June 24, 2017
June 24, 2017
June 28, 2017
Engineering Physics & Physics
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.
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
ASEE holds the copyright on this document. It may be read by the public free of charge. Authors may archive their work on personal websites or in institutional repositories with the following citation: © 2017 American Society for Engineering Education. Other scholars may excerpt or quote from these materials with the same citation. When excerpting or quoting from Conference Proceedings, authors should, in addition to noting the ASEE copyright, list all the original authors and their institutions and name the host city of the conference. - Last updated April 1, 2015