Boltzmann Gas

In classical microscopic gas kinetic theory a gas is modeled as an ensemble of hard spheres that do not interact other than by elastic collisions among themselves and with the container walls. If the walls are at a temperature , then the particles' velocity components –in the case of thermodynamic equilibrium—obey Maxwell–Boltzmann distributions, for which the probability that a given velocity component, , lies in the interval is given by

where is the mass of the atom and is the Boltzmann constant (see also The Maxwell Speed Distribution). According to the equipartition theorem, the average kinetic energy of each atom is , which shows that, at the microscopic level, the temperature is a direct measure of the energy associated with the disordered atomic motion. The atomic collisions with the container walls are at the origin of the force exerted on the wall that is commonly expressed as the gas pressure (see also Simulation of a Simple Gas Pressure Model). The temperature here is measured in Kelvin (K), and in classical theory all motion comes to a halt at the absolute zero of temperature (). The absolute (Kelvin) temperature scale is related to the most commonly used temperature scales of Celsius and Fahrenheit by simple linear relations (see also Temperature Scales and Celsius and Fahrenheit Thermometers).