Thermal conductivity and resistivity
Gases

where σ {\displaystyle \sigma } is an effective particle diameter and Ω (T) {\displaystyle \Omega (T)} is a function of temperature whose explicit form depends on the interparticle interaction law. For rigid elastic spheres, Ω (T) {\displaystyle \Omega (T)} is independent of T {\displaystyle T} and very close to 1 {\displaystyle 1}. More complex interaction laws introduce a weak temperature dependence. The precise nature of the dependence is not always easy to discern, however, as Ω (T) {\displaystyle \Omega (T)} is defined as a multi-dimensional integral which may not be expressible in terms of elementary functions, but must be evaluated numerically. However, for particles interacting through a Mie potential (a generalisation of the Lennard-Jones potential) highly accurate correlations for Ω (T) {\displaystyle \Omega (T)} in terms of reduced units have been developed.
length_constraints:number_paragraphs[5], oulipo:avoid_letter[o]