314Chapter8TemperatureMeasurementsstem of thethermometer.The stemcontainsa capillary tube,andthedifference in thermal expansionbetween the liquid and the glass produces a detectable change in the level of the liquid in the glasscapillary.Principles and practices of temperature measurement using liquid-in-glass thermometersare described elsewhere (4).During calibration, such a thermometer is subject to one of three measuring environments:1.For a complete immersion thermometer,the entire thermometer is immersed in thecalibrating temperature environment or fluid.2. For a total immersion thermometer, the thermometer is immersed in the calibratingtemperature environment up to the liquid level in the capillary.3. For a partial immersion thermometer, the thermometer is immersed to a predeterminedlevel in the calibrating environment.For the most accurate temperature measurements, the thermometer should be immersed in the samemanner in use as it was during calibration.?Temperaturemeasurements using liquid-in-glass thermometers can provide uncertainies as lowas o.01°C under very carefully controlled conditions; however, extraneous variables such aspressure and changes in bulb volume over time can introduce significant errors in scale calibration.For example, pressure changes increase the indicated temperature by approximately 0.1°C peratmosphere (6).Practical measurements using liquid-in-glass thermometers typically result in totaluncertainties that range from 0.2to 2C, depending on the specific instrument.Mercury-in-glass thermometers have limited engineering applications, but do provide reliable,accurate temperature measurement.As such,they are often used as a local standard for calibration ofother temperature sensors.BimetallicThermometersThephysical phenomenon employed in a bimetallic temperature sensor is thedifferential thermalexpansion of two metals. Figure 8.3 shows the construction and response of a bimetallic sensor to aninput signal.The sensor is constructed by bonding two strips of different metals, A and B. Theresulting bimetallic strip may be in a variety of shapes, depending on the particular application.Consider the simple linear construction shown in Figure 8.3. At the assembly temperature, Tr, thebimetallic strip is straight; however, for temperatures other than T,the strip has a curvature.Thephysical basis for the relationship between the radius of curvature and temperature is given asd(8.1)re[(C)A - (Ca)n](T2 - T.)wherere=radius of curvatureC=material thermal expansion coefficientT=temperatured=thickness2 In practice, it may not be possible to employ the thermometer in exactly the same way as when it was calibrated. In thiscase, stem corrections can be applied to the temperature reading (5)
E1C08 09/14/2010 14:53:56 Page 314 stem of the thermometer. The stem contains a capillary tube, and the difference in thermal expansion between the liquid and the glass produces a detectable change in the level of the liquid in the glass capillary. Principles and practices of temperature measurement using liquid-in-glass thermometers are described elsewhere (4). During calibration, such a thermometer is subject to one of three measuring environments: 1. For a complete immersion thermometer, the entire thermometer is immersed in the calibrating temperature environment or fluid. 2. For a total immersion thermometer, the thermometer is immersed in the calibrating temperature environment up to the liquid level in the capillary. 3. For a partial immersion thermometer, the thermometer is immersed to a predetermined level in the calibrating environment. For the most accurate temperature measurements, the thermometer should be immersed in the same manner in use as it was during calibration.2 Temperature measurements using liquid-in-glass thermometers can provide uncertainies as low as 0.01C under very carefully controlled conditions; however, extraneous variables such as pressure and changes in bulb volume over time can introduce significant errors in scale calibration. For example, pressure changes increase the indicated temperature by approximately 0.1C per atmosphere (6). Practical measurements using liquid-in-glass thermometers typically result in total uncertainties that range from 0.2 to 2C, depending on the specific instrument. Mercury-in-glass thermometers have limited engineering applications, but do provide reliable, accurate temperature measurement. As such, they are often used as a local standard for calibration of other temperature sensors. Bimetallic Thermometers The physical phenomenon employed in a bimetallic temperature sensor is the differential thermal expansion of two metals. Figure 8.3 shows the construction and response of a bimetallic sensor to an input signal. The sensor is constructed by bonding two strips of different metals, A and B. The resulting bimetallic strip may be in a variety of shapes, depending on the particular application. Consider the simple linear construction shown in Figure 8.3. At the assembly temperature, T1, the bimetallic strip is straight; however, for temperatures other than T1 the strip has a curvature. The physical basis for the relationship between the radius of curvature and temperature is given as rc / d ð Þ Ca A ð Þ Ca B ð Þ T2 T1 ð8:1Þ where rc ¼ radius of curvature Ca ¼ material thermal expansion coefficient T ¼ temperature d ¼ thickness 2 In practice, it may not be possible to employ the thermometer in exactly the same way as when it was calibrated. In this case, stem corrections can be applied to the temperature reading (5). 314 Chapter 8 Temperature Measurements
3158.4ElectricalResistanceThermometryaEnd position changes withtemperatureMetal ABonded attemperature TSpiralMetal BMetal AAt temperatureT2T2>T,Meta(C,)A(C,)BHelixEnd position rotates with temperatureFigure 8.3Expansion thermometryusing bimetallic materials: strip,spiral,and helix forms.Bimetallic strips employ onemetal having a high coefficient of thermal expansion with anotherhaving a low coefficient, providing increased sensitivity. Invar is often used as one of the metals,since for this material Ca = 1.7 × 10-8 m/m°C, as compared to typical values for other metals,suchassteels,whichrangefromapproximately2×10-to20×10-5m/m°C.The bimetallic sensor is used in temperature control systems, and is the primary element in mostdial thermometers and many thermostats.The geometries shown in Figure 8.3 serve to provide thedesired deflection in the bimetallic strip for a given application. Dial thermometers using abimetallic strip as their sensing element typically provide temperature measurements with uncer-tainties of ±1°C.8.4ELECTRICALRESISTANCETHERMOMETRYAs a result ofthe physical nature of theconduction ofelectricity,electrical resistance ofa conductoror semiconductor varies with temperature. Usingthis behavior as the basis for temperaturemeasurement is extremely simple inprinciple,and leadsto two basic classesof resistancethermometers:resistance temperature detectors (conductors)and thermistors (semiconductors).Resistance temperature detectors (RTDs)may be formed from a solid metal wire that exhibits anincrease in electrical resistance with temperature. Depending on the materials selected, theresistance may increase or decrease withtemperature.As a first-order approximation,the resistancechangeof athermistormaybeexpressed as(8.2)R- Ro = k(T - To)where k is termed the temperature coefficient. A thermistor may have a positive temperaturecoefficient(PTC)oranegativetemperaturecoefficient(NTC).Figure8.4 showsresistanceasafunction oftemperaturefor avariety of conductor and semiconductormaterialsusedtomeasuretemperature.The PTC materials are metals or alloys and the NTC materials are semiconductors.Cryogenic temperatures areincluded in this figure, and germanium is clearly an excellent choiceforlow temperature measurement because of its large sensitivity
E1C08 09/14/2010 14:53:56 Page 315 Bimetallic strips employ one metal having a high coefficient of thermal expansion with another having a low coefficient, providing increased sensitivity. Invar is often used as one of the metals, since for this material Ca ¼ 1:7 108 m=mC, as compared to typical values for other metals, such as steels, which range from approximately 2 105 to 20 105 m=mC. The bimetallic sensor is used in temperature control systems, and is the primary element in most dial thermometers and many thermostats. The geometries shown in Figure 8.3 serve to provide the desired deflection in the bimetallic strip for a given application. Dial thermometers using a bimetallic strip as their sensing element typically provide temperature measurements with uncertainties of 1C. 8.4 ELECTRICAL RESISTANCE THERMOMETRY As a result of the physical nature of the conduction of electricity, electrical resistance of a conductor or semiconductor varies with temperature. Using this behavior as the basis for temperature measurement is extremely simple in principle, and leads to two basic classes of resistance thermometers: resistance temperature detectors (conductors) and thermistors (semiconductors). Resistance temperature detectors (RTDs) may be formed from a solid metal wire that exhibits an increase in electrical resistance with temperature. Depending on the materials selected, the resistance may increase or decrease with temperature. As a first-order approximation, the resistance change of a thermistor may be expressed as R R0 ¼ k Tð Þ T0 ð8:2Þ where k is termed the temperature coefficient. A thermistor may have a positive temperature coefficient (PTC) or a negative temperature coefficient (NTC). Figure 8.4 shows resistance as a function of temperature for a variety of conductor and semiconductor materials used to measure temperature. The PTC materials are metals or alloys and the NTC materials are semiconductors. Cryogenic temperatures are included in this figure, and germanium is clearly an excellent choice for low temperature measurement because of its large sensitivity. d Helix Metal A Metal A Metal B Metal B Bonded at temperature T1 At temperature T2 T2 T1 (C )A (C )B Spiral End position changes with temperature End position rotates with temperature rc Figure 8.3 Expansion thermometry using bimetallic materials: strip, spiral, and helix forms. 8.4 Electrical Resistance Thermometry 315
316Chapter8TemperatureMeasurements106carbon-el..0.PlatinumRTD (100ohm)Rhodium-ironCernox(CX-1030)X105Rutheniumoxide(1000ohm)DGermaniumRTD(GR-200A-30)104-1+0A7中(S103口口D102D.0口0101no100 -10-110.1101001000Temperature(K)Figure 8.4 Resistance as a function of temperature for selected materials used as temperature sensors.(Adapted from Yeager, C.J. and S. S.Courts, A Review of Cryogenic Thermometry and Common TemperatureSensors,IEEESensorsJournal,1(4),2001.)ResistanceTemperatureDetectorsIn the case of a resistance temperature detector (RTD),the sensor is generally constructed bymounting a metal wire on an insulating support structure to eliminate mechanical strains, and byencasing the wire to prevent changes in resistance due to influences from the sensor's environment,such as corrosion.Figure 8.5 shows such a typical RTD construction.Mechanical strain changes a conductor's resistance and must be eliminated if accuratetemperature measurements are to be made.This factor is essential because the resistance changeswith mechanical strain are significant, as evidenced by the use ofmetal wire as sensorsfor thedirectmeasurement of strain.Suchmechanical stresses and resulting strains can be created by thermalexpansion.Thus,provision for strain-free expansion of the conductor as its temperature changes isessential in the construction ofan RTD.The support structure also expands as thetemperature of theRTD increases,and theconstruction allows for strain-free differential expansion.3 The term RTD in this context refers to metallic PTC resistance sensors
E1C08 09/14/2010 14:53:56 Page 316 Resistance Temperature Detectors In the case of a resistance temperature detector (RTD),3 the sensor is generally constructed by mounting a metal wire on an insulating support structure to eliminate mechanical strains, and by encasing the wire to prevent changes in resistance due to influences from the sensor’s environment, such as corrosion. Figure 8.5 shows such a typical RTD construction. Mechanical strain changes a conductor’s resistance and must be eliminated if accurate temperature measurements are to be made. This factor is essential because the resistance changes with mechanical strain are significant, as evidenced by the use of metal wire as sensors for the direct measurement of strain. Such mechanical stresses and resulting strains can be created by thermal expansion. Thus, provision for strain-free expansion of the conductor as its temperature changes is essential in the construction of an RTD. The support structure also expands as the temperature of the RTD increases, and the construction allows for strain-free differential expansion. 3 The term RTD in this context refers to metallic PTC resistance sensors. 0.1 10-1 100 101 102 103 104 105 106 1 10 100 1000 Temperature (K) Carbon-glass Platinum RTD (100 ohm) Rhodium-iron Cernox (CX-1030) Ruthenium oxide (1000 ohm) Germanium RTD (GR-200A-30) Resistance (OHMS) Figure 8.4 Resistance as a function of temperature for selected materials used as temperature sensors. (Adapted from Yeager, C. J. and S. S. Courts, A Review of Cryogenic Thermometry and Common Temperature Sensors, IEEE Sensors Journal, 1 (4), 2001.) 316 Chapter 8 Temperature Measurements
3178.4ElectricalResistanceThermometryEvacuatedspace0008000000000000068680001SensitivehelicalcoilPyrex tube(鲁 in. 0.D.)MicacrossformFigure8.5ConstructionofaplatinumRTD.(FromBenedict,R.P.,FundamentalsofTemperature,PressureandFlowMeasurements,3rd ed.Copyright1984byJohnWileyand Sons,NewYork.)The physical basis for therelationship between resistance and temperature is the temperaturedependence of the resistivity Pe of a material.The resistance of a conductor of length / and cross-sectional area Amaybe expressed interms of the resistivityPeasR=P/(8.3)A.The relationship between the resistance of a metal conductor and its temperature may also beexpressed as thepolynomial expansion:R = Ro1+α(T - To) +β(T - To) + ..(8.4)where Ro is a reference resistance measured at temperature To.The coefficients α,β,..:arematerial constants.Figure 8.6 shows the relative relation between resistance and temperature forthree common metals.This figure provides evidence that the relationship between temperature andresistance over specific small temperaturerangesis linear.This approximation canbe expressed asR= Ro[1 + α(T- To)](8.5)whereα is the temperature coefficient of resistivity.Forexample,forplatinumconductors the linearapproximation is accurate to within an uncertainty of ±0.3%over the range 0-200°C and ±1.2%over the range200-800°C.Table 8.2 lists a number of temperaturecoefficients ofresistivity αformaterials at20°C
E1C08 09/14/2010 14:53:56 Page 317 The physical basis for the relationship between resistance and temperature is the temperature dependence of the resistivity re of a material. The resistance of a conductor of length l and crosssectional area Ac may be expressed in terms of the resistivity re as R ¼ rel Ac ð8:3Þ The relationship between the resistance of a metal conductor and its temperature may also be expressed as the polynomial expansion: R ¼ R0 1 þ að Þþ T T0 bð Þ T T0 2 þ h i ð8:4Þ where R0 is a reference resistance measured at temperature T0. The coefficients a,b, . . . are material constants. Figure 8.6 shows the relative relation between resistance and temperature for three common metals. This figure provides evidence that the relationship between temperature and resistance over specific small temperature ranges is linear. This approximation can be expressed as R ¼ R0½ ð 1 þ að Þ T T0 8:5Þ where a is the temperature coefficient of resistivity. For example, for platinum conductors the linear approximation is accurate to within an uncertainty of 0.3% over the range 0–200C and 1.2% over the range 200–800C. Table 8.2 lists a number of temperature coefficients of resistivity a for materials at 20C. 3 8 Evacuated space Mica cross form Sensitive helical coil Pyrex tube in. O.D. l Figure 8.5 Construction of a platinum RTD. (From Benedict, R. P., Fundamentals of Temperature, Pressure, and Flow Measurements, 3rd ed. Copyright # 1984 by John Wiley and Sons, New York.) 8.4 Electrical Resistance Thermometry 317
318Chapter8TemperatureMeasurements109一ONickel,n'61:54Coppe3-Platinum21-01-111111-Figure 8.6Relativeresistanceof3002001001002003004005006007008009000three pure metals (Ro at 0°C).Temperature [°C]PlatinumResistance TemperatureDevice (RTD)Platinum is the most common material chosen for the construction of RTDs.The principle ofoperation is quite simple: platinum exhibits a predictable and reproducible change in electricalresistance with temperature,which can be calibrated and interpolated to a high degree of accuracy.The linear approximation for the relationship between temperature and resistance is valid overa wide temperature range, and platinum is highly stable. To be suitable for use as a secondarytemperature standard, a platinum resistance thermometer should have a value of α not less than0.003925°C-1. This minimum value is an indication of the purity of the platinum. In general, RTDsmay be usedfor the measurement of temperatures ranging from cryogenic to approximately 650°C.Table 8.2 Temperature Coefficient of ResistivityforSelectedMaterialsat20°Cα[°C-"]Substance0.00429Aluminum (Al)0.0007Carbon (C)0.0043Copper (Cu)0.004Gold (Au)Iron (Fe)0.00651Lead (Pb)0.0042Nickel (Ni)0.00670.00017NichromePlatinum (Pt)0.0039270.0048Tungsten (W)
E1C08 09/14/2010 14:53:56 Page 318 Platinum Resistance Temperature Device (RTD) Platinum is the most common material chosen for the construction of RTDs. The principle of operation is quite simple: platinum exhibits a predictable and reproducible change in electrical resistance with temperature, which can be calibrated and interpolated to a high degree of accuracy. The linear approximation for the relationship between temperature and resistance is valid over a wide temperature range, and platinum is highly stable. To be suitable for use as a secondary temperature standard, a platinum resistance thermometer should have a value of a not less than 0.003925C1 . This minimum value is an indication of the purity of the platinum. In general, RTDs may be used for the measurement of temperatures ranging from cryogenic to approximately 650C. –300 –200 –100 0 100 200 300 400 500 Nickel Copper Platinum 600 700 800 900 Temperature [ºC] Relative resistance, R/Ro 0 1 2 3 4 5 6 8 7 9 10 Figure 8.6 Relative resistance of three pure metals (R0 at 0C). Table 8.2 Temperature Coefficient of Resistivity for Selected Materials at 20C Substance a [ C1 ] Aluminum (Al) 0.00429 Carbon (C) 0.0007 Copper (Cu) 0.0043 Gold (Au) 0.004 Iron (Fe) 0.00651 Lead (Pb) 0.0042 Nickel (Ni) 0.0067 Nichrome 0.00017 Platinum (Pt) 0.003927 Tungsten (W) 0.0048 318 Chapter 8 Temperature Measurements