Four bench procedures are carried out on the same metal bar at a fixed mean temperature
PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Condensed Matter, Materials & Soft Matter · Electronic transport in solids
Solid State Physics, Ch Two currents, two forces: Wiedemann-Franz and thermoelectricity
Problem
Four bench procedures are carried out on the same metal bar at a fixed mean temperature. Setup A: the bar is kept at uniform temperature, a small field is applied along its length, and the resulting current is measured. Setup B: one end is heated, the circuit is left open (no current flows), and the voltage between the ends is measured once it settles. Setup C: one end is heated and the current is forced to zero by an external circuit; the steady heat input needed to maintain the temperature difference is measured. Setup D: the bar is joined to a different metal, both are held at the same uniform temperature, a current is passed across the junction, and the rate of heat absorption or release at the junction is measured.
((a)) Identify which of σ, S, κ or Π each setup measures, and state the condition on the charge current or on ∇T that defines each one.
((b)) Setup C does not directly give L22 from the coupled-transport equations. Write the relation between the measured κ and L22, and explain in words why the difference is unavoidable given the boundary condition of the measurement.