Use the Drude formula σ=ne2τ/me in the Mott formula (8.178), and assume that the scattering time τ has no energy dependence. In this case the only dependence of σ on the (Fermi) energy ϵ comes from the electron density n. Show in this case that the thermopower at low temperatures obeys
Q=−NeeS,(8.180)
where Ne is the number of conduction electrons and S is the entropy they carry. Miraculously, the scattering time τ does not appear in this expression!