James Clerk Maxwell on Rudolf Clausius

“The equation of Clausius to which I must now call your attention is of the following formpV=frac{2}{3}T-frac{2}{3}sumsum(frac{1}{2}Rr).Here p denotes the pressure of a fluid, and V the volume of the vessel which contains it. The product pV, in the case of gases at constant temperature, remains, as Boyle's Law tells us, nearly constant for different volumes and pressures. ...The other member of the equation consists of two terms, the first depending on the motion of the particles, and the second on the forces with which they act on each other. The quantity T is the kinetic energy of the system... that part of the energy which is due to the motion of the parts of the system. ...In the second term, r is the distance between any two particles, and R is the attraction between them. ...The quantity ½Rr or half the product of the attraction into the distance across which the attraction is exerted is defined by Clausius as the virial of the attraction. ∑∑(½Rr)... indicates that the value of ½Rr is to be found for every pair of particles and the results added together. Clausius has established this equation by a very simple mathematical process... it indicates two causes which may affect the pressure of the fluid on the vessel which contains it... We may therefore attribute the pressure of a fluid either to the motion of its particles or to a repulsion between them.”

“To him we are indebted for the conception of the mean length of the path of a molecule of a gas between its successive encounters with other molecules. As soon as it was seen how each molecule, after describing an exceedingly short path, encounters another, and then describes a new path in a quite different direction, it became evident that the rate of diffusion of gases depends not merely on the velocity of the molecules, but on the distance they travel between each encounter.”

“He opened up a new field of mathematical physics by shewing how to deal mathematically with moving systems of innumerable molecules.”