Controlling the Velocity and Kinetic Energy of an Ideal Gas: An EWMA Control Chart and Its Average Run Length

An ideal gas is a gas in the form of a particle or molecule. Its velocity and kinetic energy are interesting topics in several studies in physical chemistry. This research aims to evaluate the average run length based on the exponentially weighted moving average statistic for its molecular velocity and kinetic energy of Maxwell-Boltzmann distribution. Derivation of the integral equation, which is equal to the average run length and numerical method of the integral equation, was applied to evaluate the average run length of a gas molecule’s molecular velocity and kinetic energy. The Trapezoidal rule as numerical method and its error was analyzed for approximation of average run length. The findings showed that the average run length of molecular velocity decreased in the higher temperature with the given mass of the molecule. Moreover, there was a decrease in the average run length of molecular kinetic energy in the higher temperature.

New Possibilities Provided by the Analysis of the Molecular Velocity Autocorrelation Function in Liquids

Long-time tails of the molecular velocity autocorrelation function (VACF) in liquid argon at temperatures higher and lower than the spinodal temperature have been analyzed. By considering the time dependence of the VACF, the self-diffusion and shear viscosity coefficients, and the Maxwell relaxation time are determined, as well as their changes when crossing the spinodal. It is shown that the characteristic changes in the temperature dependences of the indicated kinetic coefficients allow the spinodal position to be determined with a high accuracy. A possibility toapply the proposed method to other low-molecular liquids is considered. As an example, nitrogen and oxygen are used, for which the averaged potential of intermolecular interaction has the Lennard-Jones form.