 Solution

A thermocouple uses two materials with different Seebeck coefficients. With their junctions at different temperatures, the net open-circuit voltage isUsing p-type and n-type legs makes the two contributions add. Many pairs can be connected electrically in series to add voltage while remaining thermally in parallel between the same hot and cold plates. A single homogeneous wire does not provide this same complete-circuit voltage when its return lead has the same thermopower.

The reciprocal Peltier effect transports heat when electric current passes through a junction. The Kelvin relation $\Pi =\alpha T$ connects the heat carried per unit charge to the Seebeck coefficient. The same combination of large thermopower, high electrical conductivity and low thermal conductivity gives a favorable dimensionless figure of meritThus materials useful for a generator are also useful for a cooler when electric current is driven in the appropriate direction. Joule heating and thermal leakage oppose cooling; device geometry, contact resistance and operating temperature must still be appropriate. Reversibility of the thermoelectric coupling does not make either device lossless.