Internal Pressures, Hard Core and Free Space Volumes and Boltzmann's Rule

Two fundamental relationships describing natural phenomena are posited to be functions of the free space in which atoms and molecules are confined and interact. These relationships are the Boltzmann energy distribution principle and the equation of state. In both cases the free space is that space available to the centers of mass of the atoms and molecules as they move randomly in translational motion. The hard core volume of atoms and molecules is not available for translational motion of their centers of mass and is excluded from the volume function in both Boltzmann's principle and the equation of state. Only in this way is it possible: 1) to apply Boltzmann's principle to the distribution of atoms or molecules between the two energy states of two phases in equilibrium; solid-gas, liquid-gas or solid-liquid and 2) to apply the equation of state to the gas, liquid or solid phase in order to determine the internal pressure exerted by the translational motion of atoms or molecules and to deduce the internal tension in the cohesion between atoms or molecules. These relationships are applied to water for the determination of the molar free space and molar hard core volumes of pure water.