THE SIZE OF MOLECULES We have seen that the kinetic theory explains the three phe nomen,z, of Conduction of Heat, Viscosity and Diffusion as all three depend on transport by molecules describing free paths. As a consequence the three coefficients of conduction of heat, of viscosity, and of diffusion are all proportional to the length of this free path, and a comparison of theoretical values of these coefficients with observational values provides three distinct means of evaluating the molecular free path. The validity and accuracy of the methods of the kinetic theory can be tested by examining whether the lengths of free path deduced from these different phenomena agree inter se. It is rather more convenient to discuss the values of the molecular radii, which are connected with the free path by formula (7), especially as this provides the further check of examining whether these agree with the values necessary to account for the observed deviations from Boyle's law.
The table below gives the values of the radii of the molecules of seven substances with which it is easy to experiment in the gaseous state, calculated from formulae provided by the kinetic theory of gases. For the formulae and method of calculation see J. H. Jeans, The Dynamical Theory of Gases, (4th ed.), chap. xiv., from which the following table is extracted.
Molecular Radii calculated from the Kinetic Theory of Gases The comparatively good agreement of the values obtained for the same quantity by entirely different methods provides satis factory confirmation of the truth of the molecular theory of matter as well as of the methods and formulae of the kinetic theory of gases. That the various values just tabulated do not agree even better need not cause surprise, in view of the fact that the quantities are calculated on the hypothesis that the molecules are spherical in shape. This hypothesis is introduced for the
sake of simplicity, but is known to be unjustifiable in fact. What is given by the formulae is accordingly the mean radius of an irregularly shaped solid (or, more probably, of the region in which the field of force surrounding such a solid is above a certain intensity), and the mean has to be taken in different ways in the different phenomena. This and the difficulty of obtaining accu rate experimental results fully account for the differences inter se in the values of the quantities calculated In general, the kinetic theory is found to give a satisfactory account of all physical phenomena which depend on the motions of molecules as a whole. In the closing decades of last century various attempts were made to apply the theory to problems of the internal dynamics of the molecule. The failure of the theory here was as striking as its success had been in its applications to the molecules as a whole. The reason of this failure is now satis factorily understood; it is simply that on passing to the interior of a molecule we encounter a new system of dynamics with which the kinetic theory is unable to deal. In brief, we pass from the province of the old classical kinetic theory of gases to the province of the modern quantum theory (see QUANTUM THEORY).