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 interpolating 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