problem and the outcome of the student projects will be presented. The dynamic visual output of the program can increase and enhance understanding of various thermodynamic phenomena and is therefore well suited as a teaching aid.

AU - Guenter Bischof
AU - Christian J. Steinmann
CY - Columbus, Ohio
DA - 2017/06/24
PB - ASEE Conferences
TI - Visualizing the Kinetic Theory of Gases by Student-created Computer Programs
UR - https://peer.asee.org/29109
DO - 10.18260/1-2--29109
ER -