Seeback Effect
Category : JEE Main & Advanced
(1) Definition : When the two junctions of a thermo couple are maintained at different temperatures, then a current starts flowing through the loop known as thermo electric current. The potential difference between the junctions is called thermo electric emf which is of the order of a few micro-volts per degree temperature difference \[(\mu V{{/}^{o}}C)\].
(2) Seebeck series : The magnitude and direction of thermo emf in a thermocouple depends not only on the temperature difference between the hot and cold junctions but also on the nature of metals constituting the thermo couple.
(i) Seebeck arranged different metals in the decreasing order of their electron density. Few metals forming the series are as below.
Sb, Fe, Cd, Zn, Ag, Au, Cr, Sn, Pb, Hg, Mn, Cu, Pt, Co, Ni, Bi
(ii) Thermo electric emf is directly proportional to the distance between the two metals in series. Farther the metals in the series forming the thermo couple greater is the thermo emf. Thus maximum thermo emf is obtained for Sb-Bi thermo couple.
(iii) The current flow at the hot junction of the thermocouple is from the metal occurring later in the series towards that occurring earlier, Thus, in the copper-iron thermocouple the current flows from copper (Cu) to iron (Fe) at the hot junction. This may be remembered easily by the hot coffee.
(3) Variation of thermo emf with temperature : In a thermocouple as the temperature of the hot junction increases keeping the cold junction at constant temperature (say \[{{0}^{o}}C\]). The thermo emf increases till it becomes maximum at a certain temperature.
(i) Thermo electric emf is given by the equation \[E=\alpha \,t+\frac{1}{2}\beta \,{{t}^{2}}\] where \[\alpha \] and \[\beta \] are thermo electric constant having units are volt/\[^{o}C\] and volt/\[^{o}{{C}^{2}}\] respectively (t = temperature of hot junction). For E to be maximum (at \[t={{t}_{n}}\])
\[\frac{dE}{dt}=0\] i.e.\[\alpha +\beta \,{{t}_{n}}=0\Rightarrow {{t}_{n}}=-\frac{\alpha }{\beta }\]
(ii) The temperature of hot junction at which thermo emf becomes maximum is called neutral temperature \[({{t}_{n}})\]. Neutral temperature is constant for a thermo couple (e.g. for \[Cu-Fe,\,\,{{t}_{n}}={{270}^{o}}C\])
(iii) Neutral temperature is independent of the temperature of cold junction.
(iv) If temperature of hot junction increases beyond neutral temperature, thermo emf start decreasing and at a particular temperature it becomes zero, on heating slightly further, the direction of emf is reversed. This temperature of hot junction is called temperature of inversion \[({{t}_{i}})\].
(v) Relation between \[{{t}_{n}},\,{{t}_{i}}\] and \[{{t}_{c}}\] is \[{{t}_{n}}=\frac{{{t}_{i}}+{{t}_{c}}}{2}\]
(4) Thermo electric power : The rate of change of thermo emf with the change in the temperature of the hot junction is called thermoelectric power.
It is also given by the slope of parabolic curve representing the variation of thermo emf with temperature of the hot junction, as discussed in previous section.
The thermo electric power \[\left( \frac{dE}{dt} \right)\] is also called Seebeck coefficient. Differentiating both sides of the equation of thermo emf with respect to t, we have thermoelectric power \[P=\frac{dE}{dt}=\frac{d}{dt}(\alpha \,t+\frac{1}{2}\beta \,{{t}^{2}})\]
\[\Rightarrow \]\[P=\alpha +\beta \,t\]
The equation of the thermo electric power is of the type \[y=mx+c,\] so the graph of thermo electric power is as shown.
(5) Laws of thermoelectricity
(i) Law of successive temperature : If initially temperature limits of the cold and the hot junction are \[{{t}_{1}}\] and \[{{t}_{2}},\] say the thermo emf is \[E_{{{t}_{1}}}^{{{t}_{2}}}.\] When the temperature limits are \[{{t}_{2}}\] and \[{{t}_{3}}\], then say the thermo emf is \[E_{{{t}_{2}}}^{{{t}_{3}}}\] then \[E_{{{t}_{1}}}^{{{t}_{2}}}+E_{{{t}_{2}}}^{{{t}_{3}}}=E_{{{t}_{1}}}^{{{t}_{3}}}\] where \[E_{{{t}_{1}}}^{{{t}_{3}}}\] is the thermo emf when the temperature limits are \[E_{{{t}_{1}}}^{{{t}_{3}}}\]
(ii) Law of intermediate metals : Let A, B and C be the three metals of Seebeck series, where B lies between A and C. According to this law, \[E_{A}^{B}+E_{B}^{C}=E_{A}^{C}\]
When tin is used as a soldering metal in \[Fe-Cu\] thermocouple then at the junction, two different thermo couples are being formed. One is between iron and tin and the other is between tin and copper, as shown in figure
If the soldering metal does not lie between two metals (in Seebeck series) of thermocouple then the resultant emf will be subtractive.
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