Authors: Guido F. Nelissen
The kinetic theory defines the temperature of an ideal monatomic gas as a measure for the average translational kinetic energy of its particles. This definition ignores the fact that temperature is inevitably characterized by an isotropic distribution of the velocities of the particles over all possible directions and the continuous collisions and thermal radiation that this brings about. In this paper I first demonstrate that ‘the thermal energy’ of an ideal gas is in fact a mathematical expression of the total amount of isotropic momentum flow. This allows me to conclude that the pressure in an ideal gas is a measure for the average two-sided momentum flow across any unit area of the particle system and that the temperature of an ideal gas is a measure for the average two-sided momentum flow across any unit area of that gas, for a unit number density of its molecules, so that the temperature is in fact the pressure for a unit number density. In that way I am able to demonstrate that the Maxwell-Boltzmann speed distribution function is not the fundamental characteristic of thermal motion, but that it is a result of the all-sided collisions that are typical for systems consisting of elastic particles with isotropic motion.
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