3 Thermoelectric Thermometers 3 .1 Physical Principles 3 .1 .1 Thermoelectric force It was T . Seebeck who discovered, in 1821, the effect which now bears his name . He observed that a current flows in a closed loop oftwo dissimilar metals when their junctions are at two different temperatures . As Ohm's law was not formulated by G . S . Ohm until 1826, the quantitative description of this phenomenon was not possible at the time of its discovery . In 1834, I .C .A . Peltier, discovered that a junction of two dissimilar metals is respectively heated or cooled when a current is passed through it either in one direction or the other . This phenomenon is quite distinct from and in addition to the I2 R Joule heat, which is generated by the current flowing in the lead resistance . Another effect, distinguishably different from the previous, was discovered by Lord Kelvin (W . Thomson) in 1854 . He concluded that a homogeneous current-carrying conductor, lying in a temperature gradient, will absorb or generate heat, in addition to and independently of Joule heating . This absorption or generation of heat depends upon the metal properties and the respective direction of the current . The Peltier and Thomson effects concern only heat generation or absorption but do not generate any thermoelectric forces . Thus they only represent thermal phenomena, which accompany the flow of electric current (Reed, 1992) . In practice the currents flowing in a thermoelectric circuit are so small that the Peltier and Thomson effects can be totally neglected . Of these three thermoelectric effects, only the Seebeck effect is the real source of thermoelectric force . This force results from the variation of electron density along a conductor subject to a non-uniform temperature distribution . In this book the thermoelectric force will be called thermal electromotive force which may be abbreviated to thermal emf or simply emf . The Seebeck thermoelectric force is given by : dE = 6A (6)d6 (3 .1) where 6A is the Seebeck coefficient of metal .A . Temperature Measurement Second Edition L. Michalski, K. Eckersdorf, J. Kucharski, J. McGhee Copyright © 2001 John Wiley & Sons Ltd ISBNs: 0-471-86779-9 (Hardback); 0-470-84613-5 (Electronic) 38 THERMOELECTRIC THERMOMETERS The Seebeck thermoelectric force in a homogeneous conductor whose ends are at temperatures 61 and 02 respectively, has a value given by integrating equation (3 .1) to get EA( 0 1,62)= f 6A(6)dd (3 .2) or after some transformations : EA(01,62)=EA(61)-EA(62) (3 .3) In a thermoelectric circuit composed of two homogeneous conductors A and B, whose both joined ends are at the temperatures, 01 and 02 , as represented in Figure 3 .1, the resultant sum of both thermoelectric forces is : EAB(01, 6 2) = [EA(01) - EAW2)l - [EB(01) - EB( 6 2)l (3 .4) or EAB ( 0 1, 0 2) = EA ( 0 1 , 0 2) - EB (61,62) (3 .5) It is important to adopt a convenient convention when summing thermal emfs . In this book thermal emfs are summed in a clockwise direction . Those emfs which are compatible with this direction, possess positive polarity . Summing the partial emfs in the circuit of Figure 3 .1 gives the resultant emf, E, as : EAB (61, e2) = eAB (t~1) + eBA (62) (3 .6) In summing up, it should be emphasised that the resultant thermoelectric force of the circuit of Figure 3 .1 is only a function of the types of metal A and B and of the temperatures, 19 1 and t~2 . From the principles of the double subscript notation it is known that : eBA ( 0 2 ) = - eAB (62) (3 .7) As a result, equation (3 .6) may be written as : EAB (01, 0 2) = eAB (61) - eAB (62) (3 .8) or finally : EAB ( 6 1 , 62) _ .f ( 0 1 , 62) (3 .9) PHYSICAL PRINCIPLES 39 In the application of a circuit of two metals, A and B, for temperature measurement, it is rather difficult to use a function of two variables . For this reason it will be assumed that the temperature, 62 , of one of the junctions, called the reference junction will be held constant at the reference temperature, 6, . Equation (3 .6) may now be written as : EAB(Ol,02)=EAB(01,Or)=eAB(61) - eAB(O,) = f2(61) (3 .10) Equation (3 .10) indicates that the emf of the circuit of two metals A and B is a function of the measured temperature, t9 1 , of the measuring junction, which is junction 1 in Figure 3 .1 . It is of cardinal importance, as it is the foundation of modern thermoelectric thermometry 3 .1 .2 Law of the third metal The practical application of a circuit with the two metals A and B, for the purposes of temperature measurement, also requires the introduction of an emf measuring device . Insertion of such a voltage measuring instrument necessarily involves the connection of a third metal, C, as the circuit of Figure 3 .2 shows . The internal leads of the instrument and the leads interconnecting it with the circuit to be measured constitute the third metal . This assumes that the additional circuit is of the same continuous metal . Analysing Figure 3 .2 shows that the sum of the circuital emf is : E = eAB (01) + eBC ; (Or) + eCA (0r) (3 .11) When it is assumed that 141 = O r then : E=eAB(Or)+eBC(or)+eCA(6r)=0 (3 .12) Equation (3 .12) can be rewritten in the form eBC ( 6 r) + eCA WO = - eAB (3r) (3 .13) Substituting equation (3 .13) into equation (3 .11) shows that : B C a ~1 mV 1~ t 2 ~z <7 7 eael ,8, ~l~~ e sa I'' f zl A C Figure 3 .1 A closed thermoelectric circuit Figure 3 .2 Thermoelectric circuit of metals A and B with a third metal inserted at the junction 40 THERMOELECTRIC THERMOMETERS E = eA B (t~1) - eAB (fir) (3 .14) The law of the third metal is based upon the result given in equation (3 .14) . This law may be stated as : Introducing a third metal, C, into a circuit of the two metals A and B, does not alter the resulting emf in the circuit, provided that both ends of the third metal C are at the same temperature . The third metal, C, may be introduced into a circuit at any point . For example, if metal B is cut and the indicating instrument, which is regarded as the third metal C, is connected at that point, the resulting emf in the circuit shown in Figure 3 .3 . would be : E = eAB(01)+eBC(V2)+eCB(62)+eBA(13r) (3 .15) As eBC (62) = - eCB (62) this equation may be rewritten in the form : E = eAB (61) - eAB (fir ) (3 .16) Figure 3 .4 illustrates the situation when the junctions of metals B and C are at the respectively different temperatures ofV2 and 29 3 . In that case the resulting emf is : E' = eAB (Bl) + e BC (02) + eCB (03) + eBA (&r) (3 .17) -5 1 B B C C MV ~ 12 MV C C B B 4 Figure 3 .3 Thermoelectric circuit of metals, A Figure 3 .4 Thermoelectric circuit of metals, A and B, with third metal, C, inserted across the and B, with third metal, C, inserted at any ends of metal B, cut in two point, with its ends at different temperatures PHYSICAL PRINCIPLES 41 A comparison of equations (3 .16) and (3 .17) indicates that the difference between the emf in the two cases under consideration is given by : AE =E'-E= eBC(62)-eBC(63) (3 .18) Consequently the temperatures at both junctions of the metals B and C should be equal to ensure that the circuit gives the correct value of emf . 3 .1 .3 Law of consecutive metals Different kinds of metals are widely employed in thermoelectric thermometry . Platinum is universally taken as the reference metal as it has a high resistance to atmospheric influences, its physical properties are stable and constant and its melting temperature is high . Different metals and alloys have different emfs in different application ranges . To allow a comparison of the properties of these different metals, their emfs against that of platinum are given in Table 3 .1 . The organisation of this table is by increasing magnitude of emfs against platinum, thus forming what is called a thermoelectric series . Further details also appear in Figure 3 .5 . If the emfs of different materials against platinum are known, it is easy to determine their emfs relative to a combination of any two forming a pair . Consider three thermoelectric circuits of the metals A, B and C shown in Figure 3 .6 . The equations for each circuit may be written as : EBA (t1 ,6 0 = eBA (L1) - eBA (Or) (3 .19a) Table 3 .1 Value of the emf for different metals referred to platinum at 100 °C and reference at 0 °C (Roeser and Wensel, 1941 ; Lieneweg, 1975) Metal emf (mV) Metal emf (mV) Constantan -3 .51 Iridium +0 .65 (55 %Ni-45 %Cu) Nickel -1 .48 Rhodium +0 .70 Cobalt -1 .33 Silver +0 .74 Alumel -1 .29 Copper +0 .76 (95 %Ni+Al, Si, Mn) Palladium -0 .57 Zinc +0 .76 Platinum 0 I Gold +0 .78 Aluminium +0 .42 Tungsten +1 .12 Lead +0 .44 Molybdenum +1 .45 94 %Pt, 6 %Rh +0 .614 Iron +1 .98 90 %Pt, 10 %Rh +0 .645 Chromel +2 .81 70 %Pt, 30 %Rh +0 .647 (90 %Ni, 10 %Cr) 42 THERMOELECTRIC THERMOMETERS 30 R 20 ~~o~~~ C,pQeF, 1F0N > 10 ~" PtRh10 I PLATINUM a NICKEL A I LUIy 1010 10 CO'YS r9 I PACTA01 U -zo ~rq M -30 -200 0 200 400 600 800 1000 1200 1400 TEMPERATURE .~9 . , °C Figure 3 .5 Thermal emfs as a function of temperature for various metals using platinum as the reference metal ECA ( 6 1 , 0 r) = eCA (f91) - eCA (6r) (3 .19b) EBC ( 0 1, Tar) = eBC (01) - esC (Or) (3 .19c) Subtracting on both sides of equation (3 .19a) and equation (3.19b) yields : EBA( 6 iA) - ECA( 6 1, 6 r) = eBAWI) - eBAWr) - eCA(A)+eCA( 6 r) (3 .20) Consider the thermoelectric circuit given in Figure 3 .7 . If the three junctions of the metals A, B and C are at the same temperature 0 1 then eAB (61) + eBC (61) + eCA (61) = 0 (3 .21 a) or eBC (01) = eBA (61) - eCA (e]) (3 .21 b) Replace the temperature, t9 1 , by the reference temperature, 6, . Equation (3 .21) may now be used to obtain : - eBC ( 0 r) = eCA (Or) - eBA (6r) (3 .22) Substituting equations (3 .21) and (3 .22) into equation (3 .20) gives : EBA (61, Or) - ECA ( 6 1, Or) = eBC (6r) - esC (6,) PHYSICAL PRINCIPLES 43 Figure 3 .6 The law of consecutive metals Figure 3 .7 A circuit of three metals This equation demonstrates another important thermoelectric law known as the law of consecutive metals, which may be stated as : metals B C A C A B C C A C B 00( A 13 Asi 3 1 r -1 -1 1 or finally : : and C at given temperature difference of both r equals " difference r r : and C would form with metal A, at the same temperature difference . 3 .1 .4 Law of consecutive temperatures thermoelectric . - . . - r r . r . . - (6 1 ,6 3 ) r r When equation (3 .24b) is subtracted on both sides of equation (3 .24a) it is seen that : - r r - (63,62) r r 44 THERMOELECTRIC THERMOMETERS I ~ I I (W (b) I I A E ,9i 43 ~~ E AB ( .3 4 ) ~ A ~~ I I B ~ E AB ( A '~2 ) I I A BA C BA B i $ I I aB ( ~ 4 1 A I I B ' A8 f' ? '3 r I I I I B n P2 .92 '_, .9 PA Z $ n4 Figure 3 .8 Law of consecutive metals ; (a) thermoelectric circuits, (b) determination of resulting emf by linear superposition or finally EAS( 6 ), 0 3) = EAB(O), 02) - EAB( 6 3, 62) (3 .25) This relation is known as the law of consecutive temperatures which states : The emf of a circuit whose measuring junction is at a temperature 01, andwhose reference junction is at a temperature equals the difference in the emfs of this circuit when its reference junction is at a temperature of andofa circuit whose measuring junction temperature is and its reference junction temperature is . This law of consecutive temperatures allows the application of the principle of superposition in the determination of the overall emf as shown in Figure 3 .8(b) . 3 .2 Thermocouples 3 2 .1 General information The combination of two dissimilar conductors, which may be metals, alloys or non-metals, connected at oneend is known as a thermocouple . In the notation shown in Figure 3 .9, their point of connection is called the measuring junction and their free ends are referred to as the reference junction . MEASURING CONDUCTORS JUNCTION 1! REFERENCE I JUNCTION Figure 3 .9 The physical structure and notation of a thermocouple placed THERMOCOUPLES 45 as far . " . possible " " " - series " f Table 3 . 1, form the most suitable thermocouples . In this way as high an emf as possible is ensured for a given temperature difference . Thermocouple materials should be characterised by : " high melting temperature, " high permissible working temperature, " high resistance to oxidation and atmospheric influences, " properties which are stable with time, properties repeatable in manufacture, " " - continuous " possibly dependence " " - " In practice the commonly used thermocouple materials make a compromise between the shown in Figure 3 . 10 . In this figure, and throughout this book, the convention of quoting different demands quoted above . The emf versus temperature values of the more commonly used thermocouples are the positive conductorfirst in the specific name of the thermocouple is used . The majority of the thermocouples which will be described below are given in the standard IEC 584, Part " f the International Electro-technical Commission . Moreover they also conform to the national standards of many other countries such as France, Germany, Italy, Japan, Poland, UK, USA and Russia . 80 70 60 1 ~ """" p' . " ~ "" ~" .' 30 20 1 1 ~/ " ~ 0 . 0 200 400 600 800 1000 1200 1400 16 DO 18W TEMPERATURE 3 *C Figure 3 .10 Thermal emf, E, of commonly used thermocouples as a ftinction of temperature 4 6 THERMOELECTRIC THERMOMETERS 3 .2 .2 Properties of commonly used thermocouples The International Standard IEC 584 of 1995 covers the following standardised thermocouples : Platinum-10 % rhodium / platinum, code S, Platinum-13 % rhodium / platinum, code R, Platinum-30 % rhodium / platinum - 6 % rhodium, code B, Iron / copper-nickel, code J, Copper / copper-nickel, code T, Nickel-chromium / copper-nickel, code E, Nickel-chromium / nickel-aluminium, code K, Nickel-chromium-silicon / nickel-silicon, code N . The reference calibration tables of standardised thermocouples are given at the end of the book in Tables II to IX and the tolerances upon their output values in Table X . Table XI gives the polynomials for calculating the reverse functions t 9o = f (E) for computer applications . Typical data for standardised thermocouple wires, with commonly used diameters are in Table XIII, where the maximum permissible working temperatures in pure air are also quoted . Properties of metals and alloys for thermocouples are given in Table 3 .2 . Platinum-rhodium /platinum, code S, (90 % Pt-10 % Rh / Pt), as defined in IEC 584-1, is the most popular of all the rare-metal thermocouples . Although it is specified for normal continuous use in the range -50 °C to +1300 °C it could be extended to +1600 °C for short- term readings . As its structure gives a high resistance to corrosion, quite thin wires may be used, resulting in low cost and low thermal inertia of the thermocouple . In spite of its good resistance to oxidising gases up to 1200 °C, Kinzie (1973) has pointed out that it is easily affected by Si and Fe and cannot tolerate any kind of reducing atmospheres . The presence ofSi0 2 in the insulation and sheath materials, leads to the formation of metallic Si at higher temperatures . Any resulting diffusion of Si into the thermocouple causes a change in its calibration and embrittlement of its wires . Hence it is advisable to use A1 2 0 3 as the sheath material instead . Even traces of S or C may accelerate the above-mentioned processes . Before installation, cleanliness is important . This may be accomplished by washing both wires with alcohol and avoiding manual contact of any kind . Although the Type S thermocouple is quite stable, the Rh may diffuse from the Pt-10%Rh wire into the Pt wire . It is also possible for Rh sublimation to occur from the Pt-10%Rh . Both of these effects influence the calibration of the thermocouple by introducing errors which may be as high as 2 °C after exposure in oxidising atmospheres for about 100 hours to temperatures in the region of 1200 °C . Prior to 1922 in the UK, two different classes of Pt-10 % Rh / Pt thermocouples, whose emfs differed by about 10 %, were available . When it was discovered that one of them contained a large amount of impurities, manufacturers began to supply a new type of Pt- 13 %Rh / Pt, which gave roughly the same emf versus temperature relationship as the older Pt-10 %Rh / Pt unit .