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Transport properties describe how momentum (viscosity), energy (thermal conductivity), and matter (diffusion) move through gases. All three are governed by molecular collisions characterized by the mean free path λ = 1/(√2·π·d²·N/V) and the mean speed c̄ = (8kT/πm)1/2. Viscosity η = (1/3)ρc̄λ increases with temperature as √T (unlike liquids), because faster molecules carry momentum more effectively even as the mean free path shortens. Thermal conductivity κ = (1/3)ρc̄λC_V/M is proportional to η. Chapman-Enskog theory provides more accurate expressions using Lennard-Jones collision integrals that account for the real intermolecular potential.
Verify the √T temperature dependence of gas viscosity from kinetic theory, then compare to experimental data for N₂ and Ar. Observe that the predicted (η₁/η₂) = (m₁/m₂)1/2 mass ratio is approximately correct for isomers.
From kinetic theory, you know that gas molecules are in constant random motion, colliding with each other billions of times per second. Transport properties describe what happens when this random motion carries something — momentum, energy, or molecules themselves — from one region of the gas to another. The unifying idea is that each transport property arises from the same microscopic mechanism: molecules traveling an average distance λ (the mean free path) between collisions, carrying with them whatever macroscopic quantity varies across space.
Consider viscosity first. Imagine two parallel layers of gas moving at different speeds, like cards sliding over each other. Molecules randomly crossing between layers carry momentum from the faster layer to the slower one, effectively dragging the slow layer forward and the fast layer back. This molecular momentum transfer is viscosity. The kinetic theory result η = (1/3)ρc̄λ makes physical sense: viscosity increases with density ρ (more carriers), mean speed c̄ (faster delivery), and mean free path λ (each molecule carries momentum further before surrendering it in a collision). The counterintuitive prediction is the temperature dependence. In liquids, viscosity drops with temperature because thermal energy helps molecules overcome intermolecular attractions. In gases, there are no such attractions to overcome — instead, higher temperature means faster molecules that transport momentum more effectively. Since c̄ ∝ √T and λ also changes with T, the net result is that gas viscosity increases as √T.
Thermal conductivity κ follows the same logic, but now molecules carry kinetic energy rather than momentum across a temperature gradient. The formula κ = (1/3)ρc̄λC_V/M shows that thermal conductivity is essentially viscosity multiplied by the specific heat capacity per unit mass. This proportionality between η and κ is not a coincidence — both properties originate from the same collision dynamics, differing only in what quantity is being transported. Diffusion completes the triad: when a concentration gradient exists, random molecular motion produces a net flux of molecules from high to low concentration. The self-diffusion coefficient D = (1/3)c̄λ depends on the same mean speed and mean free path but not on density, because diffusion measures how fast individual molecules spread rather than how much momentum or energy the bulk gas transfers.
The simple kinetic theory expressions are approximate because they treat molecules as hard spheres with a fixed collision diameter. Real molecules interact through softer potentials — they attract at long range and repel sharply at short range, as described by the Lennard-Jones potential you encountered in intermolecular force models. Chapman-Enskog theory incorporates these realistic potentials through temperature-dependent collision integrals Ω, which account for the fact that glancing collisions at high relative velocity are less deflected than slow head-on ones. The resulting expressions predict transport properties to within a few percent of experimental values and correctly capture features that hard-sphere theory misses, such as the stronger-than-√T temperature dependence observed in real gases.