Past exam of the physics B course of the University of Cambridge / 2015 / Paper 1 / Section A / A3

The dynamic viscosity measures the transport of tangential momentum between adjacent layers. The kinetic estimates of gas transport coefficients givewhere $n$ is number density, $m$ the molecular mass, $\lambda$ the mean free path, and ${\sigma }_c$ a collision cross section. At fixed temperature, raising the pressure increases the number of momentum carriers but shortens their mean free path by the same factor. Consequently the dynamic viscosity of a dilute gas is approximately independent of pressure.

For a temperature-independent collision cross section, the same estimate gives $\eta \propto \sqrt{m{k}_{B}T}/{\sigma }_c$, so $\eta \propto T^{1/2}$ in the hard-sphere model. Faster molecules carry momentum across layers more rapidly. Real intermolecular interactions make the effective collision cross section temperature-dependent, changing this simple exponent. The pressure-independence also fails when wall collisions, rather than molecule–molecule collisions, set the transport distance; the continuum estimate assumes a small Knudsen number.