Treat metallic sodium as a free-electron metal with Fermi energy

PHYSICS · Subjective · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Electronic transport in solids · Electronic transport in solids

Solid State Physics, Ch Two currents, two forces: Wiedemann-Franz and thermoelectricity

Problem

Treat metallic sodium as a free-electron metal with Fermi energy EF=3.24 eVE_F=3.24\,\mathrm{eV}. Using the free-electron form of the Mott formula, ∣S∣=π22kBekBTEF|S|=\dfrac{\pi^2}{2}\dfrac{k_B}{e}\dfrac{k_BT}{E_F}, estimate the Seebeck coefficient of sodium at T=300 KT=300\,\mathrm{K}, stating its predicted sign. Take kB/e=86.2 μV K−1k_B/e=86.2\,\mu\mathrm{V\,K^{-1}} and kBT=0.02585 eVk_BT=0.02585\,\mathrm{eV} at 300 K300\,\mathrm{K}.

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