The thermoelectric effect is the direct conversion of temperature differences to electric voltage or the other way around. It is the mechanism behind devices such as thermoelectric coolers for electronic cooling or portable refrigerators. While
Joule heating (resistive heating) is an irreversible phenomena, the thermoelectric effect is in principle reversible. Historically, the thermoelectric effect is known under three different names, reflecting its discovery in experiments by Seebeck, Peltier, and Thomson. The
Seebeck effect is the conversion of temperature differences into electricity, the
Peltier effect is the conversion of electricity to temperature differences, while the
Thomson effect is heat produced by the product of current density and temperature gradients. These three effects are thermodynamically related by the Thomson relations:
where P is the Peltier coefficient (SI unit:
V),
S is the Seebeck coefficient (SI unit: V/K),
T is the temperature (SI unit: K), and
μ is the Thomson coefficient (SI unit: V/K). These relations show that all three effects can be considered as one and the same effect. This example primarily uses the Seebeck coefficient and also, merely as an intermediate variable, the Peltier coefficient. The Thomson coefficient is not used.
where E is the electric field and
Q is the Joule heating.
where ρ is the density,
C is the heat capacity, and
ρc is the space charge density. In this example, consider the stationary case only:
