thermoelectric study of peltier effect using cu-fe, pb-fe and cu … · 2016-11-17 · 1...

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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: [email protected]

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/0C

2 and -0.086 0.006 V/

oC

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

International Journal of Innovative Scientific & Engineering

Technologies Research 4(4):1-12, Oct-Dec. 2016

© SEAHI PUBLICATIONS, 2016 www.seahipaj.org ISSN: 2360-896X

mailto:[email protected]

http://www.seahipaj.org/

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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

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 = [πab] - [πab] . . . (2)

T2 T1

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).

T

1dQ = 0 . . . (3)

Metal A

Metal B

Heat

absorbed

Heat Liberted

Chukwu …. Int. J. Inno. Scientific & Eng. Tech. Res. 4(4):1-12, 2016

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When we apply equation (3) to a circuit whose junction are at temperatures T and T + dT, the Peltier

coefficients become [πab]T and [πab]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 T1 and T2. It is necessary to state that T2 > T1

π2 = π1

T2 T1 . . . (5)

E = π2 - π1 . . . (6)

Using equation (5) in equation (6), we get

E = π1 T2 – T1] . . . (7)

T1

Equation (7) implies that the e.m.f in the circuit is directly proportional to (T2 – T1) 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 + βT2 . . . (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)


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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).

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 3000C 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 = 1000 cm

Length at which balance is got = 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

E K

S

G

R1 R2

R1 + R2

Standard Cell

G ʎ

Cu Fe Cu

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

H C


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= 23 x 3 x 1

8520 1000

= 8.09 x 10-6

volt

= 8.09µv.

1 cm of potentiometer wire corresponds to 8.09 µv.

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, K2 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 (T2) 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 T2 – T1) 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)

T0C 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)

TOC E (µV) dE/dT = TEP µV

OC

-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


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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).

TOC E (µV) E dE /dT = TEP µV

0C

-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)

TOC E (µV) E dE /dT = TEP µV

0C

-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 µV0C

-1 B µV

0C

-2 Π µV

0C

-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


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3.3 GRAPHICAL ANALYSIS AND DETERMINATION OF SEEBECK COEFFICIENTS

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 2800C 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) ≡ d2E = π

24

20

16

12

8

4

0

E x102

µV

0 1 2 3 4 X102 T0C


Ok

8

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

Fig. 4: Variation of (E) with (T) for Pb – Fe

0

24

20

16

12

8

4

E x102

µV

1 2 3 4 X102 T0C


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Fig. 5: Variation of E with T for Cu – Cu-CuNi

Fig 6: TEP – T Plot for Cu – Fe

0

24

20

16

12

8

4

E x102

µV

1 2 3 4 X102 T0C

0

16

12

8

14

TEP

µV0/C

1 2 3 4 X102 T0C


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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 = 14.131µV0C

-1 and

β = -0.022 ± 0.002 µV0C

-2

Also, the value of the Peltier coefficient is given by

= -0.022 ±0.002 µV0C

-2

However, theoretical values for α and β are 13.89 µV0C

-1 and -0.020 µV

0C

-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 = 70.60µV0C

-1 and β = -1.130 µV

0C

-2.

Similarly, the constants α and β for copper-constantan are 40.716 µV0C and 0.040 µV

0C

-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 µV0C

-1,

β = -0.022 ± 0.002 µV0C

-2,

0

70

60

50

40

30

20

10

TEP dE/dT

µV0/C

4 8 12 16 X102 T0C


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π

= -0.004 ±0.002 µV

0C

-2,

Lead-Iron, (Pb – Fe): α = 70.00 ± 0.114 µV0C

-2,

β = -1.136 ± 0.101 µV0C

-2,

π

= -2.272 ±0.101 µV

0C

-2,

Copper-Constantan (Cu-CuNi) α = 40.936 ± 0.434 µV0C

-1,

β = -0.043 ± 0.006 µV0C

-2,

π

= -0.086 ±0.006 µV

0C

-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 3300C because paraffin boils at about 350

0C for Cu-Fe the

reading could not go beyond 1600C because lead has a very low melting point. Also, for copper-

constantan 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.

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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.


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Coxon, W. F. (1960). Temperature measurements and Control Heywood & Coy. Ltd; London.

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heating. International J. of Heat and Mass Transfer, 40(7): Pp. 1559 – 1565.

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Sutton, G. W. (1996). Direct Energy Conversion McGraw-Hill Book Coy; New York.

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Zemansky, M. W. (1968). Heat and Thermodynamics McGraw-Hill Book Coy; New York.


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thermoelectric study of peltier effect using cu-fe, pb-fe and cu … · 2016-11-17 · 1...

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