On Van der Waals's Treatment of Laplace's Pressure in the Virial Equation: A Letter to Prof. Tait

Abstract

MY DEAR PROF. TAIT,—In Part IV. of your “Foundations of the Kinetic Theory of Gases,”¹ you take exception to the manner in which Van der Waals has introduced Laplace's intrinsic pressure K into the equation of virial. “I do not profess to be able fully to comprehend the arguments by which Van der Waals attempts to justify the mode in which he obtains the above equation. Their nature is somewhat as follows:—He repeats a good deal of Laplace's capillary work, in which the existence of a large, but unknown, internal molecular pressure is established, entirely from a statical point of view. He then gives reasons (which seem, on the whole, satisfactory from this point of view) for assuming that the magnitude of this force is as the square of the density of the aggregate of particles considered. But his justification of the introduction of the term a/v² into an account already closed, as it were, escapes me. He seems to treat the surface-skin of the group of particles as if it were an additional bounding-surface, exerting an additional and enormous pressure on the contents. Even were this justifiable, nothing could justify the multiplying of this term by (v — β) instead of by v alone. But the whole procedure is erroneous. If one begins with the virial equation, one must keep strictly to the assumptions made in obtaining it, and consequently everything connected with molecular force, whether of attraction or of elastic resistance, must be extracted from the term. Σ(Rr).”