Distribution of Molecules by Kinetic Energy Revisited

Abstract. The distribution of the molecules by their kinetic energy is treated from statistical point of view. Boltzmann's formula for the distribution of the molecules by energy was found as a limit case of digamma function. Maxwell's formula for the ideal monoatomic gas was derived directly from Boltzmann's main result without employing other sketch formulas. The analytical formulas for two speeds- one real and the other virtual- of molecules were obtained for the case when the molecules carry the kinetic energy in more than three independent components, like in polyatomic molecules. Analysis of the generalized distribution function of the molecules by their virtual speeds indicated that certain molecular states the reach a highest mode in the distribution of the molecules by their virtual speed for a deterministic value of the energy components