LII.The properties of fluids

Abstract

Abstract In continuation of previous work on the properties of liquids, as systems of attracting molecules, Maxwell's kinetic theory is extended to the properties of associated liquids. Maxwell's law of the distribution of molecular velocities, contains an undetermined coefficient, α, the most probable speed of the molecules. The equation is adapted to the properties of gases by defining temperature as equal to the mean kinetic energy of a molecule of an ideal gas, i. e. by putting where C is the mean kinetic energy velocity, which Maxwell showed to be equal to In a liquid, whose attracting molecules are mostly less than a molecular diameter apart, their average velocity is necessarily groater than in an ideal gas, where, by analogy with hydrogen, the molecules are three thousand times as far apart. By putting the most probable speed, α, equal to λP, where P is the most probable speed in an ideal gas, and allowing for the greater molecular volume of an associated liquid, Maxwell's law gives inevitably as the general equation of state of a fluid. Since p is negligible compared with K, the cohesion of the liquid, we have at once from which λ is known, because K is given by Edser's law of force, and A can be calculated from the latent heat or viscosity, and b can be determined from any other property of a liquid. With the aid of this equation, the latent heat, vapour pressure and viscosity of associated liquids are determined by straightforward Newtonian dynamics, without the introduction of any arbitrary constants. The method is applied also to the thermal conductivity and viscosity of gases. The resulting formulæ give values accurate to two significant figures. So we see that Edser's law of molecular attraction determines the properties of liquids, as the law of gravitation rules the motions of the heavenly bodies and Newton's principle of strict causality extends to both.