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4 Resistance Thermometers 4 .1  General and Historical Background Resistance thermometers, which change their resistance with temperature, are based on modulating sensors described in Chapter 1 . These sensors, which are also referred to as resistance thermometers detectors and thermo-resistors, require the supply of energy to support the flow of acquired temperature information . When Sir Humphrey Davy, the English chemist who invented the Davy Safety Lamp for use in coal mining, investigated the properties of platinum in 1821, he reported the temperature dependence of its resistance . Later, in 1871, C . W . Siemens (Siemens, 1871) delivered a lecture to the Royal Society in which he presented the possibility of temperature measurement by measuring the corresponding resistance variations of a metal conductor . The sensor presented by him, which was proposed to be of platinum wire, was subsequently investigated during 1874 by a committee . Two of the members of this committee, among others, were W . Thomson (Lord Kelvin) and James Clerk Maxwell . In these investigations, it was discovered that the resistor proposed by Siemens exhibited thermal hysteresis . When conductors are heated up to a high temperature their resistance increases . During a subsequent cooling cycle, the temperature dependent resistance did not reduce along the same path as during the heating up cycle . For this reason it was concluded that the resistor proposed by Siemens could not be used for temperature measurement because of its hysteresis . H . L . Callendar, who was not discouraged by these negative results, continued to research the problem . This research was conducted about the same time as Chappuis was realising the Normal Hydrogen Scale described in Chapter 1 . Eventually, in 1887, Callendar published the paper entitled On the practical measurement of temperature, which may be regarded as the beginning of resistance thermometry (Callendar, 1887, 1891, 1899) . In that work, Callendar proposed the temperature dependent resistance equations for Platinum resistors, which now bear his name . At low temperatures the Callendar equation for platinum resistors was found to be inaccurate when compared with gas thermometry . The proposals made by M . S . Van Dusen in 1925 allowed compensation of these inaccuracies . To indicate the manufacturing problems overcome by Siemens and Callendar, it is instructive to consider a fairly straightforward calculation . 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) 86  RESISTANCE THERMOMETERS Numericalexample The resistivity of platinum at 0 °C is 1 .1x10 -5 S2 cm . Calculate the length of 0 .025 mm diameter wire required for a resistance of 100 0 . Solution : Cross-sectional area of the wire, A = ~ d 2 = 4 (0 .025 x 0 .1 2 = 4 .90873 x 10 -6 cm 2 Hence as R = p I them = 100 x 4 .90873 x 10-6 = 44 .6248 cm A  1 .1 x 10 -5 In Imperial British units, as used by Callendar, this corresponds to 17 .56 in . Therefore, manufacturing required special techniques . Resistance thermometers use the temperature dependence of the resistance of a material in temperature measurement . As platinum is the most commonly used material for resistance thermometers they are often referred to as Pt-RTDs, an acronym for Platinum-Resistance- Thermometer-Detector . They can operate in the temperature range between 13 K (-260 °C) and 1000 K (+700 °C) with good repeatability and stability . 4 .2  Physical Principles The principle of a resistance thermometer is based upon the dependence of the resistance of metal conductors upon temperature . As the temperature of a metal increases, the amplitudes of the thermodynamic vibrations of its atomic nuclei increase . Simultaneously, the probability of collisions between its free electrons and bound ions undergoes corresponding increases . These interruptions of the motion of the free electrons, due to crystalline collisions, cause the resistance of the metal to increase . Consider the general case where a detector, with a resistance,  R, g , is measuring temperature in the neighbourhood of some reference temperature, 00, usually assumed to be 0 ° C . Assume that the temperature is the only factor responsible for the change of resistance of the sensor . Expanding in a Taylor series about 00 gives the resistance, R, y , of the sensor at the temperature, 6 °C, as : 2 R o = Ro  l + i  aR~  AO+  1  (d R6  00 2 + . . . . °  Ro°  a6 ~z)=&°  Moo  a62 Z) . . . .+ 1 a ' R, ~2~"+ . . . . n!Ro°  d O' t9=19 0 PHYSICAL PRINCIPLES  87 where R, yo is its resistance at the reference temperature, 6 0 , and AO = 6 - 7% . Assume a finite increase of temperature, neglect fourth order terms and higher and introduce the conventional definition for the coefficients A, B and C of the change of resistance . Equation (4 .1) may then be written in its most frequently encountered version as : R ay = R oo [1 + AAO + BA6 2 + CA13 3 ]  (4 .2) In equation (4 .2) the coefficients A, B and C, which are normally assumed to be independent of temperature, are defined by : A= 1 (dRO)  (4 .3) 0 do 0=130 B =  l  d 2 R,y  (4 .3a) 2!Roo doe )6=00 C =  l  d 3 R,  (4 .3b) 3! Roo  do 3 )O=t9 O In the usual range of temperatures in which RTDs are used, third order effects can sometimes be neglected so that equation (4 .2) becomes : R O = R Oo [1 + AOt9 + BA0 2 ]  (4 .4) Using a linear temperature dependence for the detector is a convenient, intuitive starting point . Assuming that  0 = 0 ° C, equation (4 .4) can be approximated as : R O = R 0 [1 + a6]  (4 .4a) The assumption, that the conversion of temperature into resistance is a linear function, is correct only for small ranges of the measured temperature . It is also important to emphasise that the coefficient A in equation (4 .4) is not equal to a in equation (4 .4a) . Equation (4 .4a) shows that the resistance increase may be described with the aid of a resistance temperature coefficient, a, which is expressed most commonly as an average value in a given temperature range . In terms of the resistances, R100 and R 0 , at the respective temperatures 100 °Cand0 °C, the defining equation for a has the form : a=  1  R100 - R0  (4 .5) R 0 100 Although equation (4 .4) is a well known representation for the resistance of a Pt-RTD it was quite revolutionary at the time of Callendar . 88  RESISTANCE THERMOMETERS Mueller (1941) quotes the original form of the Callendar (1887) equation as 0= R,,-Ro 100+6 0 -1 0  (4 .6) R100 - Ro  (100  )100 For historical reasons, Callendar's equation is now written in the form : R 6 = Ro 1+a10-6( 100 -1)100,  (4 .7) In equation (4 .7) the constant, 8, is the direct result of Callendar's interpolation algorithm . It compensates for the error, which would be introduced from assuming a linear relation as in equation (4 .4a) . In the range of temperatures below 0°C, in a similar way as for the original Callandar equation Van Dusen (1925) wrote the relation between temperature and resistance as : 73 = R o - Ro 10104 2 L-1 " +p er  1) 6 3  (4 .8) R 100 - R o  100  )100  (100 -  1003 where /3 is called the Van Dusen constant . For the same historical reasons this equation is now written as : R 6 = R0 i  1 l + a 0-6 (100 -1 )100 - P (100 -1 )(100 )']  (4 .9) Some information about further investigations based on Callendar and Van Dusen equations are presented by Mueller (1941) . The problems of nonlinearity in resistance thermometers and of the linearisation of their characteristics are discussed in more detail in Chapter 12 . 4 .3  Resistance Thermometer Detectors (RTDs) 4 .3 .1  General information Resistance thermometer detectors : These sensors, which are also called resistance thermometer elements in BS 1041, or further simply as RTDs, consist of a resistance conductor wound or deposited on an insulating support or former . The nominal resistance, R o , of an RTD is its resistance at the reference temperature of 0 °C . In industrial applications the most commonly used RTDs have a nominal resistance of 100 0 and 50 0 . Pt-RTDs, with R o equal to 10 S2 and 25 S2, are also used for calibration purposes . Metallic RTDs should preferably be made from materials exhibiting the following properties : 9  high resistance temperature coefficient, to ensure high sensitivity, RESISTANCE THERMOMETER DETECTORS (RTDs)  89 "  high resistivity to enable the construction of physically small RTDs, " possibly high melting temperature, "  stable physical properties, "  high resistance to oxidation and corrosion, "  easy reproducibility of the metal with identical properties, " continuous and smooth dependence of resistance versus temperature without any hysteresis, "  sufficient ductility and mechanical strength . In practice mostly pure metals, such as platinum, copper and nickel are used, since they guarantee perfect reproducibility and easy standardisation . As platinum fulfils all of these requirements in the best way, it is the most commonly used metal . The temperature dependence of the resistance of the three materials, platinum, nickel and copper, is shown in Figure 4 .1 . Although nickel and copper are also used, such use is restricted to lower temperatures . Tables XVI to XVIII present the resistance versus temperature relationship and the permissible tolerances of Pt-RTD, Ni-RTD and Cu-RTD . 4 .3 .2  Properties of different metals Platinum . This metal is stable, forgeable and corrosion resistant and can be used at temperatures up to 1000 °C in neutral atmospheres . However, sublimation may cause resistance variations at higher temperatures . It is used in a high purity form for the manufacture of resistance thermometer elements . The ratio, R1001R0 of its resistance at 100 °C to that at 0 °C provides a means of judging its purity, as shown in Table 4 .1 . In the temperature range from 0 to 600°C the resistance versus temperature relationship, has the form given in equation (4 .5) . Nickel : Among all RTD metals, it has the highest resistance temperature coefficient, whilst also being relatively corrosion and oxidation resistant . It is normallyused in the 4 Pt o  Ni a 2 W V Q 1 H N_ VI W = 0 -200 -100 0 100 200 300 4,00 500 600 700 800 900 1000 TEMPERATURE ,9 " °C Figure 4 .1 Resistance R g at 0 °C related to R o at 0 °C versus temperature, 9, for Pt, Ni and Cu . 90  RESISTANCE THERMOMETERS Table 4 .1 Metals used for resistance thermometers . Metal  Operating temperature (°C)  Resistivity at 0 °C  R1001R0 N orm al Sp ecial  (pQ m) Platinum  -200 to +850  -260 to +1000  0 .10 to 0 .11  1 .385 Nickel  -60 to +150  -60 to +180  0 .09 to 0 .11  1 .617 Copper  -50 to +150  -50 to +150  0 .017 to 0 .018  1 .426 Rhodium - Iron  -200 to + 200  -200 to + 25 0  1 .379 range up to about 180 °C . An inflection at about 350 °C, changes its resistance versus temperature dependence . Copper . Because of its poor oxidation resistance . copper is rarely employed . It is sometimes used about ambient temperatures and also in refrigeration engineering . One of its popular applications is the temperature measurement of the windingsof transformers and electrical machines, where the windings themselves constitute the resistance element . Rhodium-iron (0 .5%) .  Rusby (1972) originally proposed its use at temperatures below 20 K . It is now used up to 220°C (Mao Yuzhu et al . 1992) exhibiting good precision and repeatability . 4 .3 .3 Construction RTDs are manufactured in a wide range of types including special purpose units . Table 4 .2 gives the properties of typical resistance detectors . Although general purpose detectors have wire-wound elements, thin film elements are becoming increasingly popular . Only typical detectors are considered in the reviewof different types, which is given below . Wire-wound detectors :  By far the majority of all RTDs are based upon a wire-wound structure as shown in Figure 4 .2 . To ensure a minimum inductance the resistance windings are invariably of the bifilar form . For many years, it has been common practice to use detectors made from cylindrical formers of glass, quartz or ceramic with a fine wire winding of about 0 .01-0 .1 mm diameter . This resistance winding, marked 1 in Figure 4 .2(a), which is formed on a rod, 2, or tube of glass or quartz, is protected and held in place by a thin coating, 3, of the same material as the rod . Their typical application range is from -200'C to +500°C for Pt-in-glass elements, up to +600°C for quartz glass and up to +1000 °C for ceramic types (Evans, 1972) . Figure 4 .2(b) presents another construction of an RTD in which small diameter, helical-shaped, resistance windings are placed in the bores of a ceramic tube, 5 . Johnston (1975) has pointed out that this structure is especially vibration resistant . Multiple detectors, having two or three independent windings, are used for simultaneous temperature measurement and control, as well as in some bridge circuits to increase the sensitivity . In the temperature range from -60 °C to +150 °C, Ni-wire wound detectors are used . In this type, resistance wire is insulated and protected by teflon tape or glass fibre . RESISTANCE THERMOMETER DETECTORS (RTDs)  91 4 {01  4 _  (b}  ~6 5 3 2 !  6 j 1-Pt-WIRE  4-TERMINALS 2-GLASS OR QUARTZ ROD  5-CERAMICTUBE 3-COATING  6-GLAZED SEALING Figure 4 .2 Structure of wire-wound Pt-RTDs Thin-film RTDs .  In units of this type, which have been considered by Clayton (1988), the platinum material is deposited upon a suitable ceramic substrate . Some Pt-100 0 detectors, which may be used up to about 600 °C for gas and surface temperature measurement, are as small as lOx3x1 mm . This small size gives a time constant, NT, which is a dynamic performance parameter considered in greater detail in Chapter 15, with a value of 11 s, in an air flow with a velocity of 1 m/s (Heraeus GmbH Germany) . They may be either glued or soldered to the body surface (Section 16 .3 .2) . The smallest thin-film RTDs, which can be used from -50 °C to +200 °C, have the dimensions 2x2 .3xI mm (Omega Engineering Inc ., USA) . New manufacturing technology has led to the production of 1000 52, ceramic thin film RTDs, whose resistance is adjusted by a computer controlled laser (Hycal Engineering, USA) . The high detector resistance markedly reduces the influence of connecting lead resistances upon the readings of the thermometer . They are used in the range from -200 up to +540 °C . Measuring current .  To measure the actual resistance of an RTD an electric current is passed through the detector . As this current produces a heating effect, which may cause additional measuring errors, it must be limited to a permissible value . The maximum permissible current is a function of the heat exchange from the detector, which depends on the physical shape of its surface, the material of its protective sheath and on the surrounding medium . The permissible measuring current, IT,max may be expressed in terms of the maximum allowable self-heating temperature error, O&max °C, the resistance of the detector, R, ) 0, at 0 °C and the heat dissipation constant, A W/°C by the equation : Table 4 .2  Characteristics of typical RTDs Heat dissipation constant A (MW/°C) Construction  in still  in flowing Temperature air air Inner  Outer  Dimensions  range  v=1 m/s insulation insulation  Detector  (mm)  (°C) Cylindrical I Ceramic  Ceramic  Pt-100 4  d 1 to 2 .8  -220 to +750  1 .5 to 9  12 to 50 wire  125 to 50  short term to +850 Cylindrical I Ceramic  Ceramic  2xPt-100 S2  d l .7 to 2 .8  -220 to +750  3 to 8  12 to 20 wire  125 to 50  short term to +850 Cylindrical I Glass  Glass  Pt-100 S2  d2 .5 to 5  -220 to +600  4  13 wire  112 to 60 Cylindrical I Glass  Glass  2xPt-100 0  d 3 .6 to 5  -220 to +600  4  13 wire  120 to 60 Cylindrical 1,2 Ceramic  Ceramic  Pt-100 b2  d 1 .8 to 3 .8  -220 to +500  2  10 glaze  wire  120 to 30 Cylindrical 1,2 Glass  Silicon  Pt-100 S2  d 1 to 1 .8 ire  112 to 23 -60 to +350  1 .2  5 w Flatl Ceramic  Glass  Pt-100 S2 thin film  10 .2x3 .2x1  -200 to +500  1 .9  75 (in still water) Cylindrical 2 Ceramic  Ceramic  Pt-100 S2  d 3 .1  -70 to +500  _  50 thick film  128  (in still water) Cylindrical 2 Ceramic  Ceramic  Pt-100 S2 to 2000 S2  17 to 312  -50 to +600  -  - thin film F1at 2 Ceramic  Ceramic  Pt-100 12 to  2x23x1 1000 52  2x I0x 1  - 50 to +200  -  - thin film Cylindrical Ceramic  Plastics  Ni-100 92  d 5 .2  -60 to +150  4  16 .6 wire 130 1 . Heraeus, GmbH, Germany 2 . Omega Engineering Inc ., USA 94  RESISTANCE THERMOMETERS IT  AO max ``I ,max -  4 .10 R e The heat dissipation constant, A, is defined as that heating power which causes, in the thermal steady-state, the self-heating of a resistance element by 1 °C . The constant A in still water is about forty times bigger than in still air . Some values for A, in still and flowing air, are given in Table 4 .2 . Measuring currents of about 1-2 mA do not usually cause any significant self-heating errors . Numerical example A Pt-100 S2 resistance detector without any protective tube is located in still air at 60 °C . Calculate the permissible measuring current, IT,max to ensure that the self-heating error is less than 0 .5 °C . Assume that the heat dissipation constant, A, has a value of 4x10 -3 WPC and R60 = 123 .24 0 from Table XVI . Solution : From equation (4 .10) the calculation gives _  0 .5 x4 x10 -3 IT,max  4 mA 123 .24 - 4 .4  Resistance Thermometer Sensors Sometimes resistance detectors may be immersed directly in the medium whose temperature is to be measured . In general, however, they require protection against moisture, chemical influences and mechanical damage . A resistance detector with its protection sheath forms a resistance thermometer sensor or assembly . The combination, which is illustrated in Figure 4 .3, consisting of the detector with its connecting leads, ceramic insulation, terminal block and a thin steel sheath, forms a resistance thermometer insert . Compact ceramic insulation, which protects the resistance detector from vibrations, simultaneously ensures good thermal conductivity . Fitted with standard terminal heads, these inserts constitute easily exchangeable resistance thermometer sensor assemblies when combined with a protective sheath . Variations of sheath and thermowell structures for resistance thermometer assemblies have the same general properties as those for thermocouples given in Table 3 .3 . Vibrations and shocks, caused by working in a variety of different machine environments or by the flow of liquid media around them, are the principal causes of mI m 9 145 a 2025  k27 Figure 4 .3 Resistance thermometer insert made by Heraeus GmbH