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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 .