Peltier & Thomson Effects

Run the Seebeck effect backwards and a current can pump heat from one junction to another. Two more effects, Peltier’s and Thomson’s, together explain where the thermo-emf comes from.

The Peltier effect#

Keep both junctions of a thermocouple at the same temperature and drive a current round it with a battery. One junction warms and the other cools. Reverse the current and they swap. This reverse of the Seebeck effect is the Peltier effect. The heat absorbed or released at a junction is proportional to the charge that passes through it.

The Thomson effect#

Now take a single metal wire whose temperature varies along its length and pass a current through it. Some sections absorb or give out heat in addition to the Joule heat i²Rt. This is the Thomson effect. For a small section with temperature difference ΔT between its ends, carrying charge ΔQ:

σ is positive if heat is absorbed when current flows from the cold end to the hot end (copper, silver, zinc, antimony, cadmium). It is negative for iron, cobalt, nickel, bismuth and platinum, and nearly zero for lead.

Explaining all three#

• Peltier: different metals have different free-electron densities. At a junction electrons diffuse from the denser side, building up an emf, the Peltier emf. Driving current through it does positive or negative work on the carriers, releasing or absorbing heat.
• Thomson: in an unevenly heated metal the electron density varies from place to place, so electrons diffuse and an emf appears between hot and cold parts. Current forced through it again gives or takes heat.
• Seebeck: the Peltier emf depends on temperature. With the junctions at equal temperatures the two Peltier emfs cancel; at different temperatures they don’t. Each metal also has a temperature gradient, giving Thomson emfs that differ between the two metals.