Thermoelectric Effect

1. Thermoelectric Effect
UK Physics-9841895036
Department of PHYSICS
CCRC
2077
1 Defination
It deals about the conversion of heat energy into the elec-
trical energy. It encompasses three separately identified
effects.
1.1 Seebeck effect : or Thermoelectric
effect
The phenomenon of conversion of heat energy into
electric energy when the junctions of a thermocouple
(dissimilar metals joined together) are kept at different
temperature is called Seebeck effect.
The current so produced is called Thermoelectric
current, the pair of metal used is called thermocouple
and the e.m.f. produced is called thermo e.m.f. or
Seebeck e.m.f.
Its magnitude depends on the nature of metals
and the temperature difference of their junctions
It is reversible process. As in the demonstrating
Figure 1: Demonstration for Seebeck effect
figure shown below, it is observed that there is deflection
in the galvanometer from copper to iron in the hot
junction,(HotCoffee)
If the hot and cold junction are interchanged, the
e.m.f. changes the sign with its magnitude remaining
unchanged.
Mechanism
As we know that the electron density in the differ-
ent metals are different. When one metal is brought into
intimate contact with another metal, the electrons tend
to diffuse so as to equalize the electron density.
The transfer of electrons at the hot junction will
be easier than that at the cold junction. Due to this,
e.m.f. at the junctions will be different and hence the
current flow.
Uses of thermoelectric effect:
1. It is used to make solid – state refrigerator de-
vice.
2. It is used to sense temperature difference.
3. It is used to convert thermal energy directly into
electricity.
1.1.1 Variation of Thermoelectric e.m.f. with
Temperature
Consider a case in which one junction is immersed in ice
and another junction is immersed in hot oil bath as in
the figure. It is found that the thermo e.m.f. for a given
pair of metals depends on;
i) the temperature of cold junction and
ii) temperature difference between two junction.
Keeping cold junction fixed at 0°C, on gradually increas-
ing the temperature of hot junction, the thermo e.m.f.
also gradually increases and reaches maximum value at
θn called neutral temperature after which it begins to
decrease and becomes zero at θi called temperature of
1

2. Figure 2: To show Thermoelectric e.m.f. with Tempera-
ture
Figure 3: Variation of Thermoelectric e.m.f. with Tem-
perature
inversion. On further increasing, the thermo e.m.f. is
reversed.
Experiments show that e.m.f. is almost a parabolic
function of temperature as in the figure.
The relation between thermo e.m.f. E and temper-
ature difference θ between hot and cold junctions can be
expressed as;
E = αθ +
β
2
θ2
(1)
Where α and β are thermoelectric coefficient or Seebeck
coefficient, the values of which depend upon the pair of
metals constituting the thermocouple.
Note:
Neutral temperature
The temperature of hot junction at which the thermo
e.m.f. becomes maximum is called neutral temperature.
Temperature of inversion
The temperature of the hot junction at which the thermo
e.m.f. is zero and reverses the direction is called temper-
ature of inversion.
1.1.2 Relation between θc, θn
and θi
θi always exceed θn almost by the same amount as the
θn exceeds θc i.e.
θi − θn = θn − θc
or 2θn = θi + θc
orθn =
θi + θc
2
(2)
θi depends upon;
a)temperature of cold junction
b) nature of metal of thermocouple
θn is independent of a) but depends on b)
1.2 Peltire’s Effect
Figure 4: Demonstration of Peltire’s Effect
It is the phenomenon of generation or absorption of
heat at the two junctions of a thermocouple due to
passing the electric current through it.
It is the conversion of Sebeck effect and it occures
only at the junction. It is reversible phenomenon.
As in the demonstrating figure 4, it is observed
that the junction at which the current enters from Cu
to Fe is cooled and that at which currents enters from
iron to copper is heated.
Mechanism
In this effect when current is passed in a thermo-
couple, one junction becomes cool and another junction
becomes hot.
2

3. At the hot junction, the current is in the direction
of Peltire’s e.m.f. . So the e.m.f. itself does work
and some energy is absorbed from the this junction.
Consequently this junction becomes cool. At the cold
junction, current is against Peltire’s e.m.f. , work is
done and energy is liberated in the form of heat. The
cold junction thus tends to be heated.
1.3 Thomson’s Effect
It is the phenomenon of absorption or evolution of heat
energy due to the flow of current in an unequally heated
single conductor.
Explanation
Consider a thick copper rod with its ends at the
same temperature and centre maintained at the much
higher temperature.
If no current flows, P and Q are at the same temperature
due to thermal conduction alone.
If current is sent as in the figure 5, The temper-
Figure 5: Demonstration of positive Thomson’s effect
ature at P is less that at Q. Means that heat energy
transformed from P to Q (i,e, along the direction of
current). This is called +ve Thomson’s Effect. It is
observed in Cu, Cd, Zn, Ag and Sb.
In the figure 6, under the similar condition, tem-
Figure 6: Demonstration of negative Thomson’s effect
perature at P is larger than at Q, means that heat
energy is transformed from Q to P. This is called -ve
Thomson’s effect. It is observed in Fe, Pt, Bi, Co, Ni
and Hg.
If the direction of current in either of the above
cases is reversed, the Thomson’s effect is also reverse.
In Lead, Thomson’s effect is zero. Due to this
Thermoelectric behaviour of metal is studied by taking
lead as the second element.
Mechanism
It is explained on the basis of free electron theory
of metal. As we know that the electron density in
a metal depends on temperature. There is different
electrons densities in different part of an unequally
heated metal rod.
The hotter portion have more energies, so elec-
trons move from hotter parts to colder parts. In this
way at the region of low temperature the, the electron
density is more. Consequently, the potential of hotter
rgion is more.
Thus an e.m.f. acts from the colder portion to
hotter portion called Thomson’s e.m.f.
When current is passed, the work is done either
against or alomg the direction of electric intensity. This
produces absorption or evolution of energy.
Note :
The free electron theory does not explain the -ve
Thomson’s effect. It also does not explain almost zero
Thomson’s effect in case of Lead.
2 Comparision among Joule’s,
Peltire’s, Seebeck and Thom-
son’s effect
Joules’ effect
1. It is not reversible.
2. Heat is always evolved.
3. No such temperature difference is required.
4. It is independent of the direction of current.
5. Heat (evolved) α I2
Peltier’s Effect
1. If the junctions of thermocouple are at the dif-
ferent temperature and current is passed in circuit of
thermocouple heat is generated at one end and absorbed
at the other.
2. This effect is inverse of Seebeck’s effect.
3. In this effect a thermocouple is required.
4. Production and absorption of heat takes place in the
junction
Seebeck’s Effect
3

4. 1. Here the temperature difference produces the
current.
2. It is a reversible process
3. one junction evolves heat, whereas the other junction
absorbs heat.
4. It is the resultant of peltier’s effect and Thomson
effect.
Thomson’s Effect
1. It is reversible.
2. Heat is evolved or absorbed.
3. A temperature difference is required along the length
of the conductor.
4. It depends upon the direction of current.
5. Heat(evolved/absorbed) αI
3 Short Questions
1. Is it true that Seebeck’s effect is the
resultant of Peltier’s and Thomson’s
effect? Discuss.
Yes. Let us consider a Fe-Cu thermocouple as in the
figure, If one junction is kept at higher temperature,
both Peltier and Thomson’s effect will be present.
For Iron (Fe), the direction of Thomson e.m.f.
(ETI) is from hot to cold junction. Similarly, in the
copper, the direction of Thomson e.m.f. (ETC) is from
cold to hot junction. The electric field due to Peltier’s
effect at both the junctions are from Cu to Fe shown
in the figure. The resultant of these two e.m.f.s in the
closed circuit is the Seebeck’s e.m.f.
2. Does the thermoelectric effect obey the
law of conservation of energy?
Yes, it obeys the law of conservation of energy.
In Seebeck’s effect, heat energy absorbed from ex-
ternal source is converted into electrical energy.
In Peltier’s effect, one junction evolves heat, whereas
the other junction absorbs heat.
Similarly, in Thomson’s effect, electrical energy is
converted into heat energy.
3. Peltier’s effect is the converse of See-
beck’s effect. Explain.
Peltier’s effect is the conversion of electrical energy to
heat energy while Seebeck’s effect is the conversion of
heat energy to electrical energy. In Peltier’s effect, the
junction of thermocouple is placed at same temperature
and if current is passed then there is generation of heat
at one junction and absorption in the the other. For
Cu-Fe thermocouple, the junction A gets hot while the
junction B gets cooled.
In Seebeck’s effect, current flows in a circuit consisting
of two dissimilar metals kept at different temperatures.
This shows that, Peltier’s effect is converse of See-
becks effect.
4 Numerical
1. The thermo - e.m.f. E and the temperature of hot
junction θ satisfy the relation E = aθ + bθ2
, where
a = 4.1 × 10−5
V ◦
C−1
and b = −1.41 × 10−5
V ◦
C−2
. If
the cold junction temperature is θ ◦ C, find the neutral
temperature.
Solution:
At neutral temperature E is maximum,
so,
d(aθn+bθ2
n)
dθn
= 0
This gives, θn = 500◦
C
2. Temperature of two junction of a thermo couple are
maintained at 0◦
C and θ°C. The thermo e.m.f. gener-
ated is given by the relation E = 10−5
θ − 0.01 × 10−5
θ2
.
Find the neutral temperature of the thermocouple and
the maximum value of thermo e.m.f.
4

5. Solution
At neutral temperature;
dE
dθ |θn
= 0
or, 10−5
− (0.10 × 10−5
) × 2 × θn = 0 . . . . (1)
This gives,
θn = 50◦
C
Emax is obtained by putting the value of θn = 50◦
C in
the equation (1). Finally, we will get, E = 0.25mV .
5