The value of ?AB can be

positive or negative. Positive value means the electromotive force moves the

electric current from the hot junction of metal A to the cooler junction.

The

next thermoelectric effect was found thirteen years later, the Peltier effect. This

effect was observed by J. Peltier. He found that the current passes through

different metals caused the temperature difference at the junction of the

metals. The differential Peltier coefficient, ?AB, is defined as the

ratio between the heating rate of each junction to the applied current:

(2)

With q is the heating rate and I

is the applied current. The value of ?AB can be written as ?B – ?A, or the difference

between the Peltier coefficient between metal B and metal A. This effect can be

applied for cooling purpose. If ?B –

?A is negative, the value of q will be negative, therefore heat is

absorbed. This can be explained when ?B < ?A, the
electrons move from higher density region into the lower density region, and followed
by expansion, lowering the temperature.
The
dependency of these effect one to the other was first studied by Thomson in
1855. Thomson found two relationships that relate thermoelectric effects, one
with the other. The first one is that the Peltier coefficient is the
multiplication between Seebeck coefficient and Temperature or can be written:
(3)
The other relationship
is between Thomson coefficient and Seebeck coefficient. Can be written as:
(4)
Where ? is the
Thomson coefficient. This equation is helpful if we want to find a Seebeck
coefficient of a material, because usually Seebeck coefficient is found by
connecting the material with a superconductor that has zero Seebeck
coefficient. This method by using a superconductor is only applicable at sufficiently
low temperature because the superconductivity of a material might not last at
higher temperature. With Thomson relationship, it is possible to find the
Seebeck coefficient at high temperature