In this article we will discuss about the thermo-electric effect and its applications in generating electricity.
Thermo-Electric Effect:
Thermoelectric is the phenomenon in which the heat energy is converted into electric energy or vice-versa i.e.
Heat energy ⇋ Electric energy.
As we are well aware that the Joule heating effect proceeds only in one direction; reversal of the current has no effect upon it and it cannot be used to convert heat energy into electrical energy i.e. Joule heating effect is irreversible. There are thermoelectric phenomena which are reversible. In the order of their discovery, these are known as Seebeck effect, Peltier effect and Thomson effect.
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1. Seebeck Effect:
In 1926, T.J Seebeck discovered that when two dissimilar metals are joined so as to form a closed circuit and a difference of temperature is maintained between their junctions, an emf is developed and hence the current flows through the circuit. The emf so produced is known as thermo-electric emf and the phenomenon is known as Seebeck effect.
Such an arrangement of joining two dissimilar metals is called thermo-couple. The magnitude of thermo-electric emf depends upon the nature of two metals and on the temperature difference of their junctions. Seebeck investigated the thermo-electric properties of a large number of metals and arranged them in a series known as Seebeck series or thermo-electric series.
This series includes Bi, Ni, Co, Pt, Cu, Mn, Hg, Sn, Au, Ag, Zn, Cd, Fe, As, Sb, Te, etc. In this series, if the thermo-couple metals are far apart, the emf will be greater or vice-versa. Also the direction of current at the hot junction is from the metal occurring first in the series to the metal occurring later on it.
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The thermo-electric emf is zero when both the junctions are at the same temperature, let it be 0 °C, and gradually increases as the temperature of the hot junction increases. At a particular temperature of the hot junction, the thermo-electric emf becomes maximum. The corresponding temperature is known as neutral temperature Tn for the thermocouple and is constant for a given pair of metals forming thermo-couple.
If the temperature of hot junction be raised further, the thermo-emf decreases and becomes zero (see Fig. 5.22) at a particular temperature, known as temperature of inversion Ti. Beyond this temperature Ti, the thermo-emf again increases but in reverse direction. The Ti is as much above the Tn as the temperature of cold junction is below it i.e.;
Therefore, Ti not constant for a given thermo-couple rather depends upon the temperature of cold junction.
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Thermo-Electric Power:
The rate of change of thermo-electric emf with temperature of the hot junction is known as thermo-electric power of the thermo-couple at a particular temperature. Since the variation of thermo-electric emf E with temperature (see Fig. 5.22) of the hot junction T is a parabola, the thermo-electric emf E can be expressed as-
E = aT + bT2
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(Keeping cold junction at 0°C)
where a and b are constants for a given thermo-couple.
Therefore, the thermo-electric power dE/dT is
dE/dT = a + 2bT
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which is a straight line and is shown in Fig. 5.22 (a).
2. Peltier Effect:
In 1834, J Peltier discovered that when a current is passed through a thermocouple whose two junctions are kept at same temperature, then one of the junction is heated while other is cooled; showing that heat energy is being liberated at one junction and absorbed at the other junction. Thus, by the passage of electric current through a thermo-couple with junctions initially at some temperature, a difference of temperature is developed between the two junctions.
This effect is known as Peltier effect and is converse of Seebeck effect. For a given pair of metals, the heating or cooling of the junction depends upon the direction of the current. If a particular junction is heated by passing the current in one direction, some is cooled when the direction of current is reversed i.e. Peltier effect is reversible.
It is worth mentioning here that to observe Peltier effect; the direction of Seebeck current should be opposite to the battery current. The opposing current causes loss of energy and appears as heat and the junction is heated. At other junction the current flows in the direction of Peltier emf so that the Peltier emf itself does work and energy is absorbed from the junction causing it to cool.
Explanation of Seebeck and Peltier Effects:
Free electron theory of metal describes that the density and pressure of an electron gas differ from metal to metal at the same temperature. When two metals are joined together, the electron gas diffuse from one metal to the other in such a way that the net diffusion of electron gas is from a metal at high pressure to that at low pressure.
Due to diffusion of the electron gas, an emf is produced at the junction of the two metals which opposes the further diffusion of the electron gas, and the state of dynamic equilibrium is reached when the emf is sufficient to stop further diffusion. At this stage, there exists a certain emf at the junction of two metals, known as Peltier emf.
When two dissimilar metals A and B are joined together to form a thermocouple, then at each junction a Peltier emf is produced. If both the junction is at same temperature, the Peltier emf’s are equal and opposite. Therefore, the net current will be zero. If junction are kept at different temperatures, say T1 and T2 (T2 > T1) the Peltier emf’s E1 and E2 at the junctions are no longer equal. The resultant emf E2 – E1 will cause a current to flow through the thermocouple which is Seebeck effect.
Peltier Coefficient:
It is defined as the amount of heat energy absorbed or evolved when unit charge flows across the junction of two dissimilar metals. It is usually denoted by . The Peltier coefficient depends on the pair of metals in contact and on the temperature of the junction.
If a charge q flows across the junction having Peltier coefficient , then the energy absorbed or evolved at junction is-
Q = πq
If Q is measured in Joules and q is in coulomb then the units of n will be Joules per coulomb.
Now, if we consider that Peltier emf setup at junction is e, then the energy absorbed or evolved will be eq. Therefore
πq = eq
or, π = e
Thus, the Peltier coefficient is numerically equal to the Peltier emf setup at the junction.
Expression for Peltier Coefficient:
Let us again consider the thermo-couple of copper and Fe whose hot and cold junctions are respectively at temperatures T + dT and T. The corresponding Peltier coefficients are π + d and respectively.
The corresponding resultant emf dE in the circuit will be-
dE = dπ + (σCu – σFe) dT
and hence the thermo-electric power will be-
dE/dT = dπ/dT + (σCu – σFe)
Now considering the net gain in entropy in the thermo-couple must be zero i.e. Σ dQ/T = 0
Since dT is very small, we can have (T + dT) T ≈ T2. Therefore, we have-
Thus, the Peltier coefficient of a junction at temperature T is the product of the temperature T and the thermo-electric power.
3. Thomson Effect:
When a temperature gradient is maintained between the different parts of the same metal, there exists a variation of potential along the metal i.e. emf is developed in the metal due to the temperature gradient. This effect is known as Thomson effect. As heat is either absorbed or-evolved when current passes between two points having a difference of potential, therefore, the passage of electric current through such a metal results in an absorption or evolution of heat in the body of the metal.
This effect is measured in terms of Thomson coefficient a, which are different for different metals. The Thomson coefficient of a metal is defined as the amount of heat energy absorbed or evolved when one Coulomb charge flows in the metal between two points which differ in temperature by 1 °K.
Thomson Coefficient:
If charge q coulomb flows in a metal between two points having temperature difference of 1 °C, then the heat energy absorbed or evolved will be σq joules. But if E be Thomson emf developed between these two points, then this energy will be Eq joules.
Hence σq = Eq
or σ = E
which implies that the Thomson coefficient of a metal is numerically equal to the Thomson emf setup between two points differing in temperature by 1 °C. The units of σ are Joules per coulomb per °C or volts per °C. The Thomson coefficient of a metal is positive when emf E is directed from lower to higher temperature and vice-versa.
Expression for Thomson Effect:
We know that the Peltier coefficient is given by-
= T dE/dT
On differentiating above equation w.r.t. T, we have
Above expression relates the Thomson coefficients with absolute temperature and first derivative of thermo-electric power.
Depending upon the value of Thomson coefficient, materials are classified as:
(i) Positive Thomson Effect:
When the value of Thomson coefficient is positive, a current flow from hot to cold sides and is found in Ag, Cd, Cu, Zn, Sb etc.
(ii) Negative Thomson Effect:
The negative value Thomson coefficient corresponds to flow of current from cold to hot side and it is found in Fe, Ni, Co, Pt, Bi etc.
(iii) Zero Thomson Effect:
In case of Pb, heat is neither absorbed nor evolved.
Total EMF in a Thermo-Couple:
Consider a thermo-couple of Cu and Fe as shown in Fig. 5.25. Due to Peltier and Thomson effect, a total emf is produced in the circuit and causes a flow of current l round the circuit. Let the temperature of hot and cold junctions be T2 and T1 respectively. Let π1 and π2 be the Peltier coefficients at T1 and T2 respectively. The σCu and σFe are the Thomson coefficients for copper and iron respectively.
The energy absorbed at A = π2It
(∵ It represents the charge q flows through the circuit)
The energy absorbed at B = -π1It
Negative sign indicates that heat energy is evolved.
The energy absorbed along copper = 
(∵ Current flows from cold to hot end)
The energy absorbed along iron = 
(∵ Current flows from hot to cold junction)
Here integral 
indicates the total emf between points T1 and T2, t being the time for which current I flows.
Thus in whole circuit, heat energy is evolved due to Peltier effect at the cold junction and energy is absorbed at hot end due to Peltier effect. Energy is also absorbed along the two metals due to Thomson effect. Let E be the total emf which causes the flow of current I in the circuit for time t, the total energy produced is EIt and will be equal to the sum of energies produced in the various parts of the circuit
Applications of Thermo-Electric Effect:
1. Thermopile:
It is temperature measuring device consisting of thermocouples of antimony (Sb) and bismuth (Bi) which is widely separated in the thermo-electric series and comparatively a large emf is produced for small difference of temperatures between the junctions. Both metals are taken in the form of strip in order to reduce the resistance. With the help of thermopile, temperature differences upto 0.001 °C can be measured.
2. Thermoelectric Thermometers:
As is clear from Seeback effect that when a circuit is formed by two wires of different metals say copper and iron and one of the junctions is kept at higher temperature than the other one, an emf is setup that causes a flow of current in the circuit. Since the emf produced is proportional to the temperature difference of the two junctions, the property can be utilized to fabricate the thermometer, so called thermoelectric thermometer.
The most commonly used thermo-couples for such a device are copper-constantan and gold 2% cobalt-copper. Fig. 5.27 depicts the variation of emf with temperature for these mentioned thermocouples. The emf is measured by a sensitive galvanometer.
