Dalton's law as implying that "every gas is as a vacuum to every other gas,"[1] his anticipation of van't Hoff's equation in the form of Henry's law for dilute solutions of gases in liquids [2]and his genial discussion of gas-mixtures, known in Germany as,
The Paradox of Gibbs.[3]—If two different gases which can be separated reversibly by quicklime or other process are allowed to mix, a certain definite amount of work or available energy will be gained; but if two gases, which are in every respect identical, are allowed to mix, they could not be separated by any reversible process and there would consequently be no gain of available energy in their mixing nor any dissipation of energy (increase of entropy). But if we suppose two gases which differ only infinitesimally to mix, the first condition would still obtain and there would still be a certain gain of available energy. The question arises, what will happen if we proceed to the limit? Maxwell explained this paradox by saying that our ideas of dissipation of energy depend upon the extent of our knowledge of the subject. Could we invoke Maxwell's demon and borrow his gift of molecular vision, we should perceive that when two identical gases mix there is in reality a complete dissipation of energy, which the demon's intelligence might turn into available energy if he liked; for "it is only to a being in the intermediate stage who can lay hold of some forms of energy, while others elude his grasp, that energy appears to be passing inevitably from the available to the dissipated state."[4] In the reasoning of energetics, the paradox is explained by saying[5] that the more nearly alike the gases are, the slower will be the process of diffusion, so that work or available energy might indeed be gained, but only after the lapse of indefinite or infinite time, if we have such time at our disposal.
Theory of Capillarity, Liquid Films and Interfacial Phenomena.—There are two important theories of capillary action, that of Laplace, based upon the assumption that the play of molecular forces in a liquid is only possible at insensible or ultra-micrometric distances, and that of Gauss, based upon the doctrine of energy. Gibbs's exhaustive discussion of capillarity, which takes up at least one third of his memoir, is the thermodynamic or chemical completion of the purely dynamic theory of Gauss. A capillary film or interfacial layer forms a new "phase" between the two substances on either side of it, and the mathematical condition for the formation of a new chemical substance at such an interface or "surface of discontinuity" is expressible as an algebraic relation between the surface tensions of the three layers of substance and the pressure of the three phases,[6] the surface tensions
