Thermoelectric Effect Peltier Seebeck and Thomson

Uri Lachish, guma science

Abstract: A simple model system is generated to derive explicit thermoelectric effect expressions for Peltier, Seebeck and Thomson. The model applies an n-type semiconductor junction with two different charge-carrier concentration nL and nR. Peltier effect and Seebeck effect are calculated by applying a reversible closed Carnot cycle, and Thomson effect by the Boltzmann transport equation.

Peltier's heat rate for the electric current I is:               dQ/dt=(ΠA-ΠB ) I.

Peltier's coefficients calculated by the model are:       ΠA=(kT/e)ln(nL)       ΠB=(kT/e)ln(nR).

Seebeck's EMF of two junctions at different temperatures TH and TC is:          V=-S(TH-TC).

Seebeck's coefficient calculated by the model is:       S=(k/e) ln(nL/nR ).

Thomson's heat rate for the current density J is:        dq/dt=-K J ΔT.

Thomson's coefficient calculated by the model is:      K=(3/2)(k/e).

Seebeck effect and Peltier effect are discussed by applying a Carnot cycle in order to show that they are basically reversible thermodynamic processes. Discussing them in terms of non-equilibrium irreversible theories is meaningless.

Thomson's (Kelvin's) second relation, K=T dS/dT, does not comply with these calculated coefficients. According to the relation there should not be Thomson heat for a linear Seebeck effect, that is, when Seebeck's EMF is linear with the temperature difference, or equivalently, when Seebeck's coefficient is temperature independent. Linearity is observed in literature data. But yet, when charge carriers enter a wire at a cold end, and leave it at a hot end, their heat content changes and they must cool the wire or absorb heat from its vicinity. So that Thomson effect can't be reduced to zero even for the linear case.

Full web page: Thermoelectric Effect Peltier Seebeck and Thomson

Conclusions:
Charge flow within a conductor involves two irreversible processes where energy gained from the electric field is transferred to the conductor, heat conduction and Thomson heating. The Thomson effect takes place in a steady state system of heat flow rather than in an equilibrium system. However, reversing the current direction will reverse the direction of Thomson heat flow. This property is shared with reversible processes.

Seebeck's calculated EMF varies linearly with the temperature difference and its corresponding coefficient is a constant that does not depend on the temperature. According to the second Thomson relation there should not be Thomson heat for a linear effect. But yet, when charge carriers enter a wire at a cold end, and leave it at a hot end, their heat content changes and they must cool it or absorb heat from its vicinity. So that Thomson effect can't be reduced to zero.

Thermoelectric effects in systems are much more complicated than the presented simple model. In metals only electrons with energy within a few kT around the Fermi energy contribute to the current, and their number is strongly temperature dependent, mainly at low temperatures. In addition, their thermal energy is not that of free particles. Yet, Seebeck effect and Peltier effect are basically reversible thermodynamic processes. Discussing them in terms of non-equilibrium irreversible theories is meaningless.


On the net: February, 2014.

By the author:

  1. "Thermoelectric Effects Peltier Seebeck and Thomson",
    Abstract: http://urila.tripod.com/Thermoelectric_abstract.htm
    Full page: http://urila.tripod.com/Thermoelectric.pdf, February 2014.
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