= Solution
The <dynamic viscosity> measures the transport of tangential <momentum> between adjacent layers. The <kinetic estimates of gas transport coefficients> give
$$
\eta\sim\frac13nm\overline v\lambda,\qquad
\lambda\sim\frac1{\sqrt2n\sigma_c},\qquad
\overline v\propto\sqrt{\frac{k_BT}{m}},
$$
where $n$ 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 \b[the <dynamic viscosity> of a dilute gas is approximately independent of <pressure>].
For a temperature-independent collision <cross section>, the same estimate gives $\eta\propto\sqrt{mk_BT}/\sigma_c$, so \b[$\eta\propto T^{1/2}$ 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>.
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