Simulating kinetic theory of gases

Contact: Omid Etesami
Room: BC 150
Tel: 36793
Email: omid [dot] etesami

A simple model to relate macroscopic properties of gases to the microscopic properties of their molecules is the kinetic model for gases. (See for example Feynman Lectures on Physics, Volume 1, Chapter 39, “Kinetic theory of gases”). For simplicity, you can assume that the gas is monatomic like Helium. Then, you can think of the gas as a lot of small balls (atoms) colliding to each other or colliding to the container elastically. These collisions constantly change the directions of the movement of the balls.

The goal of this project is to simulate such a system. You can then see 1. the relation between pressure and average kinetic energy, 2. the velocity distribution of the molecules, 3. the time it takes that the distribution of velocities approaches the final so-called equilibrium distribution.

The simulation can be generalized in many ways:

1. You can consider two different types of molecules in the same container, for example, both Helium and Argon. You can verify that the molecule with more mass has on average a smaller velocity.

2. You can consider polyatomic molecules by modeling each molecule as a bunch of atoms connected together with sticks. Then, there will be rotational as well as translational movements. You can then check the “equipartition theorem” that relates the average rotational energy to the average translational energy. You can further generalize the model by letting springs, instead of sticks, connect the atoms.

3. You can add pistons that allow interaction between two containers. Then, you can verify that the piston equalizes the average kinetic energy of the molecules in the two containers.

The prerequisite for this project is the ability to find algorithms and data structures to simulate the model efficiently + knowing the basic probability required to analyze the results of the simulation.