## When hot junction of metal A to the

When the deflection of
the needle was observed, Seebeck believe it was caused by the magnetism induced
by the temperature difference between the junction. That is why initially this
effect was called thermo-magnetic effect. It was later found by a Danish
physicist Hans Christian Orsted, that the deflection of the needle was caused
by electrical currents that produced when the temperature difference was
applied between two junctions of the metals 3. According to the Ampere’s law,
this electrical current induces a magnetic field around the closed loop, thus
deflects the compass needle. Suppose the temperature at hotter side is T1
and at the cooler side is T2, the differential Seebeck coefficient,
?AB, is the potential difference (V) divided by temperature
difference, ?T (T1-T2).

(1)

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 3,16.