《工程测试与信号处理》课程教学资源（文献资料）TEMPERATURE MEASUREMENT

Chapter 8Temperature Measurements8.1INTRODUCTIONTemperature is one of the most commonly used and measured engineering variables. Much of ourlives is affected by the diurnal and seasonal variations in ambient temperature,but the fundamentalscientific definition of temperature and a scale for the measurement of temperature are notcommonly understood.This chapter explores the establishment of a practical temperature scaleand common methods of temperature measurement. In addition, errors associated with the designand installation of a temperature sensor are discussed.Upon completion of this chapter, the reader will be able to·describe theprimary standards fortemperature,.state the role of fixed point calibration and thenecessityforaninterpolation method inestablishing a temperature standard,.describeand analyzethermal expansion thermometry.state the physical principle underlying electrical resistance thermometry,.employ standard relationships todeterminetemperaturefrom resistancedevices,analyze thermoelectric circuits designed to measure temperature,describe experiments to determine thermoelectric potential formaterial pairs,.statetheprinciples employed in radiationtemperaturemeasurements,and.estimate the impact of loading errors in temperature measurement.HistoricalBackgroundGuillaume Amontons (1663-1705), a French scientist, was one of the first to explore thethermodynamic nature of temperature. His efforts examined the behavior of a constant volumeof air that was subject to temperature changes.The modern liquid-in-glass bulb thermometertraces itsorigintoGalileo(1565-1642),whoattemptedtousethevolumetric expansionofliquids intubes as a relative measure of temperature.Unfortunately,this open tubedevicewasactually sensitiveto bothbarometric pressure and temperature changes.Amajor advance intemperaturemeasurementoccurred in1630 as a result of a seeminglyunrelated event:the309

E1C08 09/14/2010 14:53:55 Page 309 Chapter 8 Temperature Measurements 8.1 INTRODUCTION Temperature is one of the most commonly used and measured engineering variables. Much of our lives is affected by the diurnal and seasonal variations in ambient temperature, but the fundamental scientific definition of temperature and a scale for the measurement of temperature are not commonly understood. This chapter explores the establishment of a practical temperature scale and common methods of temperature measurement. In addition, errors associated with the design and installation of a temperature sensor are discussed. Upon completion of this chapter, the reader will be able to
describe the primary standards for temperature,
state the role of fixed point calibration and the necessity for an interpolation method in establishing a temperature standard,
describe and analyze thermal expansion thermometry,
state the physical principle underlying electrical resistance thermometry,
employ standard relationships to determine temperature from resistance devices,
analyze thermoelectric circuits designed to measure temperature,
describe experiments to determine thermoelectric potential for material pairs,
state the principles employed in radiation temperature measurements, and
estimate the impact of loading errors in temperature measurement. Historical Background Guillaume Amontons (1663–1705), a French scientist, was one of the first to explore the thermodynamic nature of temperature. His efforts examined the behavior of a constant volume of air that was subject to temperature changes. The modern liquid-in-glass bulb thermometer traces its origin to Galileo (1565–1642), who attempted to use the volumetric expansion of liquids in tubes as a relative measure of temperature. Unfortunately, this open tube device was actually sensitive to both barometric pressure and temperature changes. A major advance in temperature measurement occurred in 1630 as a result of a seemingly unrelated event: the 309

310Chapter8Temperature Measurementsdevelopment of thetechnologyto manufacture capillaryglass tubes.Thesetubeswerethenused with waterand alcohol ina thermometricdevice resemblingthebulbthermometer,andthese devices eventually led to the development of a practical temperature-measuringinstrument.A temperature scale proposed by Gabriel D. Fahrenheit, a German physicist (1686-1736), in1715attempted to incorporatebodytemperature as the median point on a scalehaving180 divisionsbetween the freezing point and the boiling point of water.Fahrenheit also successfullyused mercuryas the liquid in a bulb thermometer, making significant improvements over the attempts of IsmaelBoulliau in 1659.In 1742, the Swedish astronomer Anders Celsius(1701-1744) described atemperature scale that divided the interval between the boiling and freezing points of water at I atmpressure into 100 equal parts. The boiling point of water was fixed as O, and the freezing point ofwateras100.ShortlyafterCelsius'sdeath,CarolusLinnaeus(1707-1778)reversedthescalesothatthe O point corresponded to thefreezingpoint of water at 1 atm.Even though this scale may not havebeen originated by Celsius (1), in 1948 the change from degrees centigrade to degrees Celsius wasofficiallyadopted.As stated by H. A. Klein in The Science of Measurement: A Historical Survey (2),From the original thermoscopes of Galileo and some of his contemporaries, the measurement oftemperature has pursuedpaths of increasing ingemuity,sophistication and complexity.Yettemperatureremains in its inmermostessence theaverage molecularor atomic energy of the least bits making upmatter, in their endless dance.Matter without motion is unthinkable.Temperature is the mostmeaningfulphysicalvariablefordealingwith the effectsofthoseinfinitesimal,incessant internalmotionsofmatter.8.2TEMPERATURESTANDARDSANDDEFINITIONTemperature can be loosely described as the property of an object that describes its hotnessor coldness,concepts thatareclearly relative.Our experiences indicatethat heat transfertendsto equalize temperature,or more precisely,systems that are in thermal communicationeventually have equal temperatures.The zeroth law of thermodynamics states that twosystems in thermal equilibrium with a third system are in thermal equilibrium with eachother.Thermal equilibrium implies that no heat transfer occurs between the systems, definingtheequalityoftemperature.Althoughthezerothlawofthermodynamicsessentiallyprovidesthe definition of the equality of temperature, it provides no means for defining atemperature scale.A temperature scale provides for three essential aspects of temperature measurement: (l) thedefinition of the size of the degree, (2) fixed reference points for establishing known temperatures,and (3)a means for interpolating between these fixed temperature points.These provisions areconsistent with the requirements for any standard, as described in Chapter 1.'It is interesting to note that in addition to his work in thermometry, Celsius published significant papers on the auroraborealis and thefalling level of the Baltic Sea

E1C08 09/14/2010 14:53:55 Page 310 development of the technology to manufacture capillary glass tubes. These tubes were then used with water and alcohol in a thermometric device resembling the bulb thermometer, and these devices eventually led to the development of a practical temperature-measuring instrument. A temperature scale proposed by Gabriel D. Fahrenheit, a German physicist (1686–1736), in 1715 attempted to incorporate body temperature as the median point on a scale having 180 divisions between the freezing point and the boiling point of water. Fahrenheit also successfully used mercury as the liquid in a bulb thermometer, making significant improvements over the attempts of Ismael Boulliau in 1659. In 1742, the Swedish astronomer Anders Celsius1 (1701–1744) described a temperature scale that divided the interval between the boiling and freezing points of water at 1 atm pressure into 100 equal parts. The boiling point of water was fixed as 0, and the freezing point of water as 100. Shortly after Celsius’s death, Carolus Linnaeus (1707–1778) reversed the scale so that the 0 point corresponded to the freezing point of water at 1 atm. Even though this scale may not have been originated by Celsius (1), in 1948 the change from degrees centigrade to degrees Celsius was officially adopted. As stated by H. A. Klein in The Science of Measurement: A Historical Survey (2), From the original thermoscopes of Galileo and some of his contemporaries, the measurement of temperature has pursued paths of increasing ingenuity, sophistication and complexity. Yet temperature remains in its innermost essence the average molecular or atomic energy of the least bits making up matter, in their endless dance. Matter without motion is unthinkable. Temperature is the most meaningful physical variable for dealing with the effects of those infinitesimal, incessant internal motions of matter. 8.2 TEMPERATURE STANDARDS AND DEFINITION Temperature can be loosely described as the property of an object that describes its hotness or coldness, concepts that are clearly relative. Our experiences indicate that heat transfer tends to equalize temperature, or more precisely, systems that are in thermal communication eventually have equal temperatures. The zeroth law of thermodynamics states that two systems in thermal equilibrium with a third system are in thermal equilibrium with each other. Thermal equilibrium implies that no heat transfer occurs between the systems, defining the equality of temperature. Although the zeroth law of thermodynamics essentially provides the definition of the equality of temperature, it provides no means for defining a temperature scale. A temperature scale provides for three essential aspects of temperature measurement: (1) the definition of the size of the degree, (2) fixed reference points for establishing known temperatures, and (3) a means for interpolating between these fixed temperature points. These provisions are consistent with the requirements for any standard, as described in Chapter 1. 1 It is interesting to note that in addition to his work in thermometry, Celsius published significant papers on the aurora borealis and the falling level of the Baltic Sea. 310 Chapter 8 Temperature Measurements

8.2311TemperatureStandardsandDefinitionFixedPoint TemperaturesandInterpolationTo begin, consider the definition of the triple point of water as having a value of 0.01 for ourtemperature scale, as is donefor the Celsius scale (O.01°C).This provides for an arbitrary startingpointfor a temperature scale;infact,thenumber valueassigned to this temperaturecouldbeanything. On the Fahrenheit temperature scale it has a value very close to 32.Consider another fixedpointon ourtemperature scale.Fixed points aretypicallydefinedbyphase-transitiontemperaturesor the triple point of a pure substance.The point at which pure water boils at one standardatmosphere pressure is an easily reproducible fixed temperature. For our purposes let's assign thisfixedpointanumerical valueof100.The next problem is to define the size of the degree. Since we have two fixed points on ourtemperature scale, we can see that the degree is 1/10Oth of the temperature difference between theicepoint and the boilingpoint of water at atmospheric pressure.Conceptually,this defines a workable scale for the measurement of temperature; however, as yetwe havemade no provision for interpolating between the two fixed-point temperatures.InterpolationThe calibration of a temperature measurement device entails not only the establishment of fixedtemperaturepointsbutalsothe indicationofanytemperaturebetweenfixedpoints.Theoperationofa mercury-in-glass thermometer is based on the thermal expansion of mercury contained in a glasscapillary where the level of the mercury is read as an indication of the temperature. Imagine that wesubmerged the thermometer in water at the icepoint, made a mark on the glass at the height of thecolumn of mercury, and labeled it 0°C, as illustrated in Figure 8.1.Next we submerged thethermometer in boiling water, and again marked the level of the mercury,thistime labeling it 10°C.Using reproducible fixed temperature points we have calibrated our thermometer at two points;however,wewanttobe abletomeasuretemperatures otherthanthesetwofixed points.Howcan wedeterminetheappropriateplaceon the thermometer tomark, say,50°C?The process of establishing 50°C without a fixed-point calibration is called interpolation. Thesimplest option would be to divide the distance on the thermometer between the marks representing100Fixed point:boiling point (1 atm)50Interpolated pointJ2CFixed point:freezing point (1 atm)Figure 8.1 Calibration and interpolation for a liquid-in-glass thermometer

E1C08 09/14/2010 14:53:55 Page 311 Fixed Point Temperatures and Interpolation To begin, consider the definition of the triple point of water as having a value of 0.01 for our temperature scale, as is done for the Celsius scale (0.01C). This provides for an arbitrary starting point for a temperature scale; in fact, the number value assigned to this temperature could be anything. On the Fahrenheit temperature scale it has a value very close to 32. Consider another fixed point on our temperature scale. Fixed points are typically defined by phase-transition temperatures or the triple point of a pure substance. The point at which pure water boils at one standard atmosphere pressure is an easily reproducible fixed temperature. For our purposes let’s assign this fixed point a numerical value of 100. The next problem is to define the size of the degree. Since we have two fixed points on our temperature scale, we can see that the degree is 1/100th of the temperature difference between the ice point and the boiling point of water at atmospheric pressure. Conceptually, this defines a workable scale for the measurement of temperature; however, as yet we have made no provision for interpolating between the two fixed-point temperatures. Interpolation The calibration of a temperature measurement device entails not only the establishment of fixed temperature points but also the indication of any temperature between fixed points. The operation of a mercury-in-glass thermometer is based on the thermal expansion of mercury contained in a glass capillary where the level of the mercury is read as an indication of the temperature. Imagine that we submerged the thermometer in water at the ice point, made a mark on the glass at the height of the column of mercury, and labeled it 0C, as illustrated in Figure 8.1. Next we submerged the thermometer in boiling water, and again marked the level of the mercury, this time labeling it 100C. Using reproducible fixed temperature points we have calibrated our thermometer at two points; however, we want to be able to measure temperatures other than these two fixed points. How can we determine the appropriate place on the thermometer to mark, say, 50C? The process of establishing 50C without a fixed-point calibration is called interpolation. The simplest option would be to divide the distance on the thermometer between the marks representing Fixed point: boiling point (1 atm) Fixed point: freezing point (1 atm) Interpolated point 100 50 0 L 2 L Figure 8.1 Calibration and interpolation for a liquid-in-glass thermometer. 8.2 Temperature Standards and Definition 311

312Chapter8TemperatureMeasurements0 and 100 into equally spaced degree divisions. This places 50°C as shown in Figure 8.1.Whatassumption is implicit in this method of interpolation? It is obvious that we do not have enoughinformation to appropriately divide the interval between O and 100 on the thermometer into degrees.A theory of the behavior of themercuryin the thermometer or manyfixed points for calibration arenecessary to resolve our dilemma.Evenby the late eighteenthcentury,there was no standardfor interpolating betweenfixedpointson the temperature scale;the result was that different thermometers indicated differenttemperaturesaway from fixed points, sometimes with surprisingly large errors.Temperature Scales and StandardsAt this point, it is necessary to reconcile this arbitrary temperature scale with the idea of absolutetemperature.Thermodynamics defines a temperature scale that has an absolute reference,anddefines an absolute zero for temperature. For example,this absolute temperature governs the energybehavior of an ideal gas, and is used in the ideal gas equation of state.The behavior of real gases atvery low pressure maybe used as a temperature standard to define a practical measure oftemperature that approximates the thermodynamic temperature. The unit of degrees Celsius(°C) is apractical scale related to theKelvin as°C=K-273.15.The modern engineering definition of the temperature scale is provided by a standard called theInternational Temperature Scale of 1990 (ITS-90)(3).This standard establishes fixed points fortemperature, and provides standard procedures and devices for interpolating between fixed points. Itestablishes the Kelvin (K) as the unit for the fundamental increment in temperature. Temperaturesestablished according toITS-9Odonotdeviatefrom thethermodynamic temperature scalebymorethan the uncertainty in the thermodynamic temperature at the time of adoption of ITS-90. Theprimary fixed points from ITS-90 are shown in Table 8.1. In addition to these fixed points, otherfixedpoints of secondaryimportanceareavailableinITS-90.Table8.1TemperatureFixedPoints asDefinedbyITS-90TemperatureaKoCDefining Suite259.346713.8033Triple point of hydrogen~17~-256.15Liquid-vapor equilibrium for hydrogen at 25/76 atm~20.3Liquid-vapor equilibriumforhydrogen at I atm~-252.8724.5561248.5939Triple point of neon54.3584218.7916Triple point of oxygen83.8058Triple point of argon189.3442273.160.01Triple point of waterSolid-liquid equilibrium for gallium at 1 atm302.914629.7646505.078231.928Solidliquid equilibrium for tin at 1 atm692.677419.527Solid-liquid equilibrium for zinc at 1 atm1234.93961.78Solid-liquid equilibrium for silver at 1 atm1337.331064.18Solid-liquid equilibrium for gold at 1 atm1357.771084.62Solid-liquid equilibriumforcopper at1 atm"significant digits shown are as provided in ITS-90

E1C08 09/14/2010 14:53:56 Page 312 0 and 100 into equally spaced degree divisions. This places 50C as shown in Figure 8.1. What assumption is implicit in this method of interpolation? It is obvious that we do not have enough information to appropriately divide the interval between 0 and 100 on the thermometer into degrees. A theory of the behavior of the mercury in the thermometer or many fixed points for calibration are necessary to resolve our dilemma. Even by the late eighteenth century, there was no standard for interpolating between fixed points on the temperature scale; the result was that different thermometers indicated different temperatures away from fixed points, sometimes with surprisingly large errors. Temperature Scales and Standards At this point, it is necessary to reconcile this arbitrary temperature scale with the idea of absolute temperature. Thermodynamics defines a temperature scale that has an absolute reference, and defines an absolute zero for temperature. For example, this absolute temperature governs the energy behavior of an ideal gas, and is used in the ideal gas equation of state. The behavior of real gases at very low pressure may be used as a temperature standard to define a practical measure of temperature that approximates the thermodynamic temperature. The unit of degrees Celsius ( C) is a practical scale related to the Kelvin as C ¼ K  273.15. The modern engineering definition of the temperature scale is provided by a standard called the International Temperature Scale of 1990 (ITS-90) (3). This standard establishes fixed points for temperature, and provides standard procedures and devices for interpolating between fixed points. It establishes the Kelvin (K) as the unit for the fundamental increment in temperature. Temperatures established according to ITS-90 do not deviate from the thermodynamic temperature scale by more than the uncertainty in the thermodynamic temperature at the time of adoption of ITS-90. The primary fixed points from ITS-90 are shown in Table 8.1. In addition to these fixed points, other fixed points of secondary importance are available in ITS-90. Table 8.1 Temperature Fixed Points as Defined by ITS-90 Temperaturea Defining Suite K C Triple point of hydrogen 13.8033 259.3467 Liquid–vapor equilibrium for hydrogen at 25/76 atm 17 256.15 Liquid–vapor equilibrium for hydrogen at 1 atm 20.3 252.87 Triple point of neon 24.5561 248.5939 Triple point of oxygen 54.3584 218.7916 Triple point of argon 83.8058 189.3442 Triple point of water 273.16 0.01 Solid–liquid equilibrium for gallium at 1 atm 302.9146 29.7646 Solid–liquid equilibrium for tin at 1 atm 505.078 231.928 Solid–liquid equilibrium for zinc at 1 atm 692.677 419.527 Solid–liquid equilibrium for silver at 1 atm 1234.93 961.78 Solid–liquid equilibrium for gold at 1 atm 1337.33 1064.18 Solid–liquid equilibrium for copper at 1 atm 1357.77 1084.62 a significant digits shown are as provided in ITS-90. 312 Chapter 8 Temperature Measurements

3138.3ThermometryBasedonThermalExpansionStandardsforInterpolationAlong with the fixed temperature points established by ITS-90, a standard for interpolation betweenthese fixed points is necessary.Standards for acceptable thermometers and interpolating equationsareprovided in ITS-90.For temperatures ranging from 13.8033 to 1234.93K,ITS-90 establishes aplatinum resistance thermometer as the standard interpolating instrument, and establishes interpo-lating equations that relate temperature to resistance.Above1234.93K, temperature is defined interms of blackbody radiation, without specifying an instrument for interpolation (3).In summary, temperature measurement, a practical temperature scale, and standards for fixedpoints and interpolation have evolved over a period of about two centuries.Present standards forfixed-point temperatures and interpolation allow for practical and accurate measurements oftemperature. In the United States,the National Institute of Standards and Technology (NIST)provides for a means to obtain accurately calibrated platinum wire thermometers for use assecondary standards in the calibration of a temperature measuring system to any practical levelof uncertainty.8.3THERMOMETRYBASEDONTHERMALEXPANSIONMost materials exhibit a change in size with changes in temperature.Since this physicalphenomenon is well defined and repeatable, it is useful for temperature measurement. Theliquid-in-glass thermometer and the bimetallic thermometer are based on this phenomenon.Liquid-in-GlassThermometersA liquid-in-glass thermometer measures temperature byvirtue of the thermal expansion ofa liquid.The construction of a liquid-in-glass thermometeris shown in Figure8.2.The liquidis contained in aglass structure that consists of a bulb and a stem.The bulb serves as a reservoir and providessufficient fluid for the total volume change ofthe fluid to cause a detectable rise of the liquid in theImmersion typePartialTotalComplete??oImmersionlevelCapillaryStemImmersionlevelImmersionlevelBulbFigure8.2Liquid-in-glassthermometers

E1C08 09/14/2010 14:53:56 Page 313 Standards for Interpolation Along with the fixed temperature points established by ITS-90, a standard for interpolation between these fixed points is necessary. Standards for acceptable thermometers and interpolating equations are provided in ITS-90. For temperatures ranging from 13.8033 to 1234.93 K, ITS-90 establishes a platinum resistance thermometer as the standard interpolating instrument, and establishes interpo￾lating equations that relate temperature to resistance. Above 1234.93 K, temperature is defined in terms of blackbody radiation, without specifying an instrument for interpolation (3). In summary, temperature measurement, a practical temperature scale, and standards for fixed points and interpolation have evolved over a period of about two centuries. Present standards for fixed-point temperatures and interpolation allow for practical and accurate measurements of temperature. In the United States, the National Institute of Standards and Technology (NIST) provides for a means to obtain accurately calibrated platinum wire thermometers for use as secondary standards in the calibration of a temperature measuring system to any practical level of uncertainty. 8.3 THERMOMETRY BASED ON THERMAL EXPANSION Most materials exhibit a change in size with changes in temperature. Since this physical phenomenon is well defined and repeatable, it is useful for temperature measurement. The liquid-in-glass thermometer and the bimetallic thermometer are based on this phenomenon. Liquid-in-Glass Thermometers A liquid-in-glass thermometer measures temperature by virtue of the thermal expansion of a liquid. The construction of a liquid-in-glass thermometer is shown in Figure 8.2. The liquid is contained in a glass structure that consists of a bulb and a stem. The bulb serves as a reservoir and provides sufficient fluid for the total volume change of the fluid to cause a detectable rise of the liquid in the Capillary Immersion level Immersion level Immersion level Total Complete Immersion type Partial Stem Bulb Figure 8.2 Liquid-in-glass thermometers. 8.3 Thermometry Based on Thermal Expansion 313

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 uncer￾tainties 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 cross￾sectional 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