The kinetic theory of gases relates the kinetic energy of a gas to the temperature. This relation is perhaps the most basic aspect of transport properties. The temperature dependence in transport phenomena most often arises from the increase in velocity of particles proportional to (square root) of temperature. Therefore, we present a more formal discussion of the kinetic theory of gases than that discussed previously. We include the Maxwell-Boltzmann distribution function, which tells how velocities are distributed as a function of temperature. This is the basis for the calculation of the root-mean-square speed of a gas. The M-B distribution also tells us that the variance of the velocity distribution increases with the temperature as well.
We can describe diffusion using Fick's first and second law. Fick's first law states that the flux, J, is proportional to change in concentration with distance (i.e. the concentration gradient, dc/dz). The constant of proportionality is the diffusion coefficient, D. The flux is the number of particles passing through a given area per second. So the law is J = -D dc/dz. Fick's second law describes the process of spreading such as the diffusion of ink in a beaker shown above. That law relates both time and spatial distribution dc/dt = D d2c/dz2.
