Thermoelectric Study of Peltier Effect Using Cu-Fe, Pb-Fe and Cu-Constantan Couples

International Journal of Innovative Scientific & Engineering Technologies Research 4(4):1-12, Oct-Dec. 2016 SEAHI PUBLICATIONS, 2016 www.seahipaj.org ISSN: 2360-896X Thermoelectric Study of Peltier Effect Using Cu-Fe, Pb-Fe and Cu-Constantan Couples G.U. Chukwu Department of Physics, Michael Okpara University of Agriculture, Umudike, P.M.B 7267, Umuahia, Abia State, Nigeria E-mail: chukwug@yahoo.com phone: +2348025691478 ABSTRACT Peltier effect is one of the thermoelectric effects that take place when two different conductors are joined together at two junctions. By keeping the two junctions at different temperatures, heat is absorbed at one junction while same is liberated at the other. Lengths of wires of uniform cross-section were joined to form pairs of thermocouples. With ten potentiometers connected in series and paraffin wax in hot bath, data were collected for different pairs of couples. One of the junctions was kept constant at ice-point whereas the temperature of the other junction was varying continuously by the application of heat. The thermo electromotive force (e.m.f) generated in the circuit was also changing with temperature of the hot junction. Plots of e.m.f versus temperature for Cu-Fe, Pb-Fe and Cu-CuNi thermocouples were obtained from which thermoelectric powers (TEP) were deduced. TEP-temperature plots from of the experiments yielded Peltier coefficient values of -0.044 ± 0.002, -2.272 ± 0.101 µv/ 0 C 2 and -0.086 0.006 V/ o C 2 for copper-iron, lead-iron and copper-constantan, respectively. Keywords: Peltier effect, thermocouple, coefficient, thermoelectricity, junction. INTRODUCTION If two conductors are joined together, it is observed that current flows provided the junctions are maintained at different temperatures. This current is called thermoelectric current (Chukwu, 1982; Faires, 1970; King, 1962) and some thermoelectric effects are set up. These occur as a result of coupling which exists between the statistical properties of the electrons, the holes and the crystal lattice of a solid according to Kittel (1976). In the case of metals it is the conduction electrons which are largely responsible while in semiconductors both electrons and holes are of importance. The three main thermoelectric effects are Seebeck, Thomson and Peltier effects. Specifically, when a current passes across the junction between two dissimilar metals there is either an evolution or absorption of heat i.e. the junction becomes heated or cooled. This heat is referred to as Peltier heat and the phenomenon itself is termed Peltier effect. It is different from Joule effect which is reversible. It takes place whether the current is provided by an external source or generated by the couple itself. Again, the Peltier heat is proportional to the current whereas the Joule heat is proportional to the square of the current; hence, the two effects are not the same (Tye, 1969). In this paper a study of Peltier thermoelectricity is made experimentally using pairs of metals: Cu-Fe, Pb- Fe and Cu-Constantan. The aim is to determine by experiments (Prakash and Krishna, 1977) the Peltier coefficients for the couples mentioned above as well as their thermoelectric constants. The study is significant and relevant because Peltier effect is useful to mankind. It has applications in the operational principle and construction of thermoelectric devices like thermoelectric generators, refrigerators, air 1

conditioners for cooling and/or warming rooms (Altman, 1969 and Sutton, 1966). Again, Peltier heating is used at the junction between the solid and liquid phases (Olmstead and Brodwin, 1977). Also the design of a thermoelectric oscillator is based upon the alternate changes in dimension arising from Peltier heating and cooling in addition to other numerous applications. BRIEF THEORY OF THERMOELETRICITY Metal A Heat Heat Liberted Metal B Fig.1: Peltier effect Peltier placed a battery in the circuit formed by A and B (two dissimilar metals); the two junctions being at the same temperature initially. He observed that heat was absorbed at the junction which became hot and liberated at the other junction which was cold. If the current is reversed the heating at one junction is replaced by cooling and vice versa. This suggests that the thermoelectric current due to the Seebeck effect is maintained by the energy absorbed from the source less than that supplied to the sink. Since there is a current in the circuit there must be emf acting on it. If the emf in the circuit is E, the energy gained when the charge dq is taken round is E.dQ. E = dw... (1) dq where dw is gain in potential energy. Thus, E = [π ab ] - [π ab ]... (2) T 2 T 1 From thermodynamic point of view we can consider a heat engine where energy can be drawn from the source at a higher temperature T+dT and given to the sink at a lower temperature T. In the process energy is expanded and such an engine is called a Carnot engine. Meanwhile, the thermoelectric effects being considered in this circuit are reversible. This implies that we have a reversible engine of the type contemplated in thermodynamics. Here the total sum of the quantities for all the source and sinks in a reversible cycle is zero (Faires, 1970; Kinnard, 1962). 1 T dq = 0... (3) 2

When we apply equation (3) to a circuit whose junction are at temperatures T and T + dt, the Peltier coefficients become [π ab ] T and [π ab ] T + dt respectively. Hence, we have [π + d π]dq - πdq = 0 T + dt T... (4) Thus, π is a constant. T With a thermocouple whose junctions are at temperatures T 1 and T 2. It is necessary to state that T 2 > T 1 π 2 = π 1 T 2 T 1... (5) E = π 2 - π 1... (6) Using equation (5) in equation (6), we get E = π 1 T 2 T 1 ]... (7) T 1 Equation (7) implies that the e.m.f in the circuit is directly proportional to (T 2 T 1 ) which is not true, hence there must be some other reversible effect in the circuit which is the Thomson effect. Hence any true expression of the thermoelectric force between two junctions must take into account the Thomson coefficient for each of the two metals involved. The Thomson coefficients are measures of the thermal emf s created in the metal by the metal through a temperature gradient. This explains, in part, the non-linear behavior of a thermocouple and in fact experimental results show that the thermoelectric force, E is a parabolic function of the temperature, T (Nelkon, 1979; Jenkins and Jarvis, 1973) which means that E = αt + βt 2... (8) where α and β are thermoelectric constants. For copper-iron junction, copper is thermoelectrically positive with respect to iron, so when a current is passed from iron to copper, work is done to overcome the electromotive force at the junction and this appears as heat, thus the junction becomes heated up. Reversing the current makes the junction become cooled (England et al., 1993; Jang et al., 1998). This is also applicable to lead-iron and copper-constantan (constantan = Cu 60%, Ni 40%) couples. Measuring procedure The Peltier coefficient is obtained by measuring the thermoelectric power (TEP) when equation (9) is applied: TEP T... (9) 3

where T= temperature = Peltier coefficient The relation in equation (9) is usually applicable with the thermocouple method. The method works with the principle of Seebeck effect where the two thermo-junctions are maintained at different temperatures and current is produced as a result of the temperature contrast. Theoretically, the thermoelectric e.m.f. E which is set up is given in equation (8). R 1 R 2 E K ʎ G G R 1 + R 2 Cu Fe Cu S Standard Cell - H - C Fig. 5 Measurement of Thermoelectric e.m.f. The circuit in (Fig 2) was used to carry out the experiment. Two equal lengths of insulated iron and copper wires were fused together to make a perfect contact (Coxon, 1960). Ten potentiometers were connected in series and resistance of the whole length measured. At the hot junction, a liquid of high boiling point (paraffin wax) was used. Paraffin wax has a boiling point which is greater than 300 0 C unlike water. Before the actual measurements are taken, the following information is necessary (Nelkon, 1979): Battery voltage. E = 3 volts Resistance used, R = 8520 ohms Current, i = E R Potentiometer (wire), r = 23 ohms P.d at end of wire = ir volts Length of potentiometer wire, L = Length at which balance is got = 1000 cm ʎ cm :. P.d at end of L cm of the wire = r. E. ʎ volts R L Hence, for one cm of wire, p.d = r. E. 1. ʎ volts R L 4

= 23 x 3 x 1 1 cm of potentiometer wire corresponds to 8.09 µv. 8520 1000 = 8.09 x 10-6 volt = 8.09µv. One junction of the thermocouple is placed inside a beaker containing ice blocks and the other junction in another beaker containing paraffin wax. One end of the copper wire connected to a sensitive galvanometer through a two- way key, K 2 and the galvo joins the potentiometer wire AB at A. The other end of the copper wire was attached to a jockey. As the temperature (T 2 ) of the hot joint measured by a long range thermometer was varying, the balance point was obtained by tapping the jockey over the potentiometer wire and the balancing length ʎ when there was zero deflection of the galvanometer was noted. Each temperature change T (i.e T 2 T 1 ) and its corresponding balancing length, ʎ were carefully observed and recorded. A conversion factor of 8.09 was used to obtain the corresponding values of the varying e.m.f, in Table 1. Table 1: Variation of e.m.f with temperature (for Cu-Fe) T 0 C ʎ (cm) E(uv) 30 49.2 398.03 60 92.8 750.75 90 133.6 1080.82 120 167.4 1354.27 150 199.1 1610.72 180 224.9 1819.44 210 247.1 1999.04 240 263.8 2134.14 270 276.2 2234.46 300 275.8 2231.22 330 263.5 2131.72 Table 2: Seebeck coefficients de/dt (for Cu-Fe) T O C E (µv) de/dt = TEP µv O C -1 50 612.41 12.113 100 1178.71 9.574 150 1610.72 7.463 200 1944.03 5.468 250 2160.84 3.387 280 2252.26 2.058 5

Table 3: Variation of emf with temperature (for Pb Fe) E ʎ (cm) E (µv) 28 25.3 1774.01 30 26.1 1866.0 50 33.5 2440.05 70 41.8 3011.20 90 51.3 3637.48 110 60.1 4290.80 130 67.8 4861.96 150 75.0 5293.90 160 76.1 5445.11 Table 4: Seebeck coefficients de / dt (for Pb Fe). T O C E (µv) E de /dt = TEP µv 0 C -1 120 4755.13 29.44 130 4861.96 25.51 140 5109.42 22.01 150 5293.90 18.90 160 5445.11 14.56 Table 5: Variation of e.m.f with temperature (for Cu constantan) T O C E (µv) E de /dt = TEP µv 0 C -1 30 156.1 1266.41 60 321.8 2604.03 90 496.1 4014.20 120 679.3 5496.51 150 871.4 7050.00 160 936.3 7574.40 Table 6: Experimental results Couple α µv 0 C -1 B µv 0 C -2 Π µv 0 C -2 Cu Fe 14.131 ± 0.085-0.002 ±0.002-0.044 ±0.002 Pb Fe 70.00 ±0.114-1.136 ±0.101-2.272 ±0.101 Cu CuNi 40.936 ±0.434-0.043 ± 0.006-0.086 ±0.006 6

3.3 GRAPHICAL ANALYSIS AND DETERMINATION OF SEEBECK COEFFICIENTS E x10 2 µv 24 20 16 12 0 1 2 3 4 X10 2 T 0 C Fig. 3 Variation (E) with tempt (T) for Cu-Fe From the graph in Figure 3, thermoelectric powers at 50, 100, 150, 200, 250, and 280 0 C were obtained by taking the gradient at these temperatures. This, in effect, implies determining the derivatives of the e.m.f with respect to temperature i.e de/dt which are called Seebeck coefficients. The values obtained from this exercise are shown in Table 2. 3.4 PELTIER COEFFICIENT, π If we recall equation (8), it is easy to see mathematically that TEP = De = α + 2βT dt... (10) This clearly shows that if we differentiate the accruing emf of two dissimilar metals with respect to temperature, the result is Seebeck coefficient. A second derivative of eqn. (8) gives us the Peltier coefficient which is D(TEP) d 2 E = π 7

dt... (11) But using equation (10) and plotting a graph of TEP versus T, a straight-line graph whose intercept α is on the TEP-axis with a gradient β. This graph is shown in Figure (6) and it implies that the gradient 2β = π. That is, Π = - 0.022 E x10 2 µv 24 20 16 12 0 1 Fig. 4: 2 Variation 3 of (E) 4 with X10 2 (T) T 0 C for Pb Fe 8

E x10 2 µv 24 20 16 12 0 1 Fig. 5: Variation 2 3 of E with 4 T X10 for 2 TCu 0 C Cu-CuNi TEP 16 12 8 0 1 2 3 4 X10 2 T 0 C Fig 6: TEP T Plot for Cu Fe 9

TEP de/dt µv 0 /C 70 60 50 40 0 4 8 12 16 X10 2 T 0 C Fig. 7: TEP-T Plot for Pb-Fe 2. RESULT AND DISCUSSION The values of the vertical intercept on TEP-axis is observed to be thermoelectric constants from the study are: α = 14.131µV 0 C -1 and β = -0.022 ± 0.002 µv 0 C -2 Also, the value of the Peltier coefficient is given by = -0.022 ±0.002 µv 0 C -2 However, theoretical values for α and β are 13.89 µv 0 C -1 and -0.020 µv 0 C -2 respectively (Nelkon and Parker, 1995). Within the limits of experimental error, the practical results agree with the theoretical results. Also, for Pb-Fe couple, the results of the experiment show that α = 70.60µV 0 C -1 and β = -1.130 µv 0 C -2. Similarly, the constants α and β for copper-constantan are 40.716 µv 0 C and 0.040 µv 0 C -2 respectively. It is discovered that the couple made up of copper-constantan generates thermoelectric e.m.f that is very much higher (over nine times) than that of copper-iron. This particular behavior for this makes it a satisfactory combination for temperature measurements as its e.m.f temperature curve is linear over a very large range of temperature; balance point was not easy to reach. The summary of experimental results obtained is as follows: For Copper Iron (Cu-Fe): α = 14.131 ± 0.085 µv 0 C -1, β = -0.022 ± 0.002 µv 0 C -2, 10

π = -0.004 ±0.002 µv 0 C -2, Lead-Iron, (Pb Fe): α = 70.00 ± 0.114 µv 0 C -2, β = -1.136 ± 0.101 µv 0 C -2, π = -2.272 ±0.101 µv 0 C -2, Copper-Constantan (Cu-CuNi) α = 40.936 ± 0.434 µv 0 C -1, β = -0.043 ± 0.006 µv 0 C -2, π = -0.086 ±0.006 µv 0 C -2, These results compare favourably well with the theoretical values. Peltier relates to the heat reversibly liberated or absorbed at a junction between two dissimilar metals when a current passes through the junction. The heat is easily distinguished experimentally from Joule heat which is independent of the direction of current flow (Blatt et al., 1976). The effect is not a contact phenomenon and therefore does not depend on the nature of the contact but on the intrinsic properties of the two conductors, that is why the value of Peltier coefficient varies from couple to couple as can be seen in the result (Gaur and Gupta, 1997; Jang et al., 1998). It is easy to see that the reading stopped at 330 0 C because paraffin boils at about 350 0 C for Cu-Fe the reading could not go beyond 160 0 C because lead has a very low melting point. Also, for copperconstantan couple, the reading stopped at ʎ = 936.3 cm. No further reading was possible because the potentiometer scale ended at ʎ (maximum) = 1000cm; see Tables, 1, 2, 3, with their corresponding graphs in Figures 3, 4 and 5 respectively. The first derivatives of e.m.f with respect to temperature give the values in Tables 2 and 4 from which thermoelectric power (TEP) temperature (T) plots (Seebeck coefficients, de/dt) are obtained in Figures 6 and 7. The gradients of the TEP T plots give the Peltier coefficient of the various couples investigated. CONCLUSION Concerted effort has been made to study experimentally the thermoelectricity of Peltier effect and the results have been very encouraging. Because of the usefulness and wide applicability of this phenomenon and its contribution to science in general the effect deserves some practical approach. The reversibility of the effect makes it peculiar and worth studying. As the physics of semiconductors is becoming more popular and wide spread owing to their numerous applications in technology and industry, there is need to direct more attention towards further research in this study using semiconductor devices. This idea originates from the fact that semiconductors have much larger Seebeck coefficients, better electrical conductivities and poorer thermal conductivities than pure conductors or metals. REFERENCES Altman, M. (1969). Elements of Solid State Energy Conversion Nostrand Reinhold Coy. Ltd; Canada. Animalu, A. O. E. (1977). Intermediate Quantum Theory of Crystalline Solids. Prentice Hall Inc, Eaglewood Cliffs New Jessy. Blatt, F. J. (1968). Physics of Electronic Conduction in Solids McGraw-Hall Book Coy; New York. Blatt, F. J., Schroeder, P. A., Foiles, C. L. and Greg, D. (1976). Thermoelectric Power of Metals. Plenum Press, New York. Pp. 49 57. Clement, P. R. and Johnson, W.C. (1960). Electrical Engineering Science. McGraw Hill Book Coy. Inc; Tokyo. 11

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