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| Thermoelectricity (Contd…) |
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| In 1834, a French scientist Peltier, found an effect that was the converse of the Seebeck effect. |
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| Figure (a) |
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| The above figure shows the copper-constantan thermocouple again, but now a battery is inserted in the circuit. The direction of the electric current is the same as in the below figure i.e., from copper to constantan at the junction 1. It is found that the heat is absorbed at the junction 1 (junction 1 gets cooled) and liberated at the junction 2 (it gets heated). In general, if the Seebeck emf is from A to B at the hot junction, an external emf applied in this direction produces cooling at this junction and heating at the other junction. |
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| Figure (b) |
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| This phenomenon is known as Peltier effect. |
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| As shown in the figure (a), Peltier effect is reversible. Further, the heat absorbed or liberated at a junction is found to be proportional to the first power of current (contrast this with the irreversible Joule effect that is proportional to the square of current). Thus, if a charge q passes across a junction from metal A to B, heat absorbed at the junction is given by pAB q where pAB is known as the Peltier coefficient. The magnitude of pAB depends on the temperature of the junction. (By this definition, pAB is negative if heat is liberated.) The absorption of heat indicates that there is a seat of emf at the junction, and energy is taken from the environment (resulting in cooling) to provide electrical energy to the current. |
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| In 1851, William Thomson (later Lord Kelvin) argued that each element of a single conductor would be a source of emf whenever there is a temperature gradient, i.e., the conductor has a non-uniform temperature. Suppose a current is maintained in a conductor with some temperature gradient. Let DT be the temperature difference between the ends of a small section of the conductor. Thomson emf is then given by sDT where s is called the Thomson Coefficient. As before, the existence of emf is indicated by heat absorbed or released per unit quantity of charge transferred. Thomson effect is again reversible. The Thomson coefficient s depends on temperature and on the material of the conductor. |
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| 1. The electron density of a conductor depends on the material of the conductor. When two materials are in contact at the junction, free electrons diffuse from metals having higher number density (i.e., free electrons per unit volume) to the other metal having a lower electron density. This diffusion creates a potential difference called the contact potential at the two junctions as shown. This contact potential is the origin of the Peltier emf at the junction. |
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| n1 > n2 |
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| Hence, e1 = e2 |
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| e1 - e2 = 0 |
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| Since the functions are at the same temperature, the net emf of the circuit is zero and no current flows through it. But if a temperature difference is maintained, then the rate of diffusion of free electrons at one of the junctions (i.e., hot junction) is greater and this creates a net emf e1 - e2 and hence the current flows. |
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| Note: |
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 The magnitude and direction of thermo emf in a thermo couple depends on the |
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| a) nature of the metals and |
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| b) temperature difference between the two junctions. |
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 Seebeck effect is a reversible effect. |
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| Each metal is characterized by a work function f which is the energy required to remove the highest energy face electron in the metal to infinity. Now, f varies slightly with temperature and this variation is different for different metals. So, the contact potential at a junction varies with temperature. In a thermocouple, if both the junctions are at the same temperature, the two contact potentials are equal and opposite. So, there is no net emf. But when the temperatures are different, the different contact potentials give rise to a net emf in the circuit. |
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| 2. The origin of Thomson emf can be explained by noting that in a conductor with temperature gradient, the free electrons in the region at higher temperature will have higher energy. The resulting not diffusion of electrons from one region to the other gives rise to a potential difference. This continues until the difference is enough to counter the not diffusion due to the temperature gradient. |
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| 3. A detailed proof (not shown here) shows that the seebeck emf VAB is given by |
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| where T, T0 are the junction temperature. This is clear quantitatively |
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| The seebeck emf is of the difference in Peltier emfs at the two junctions and the difference in Thomson emfs as one traverses the two conductors in opposite directions in a closed circuit. |
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