A student argues: "copper's electrons each have kinetic energy

PHYSICS · Subjective · Fermi University Physics · Thermal, Statistical & Complex Systems · Condensed Matter, Materials & Soft Matter · Free electrons, energy bands and electronic structure

Condensed Matter Physics, Ch The free-electron gas: what Drude gets right and what only Fermi fixes

Problem

A student argues: "copper's electrons each have kinetic energy EF=7.03 eVE_F=7.03\,\mathrm{eV}, and EFE_F barely changes with temperature, so the electronic heat capacity should be zero." Identify the two errors in this reasoning, and state copper's predicted electronic heat capacity at 300 K300\,\mathrm{K}, using γ=0.503 mJ mol−1K−2\gamma=0.503\,\mathrm{mJ\,mol^{-1}K^{-2}}.

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