Chapter 7 used the kinetic formula with copper's measured molar heat capacity ( ,…

PHYSICS · Subjective · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Lattice dynamics and thermal properties of solids · Electronic transport in solids

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

Problem

Chapter 7 used the kinetic formula κ=13cVvℓ\kappa=\tfrac13c_Vv\ell with copper's measured molar heat capacity (CV=24.4 J mol−1K−1C_V=24.4\,\mathrm{J\,mol^{-1}K^{-1}}, Chapter 6), its molar volume (Vm=7.11×10−6 m3 mol−1V_m=7.11\times10^{-6}\,\mathrm{m^3\,mol^{-1}}) and an average sound speed (vˉ=2612 m s−1\bar v=2612\,\mathrm{m\,s^{-1}}, Chapter 6) to estimate copper's lattice-only thermal conductivity, borrowing a phonon mean free path of 33 to 5 nm5\,\mathrm{nm} from the insulators: the result was 99 to 15 W m−1K−115\,\mathrm{W\,m^{-1}K^{-1}}. Using this chapter's Wiedemann-Franz prediction and copper's resistivity ρe=1.70×10−8 Ω m\rho_e=1.70\times10^{-8}\,\Omega\,\mathrm{m} at 295 K295\,\mathrm{K}, find copper's electronic thermal conductivity, and say what percentage of copper's measured total thermal conductivity (400 W m−1K−1400\,\mathrm{W\,m^{-1}K^{-1}}) the lattice, by Chapter 7's own estimate, could ever supply.

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