Controlling the Velocity and Kinetic Energy of an Ideal Gas: An EWMA Control Chart and Its Average Run Length
Keywords:Maxwell-Boltzmann distribution, Average run length, Integral equation, Ideal gas, Molecular velocity, Kinetic energy
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.
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