Graham’s law of diffusion: Quantum analogy and non-ideality

Abstract

We focus attention on two equivalent forms of Graham’s law of diffusion that is valid for an ideal gas mixture. This equivalence is shown to be lost by the empirical equations of state in presence of an attractive nonideality. The modified forms are noted. We then construct a simple quantum mechanical model to simulate these results and obtain a one-to-one correspondence. We see how these equations of interest may be extended to D-dimensions. By employing the quantum model, we next observe the equivalence of the results found above with those obtained via statistical mechanics. As an added advantage, we demonstrate that the virial theorem for confined quantum stationary states retains its validity in the statistical domain too, though here the averaging scheme is correspondingly different.