Chapter 8 Temperature and Heat-Flux Measurement by Yixin Ma 08/05/2013 2/47 Contents 8.1 Standards and Calibration 8.2 Thermo-Expansion Methods 8.3 Thermoelectric sensors (Thermocouples) 8.4 Electrical-Resistance Sensors 8.5 Junction Semiconductor Sensors 8.6 Digital Thermometers 8.7 Radiation Methods 8.8 Temperature-Measuring Problems in Flowing Fluids 8.9 Dynamic Response of Temperature Sensors 8.10 Heat Flux Sensors
Chapter 8 Temperature and Heat-Flux Measurement by Yixin Ma 08/05/2013 Contents 8.1 Standards and Calibration 8.2 Thermo-Expansion Methods 8.3 Thermoelectric sensors (Thermocouples) 8.4 Electrical-Resistance Sensors 8.5 Junction Semiconductor Sensors 8.6 Digital Thermometers 8.7 Radiation Methods 8.8 Temperature-Measuring Problems in Flowing Fluids 8.9 Dynamic Response of Temperature Sensors 8.10 Heat Flux Sensors 2/47
3147 8.1 Standards and Calibration One of the four fundamental quantities: length,time,mass,temperature Statistical mechanics relates temperature to the mean kinetic energies of molecules,these kinetic energies(which are dependent on only mass, length,and time standards for their description)are not measureable at present.Thus an independent temperature standard is required. The zeroth law of thermodynamics give a useful concept of the fundamental meaning of temperature:for two bodies to be said have the same temperature,they must be in thermal equilibrium.Or,when two bodies are each in thermal equilibrium with a third body,they are in thermal equilibrium with each other. The means of defining the standard temperature scale could be any of the many physical properties of materials that vary reproducibly with temperature. 4/47 8.1 Standards and Calibration Thermodynamic temperature scale proposed by Lord Kelvin in 1848 provides the theoretical base for a temperature scale independent of any material property and is based on the Carnot cycle. -The Kelvin absolute thermodynamic scale is ideal in the sense that it is independent of any material properties. T=t+273.15 Q=Qo(t+273.15)/273.15 →Q=QoT/273.15 ◆The perfect gas law: k =Pv PV kT -Constant-Volume Gas Thermometer -Constant-Pressure Gas Thermometer
One of the four fundamental quantities: length, time, mass, temperature Statistical mechanics relates temperature to the mean kinetic energies of molecules, these kinetic energies (which are dependent on only mass, length, and time standards for their description) are not measureable at present. Thus an independent temperature standard is required. The zeroth law of thermodynamics give a useful concept of the fundamental meaning of temperature: for two bodies to be said have the same temperature, they must be in thermal equilibrium. Or, when two bodies are each in thermal equilibrium with a third body, they are in thermal equilibrium with each other. The means of defining the standard temperature scale could be any of the many physical properties of materials that vary reproducibly with temperature. 8.1 Standards and Calibration 3/47 Thermodynamic temperature scale proposed by Lord Kelvin in 1848 provides the theoretical base for a temperature scale independent of any material property and is based on the Carnot cycle. ▬ The Kelvin absolute thermodynamic scale is ideal in the sense that it is independent of any material properties. ܳ=ܳ (ݐ + 273.15) 273.15 ⁄ ்ୀ௧ାଶଷ.ଵହ ܳ = ܳ ܶ 273.15 ⁄ The perfect gas law: ݇ = ் ⇔ ܸܲ = ݇ܶ ▬ Constant-Volume Gas Thermometer ▬ Constant-Pressure Gas Thermometer 8.1 Standards and Calibration 4/47
8.1 Standards and Calibration 5147 Add mercury Measure Ice-point apparatus pressure Index point for constont volume Constant-volume gas thermometer (much simplified) Steam-point apparatus Fig 8.1 Gas-thermometer Temperature Scale Schematics shows the calibration process for non-idea-gas behavior.The gas volume is retained at constant volume for ice-point and steam-point by changing the among of mercury added on. 6/47 8.1 Standards and Calibration With different mass of gas, the repeated experiment gives different pressure Pi ratios, but for Ps Pi Piz idea gas,there should be P52 Various gases Ps2 Pi Pi让 Pi2 1.36609 Real-gases approaches idea- Extrapolated gas behavior once their pressure is reduced to zero. Pi Pi Pi Figure 8.1 Gas-thermometer Temperature Scale
8.1 Standards and Calibration Fig 8.1 Gas-thermometer Temperature Scale Schematics shows the calibration process for non-idea-gas behavior. The gas volume is retained at constant volume for ice-point and steam-point by changing the among of mercury added on. 5/47 8.1 Standards and Calibration With different mass of gas, the repeated experiment gives different pressure ratios, ೞభ భ ೞమ మ , but for idea gas, there should be ೞభ భ ೞమ మ . Real-gases approaches ideagas behavior once their pressure is reduced to zero. Figure 8.1 Gas-thermometer Temperature Scale 6/47
7147 8.1 Standards and Calibration IPTS(International Practical Temperature Scale)is set up as close as possible with the thermodynamic scale. Six primary fixed points are used in defining IPTS(1927). 1.At the triple point of water,the two scales are in exact agreement,by definition. 2.The boiling points of liquid oxygen(-182.962C) 3.The boiling points of water (100 C) 4.The freezing points of zinc(锌，419.58℃) 5.The freezing points of silver(961.93 C) 6.The freezing points of gold(1064.43 C) Various secondary fixed points are established,with the lowest being the triple point of hydrogen(氢，-259.34℃). Certain instruments,equations and procedures are also specified by IPTS to interpolate between the fixed points,e.g.,from-259.34C to 630.74C,a platinum resistance thermometer is the interpolating instrument with equations for several subranges. 8/47 8.1 Standards and Calibration Above the gold point,the IPTS is defined and uses a narrow-band radiation pyrometer ()("optical"pyrometer)and Planck equation to establish temperatures. In practice,few reliable results above 4000 C are known. Calibration of a given temperature-measuring device generally is accomplished by subjecting it to some established fixed-point environment, such as the melting points and boiling points of standard substances,or by comparing its readings with those of some more accurate (secondary standard)temperature sensor which itself has been calibrated. Some secondary standards: -Accurate resistance thermometers, Thermocouples,or Mercury-in-glass expansion thermometers How to calibrate a thermometer with a secondary standard temperature sensor?What are critical matters to the calibration accuracy?
• IPTS(International Practical Temperature Scale) is set up as close as possible with the thermodynamic scale. • Six primary fixed points are used in defining IPTS (1927). 1. At the triple point of water, the two scales are in exact agreement, by definition. 2. The boiling points of liquid oxygen (-182.962℃) 3. The boiling points of water (100 ℃) 4. The freezing points of zinc (锌, 419.58 ℃) 5. The freezing points of silver (961.93 ℃) 6. The freezing points of gold (1064.43 ℃) • Various secondary fixed points are established, with the lowest being the triple point of hydrogen (氢, -259.34℃). • Certain instruments, equations and procedures are also specified by IPTS to interpolate between the fixed points, e.g., from -259.34℃ to 630.74℃, a platinum resistance thermometer is the interpolating instrument with equations for several subranges. 8.1 Standards and Calibration 7/47 • Above the gold point, the IPTS is defined and uses a narrow-band radiation pyrometer (高温计) (“optical” pyrometer) and Planck equation to establish temperatures. • In practice, few reliable results above 4000 ℃ are known. • Calibration of a given temperature-measuring device generally is accomplished by subjecting it to some established fixed-point environment, such as the melting points and boiling points of standard substances, or by comparing its readings with those of some more accurate (secondary standard) temperature sensor which itself has been calibrated. • Some secondary standards: − Accurate resistance thermometers, − Thermocouples, or − Mercury-in-glass expansion thermometers • How to calibrate a thermometer with a secondary standard temperature sensor? What are critical matters to the calibration accuracy? 8.1 Standards and Calibration 8/47
9/47 8.1 Standards and Calibration One part in os 106 Accuracy of realization of the thermodynamic temperature scale Existing capabilities Gas Object of existing projects thermometry 105 104 Photoelectric pyrometry 103 102 Spectroscopic Magnetic thermometry Ultrasonic thermometry Gas thermometry /techniques 10 0.51.0 510 50100 5001,000 5.00 100,000 Temperature,K 10,000 50,000 Figure 8.2a Summarization of Temperature Standards 10/47 8.1 Standards and Calibration Calibration of temperature-measuring instrume/64 -NBS capability in reproducing temperature scales Accuracies based upon limits of error assigned to calibration results Degrees celsius(centigrade) -262 -183 06301,0634,000 One part in 1953 NBS 十LIPTS-1L 107 Platinum resistance thermometer Standard platinum thermocouple Acoustic therm Platinum metal thermocouples Helium 4 vapor pressure Liquid-in-glass-l Standard optical pyrometer thermometers 103 Germanium resistors Base metal thermocouples Base metal thermocouples Optical pyrometers 10 L L上LLL LLLLL 10 100 1.000 10,000 100,000 Temperature.K(int.1948) Figure 8.2b More Recent Temperature Standards
8.1 Standards and Calibration Figure 8.2a Summarization of Temperature Standards 9/47 8.1 Standards and Calibration Figure 8.2b More Recent Temperature Standards 10/47
11/47 8.2 Thermal-Expansion Methods ◆Expansion of solids is mainly in bimetallic(双金属)elements by utilizing the differential expansion of bonded(连接，结合)strips of two metals. Liquid expansion at essentially constant pressure is used in the common liquid-in-glass thermometers. Restrained expansion of liquids,gases,or vapors results in a pressure rise,which is the basis of pressure thermometers. Fahrenheit ['faeranhait]Degree:degree F,F.A scale and a unit of temperature,its defining points being 32 at the freezing point of pure water and 212 at its boiling point at atmospheric pressure,and with 180 degrees between the two.Conversion from F to C: c=5p-32 12/47 8.2.1 Bimetallic Thermometers(双金属温度计) Two strips of metal A&B of same temperature,with thermal- expansion coefficients &a,are firmly bonded together,a temperature change causes a differential expansion and the strip,if unrestrained,will deflect into a uniform circular arc with the following analytical relationship: r=t43(1+m2+(1+mm[m2+1/mml 6(aA-aB)(T2-T1)(1+m)2 (8.3) where r:radius of curvature t:total strip thickness,0.0005<t<0.125 in practice n:elastic modulus ratio EB/EA m:thickness ratio te/ta T2-T1:temperature rise Accurate results require the use of experimentally determined factors which are available from bimetal manufacturers
Expansion of solids is mainly in bimetallic(双金属) elements by utilizing the differential expansion of bonded(连接, 结合) strips of two metals. Liquid expansion at essentially constant pressure is used in the common liquid-in-glass thermometers. Restrained expansion of liquids, gases, or vapors results in a pressure rise, which is the basis of pressure thermometers. Fahrenheit [ˈfærənhait] Degree: degree F, ℉. A scale and a unit of temperature, its defining points being 32 at the freezing point of pure water and 212 at its boiling point at atmospheric pressure, and with 180 degrees between the two. Conversion from ℉ to ℃: = ૢ ( −32) 8.2 Thermal-Expansion Methods 11/47 Two strips of metal A & B of same temperature, with thermalexpansion coefficients ߙ & ߙ , are firmly bonded together, a temperature change causes a differential expansion and the strip, if unrestrained, will deflect into a uniform circular arc with the following analytical relationship: ⁄ା ା ା ା ࢚ (3.8 (ା ࢀିࢀ ࢻିࢻ where r: radius of curvature t: total strip thickness, 0.0005<t<0.125 in practice n: elastic modulus ratio ܧ/ܧ m: thickness ratio ݐ/ݐ ܶଶ − ܶଵ: temperature rise Accurate results require the use of experimentally determined factors which are available from bimetal manufacturers. 8.2.1 Bimetallic Thermometers (双金属温度计) 12/47
8.2.1 Bimetallic Thermometers 13/47 ☑Temperature=T Separate A XA>O8 B Bonded Cantilever ['kaentili::va】悬臂梁 U-shape Temperature changed Spiral Helix Washer Double helix (a)Principle of Bimetallic Thermometer (b)Variety shapes of Bimetallic Thermometer Figure 8.3 Bimetallic Sensors 14/47 8.2.1 Bimetallic Thermometers Material for B element:Invar,a nickel steel with a nearly zero [1.7x10-6 in/(in.C)]expansion coefficient. Material for A element:Originally brass,now variety of alloys depends on the mechanical and electrical characteristics required. Working range from -100~1000F (-73.3~537.8C),inaccuracy of the order of 1%of scale range for bimetal thermometers of high quality. ◆Application: -Temperature measurement; -Very widely as combined sensing and control elements in temperature-control systems,mainly of the on-off type; -Temperature compensating devices for various instruments that has temperature as interfering or modifying input; -Motion compensation due to temperature change; -Automotive sensing application,combined with conductive plastic potentiometers
(a) Principle of Bimetallic Thermometer 8.2.1 Bimetallic Thermometers Figure 8.3 Bimetallic Sensors (b) Variety shapes of Bimetallic Thermometer 13/47 8.2.1 Bimetallic Thermometers 14/47 Material for B element： Invar, a nickel steel with a nearly zero [1.7x10ି in/(in ∙ ℃)] expansion coefficient. Material for A element: Originally brass, now variety of alloys depends on the mechanical and electrical characteristics required. Working range from -100~1000℉ (-73.3~537.8℃), inaccuracy of the order of 1% of scale range for bimetal thermometers of high quality. Application: ▬ Temperature measurement; ▬ Very widely as combined sensing and control elements in temperature-control systems, mainly of the on-off type; ▬ Temperature compensating devices for various instruments that has temperature as interfering or modifying input; ▬ Motion compensation due to temperature change; ▬ Automotive sensing application, combined with conductive plastic potentiometers
15/47 8.2.2 Liquid-in-Glass Thermometers ◆Mercury is the most common liquid utilized at intermediate(中等的)and high temperatures.Freezing point of-38F(-38.9C),upper limit of 1000℉(537.8C). Other liquids and their lowest measurable temperature: 一Alcohol(酒精)，-80F(-38.9℃) 一Toluol(甲苯)，-130℉(-90C) 一Pentane(戊烷)，-330F(-201.1℃) 一Mixture of propane(丙烷)and propylene(丙烯)，-360F(-217.8C) ◆Two types: 1Total immersion:during calibration,the liquid column is completely immersed in the measured liquid.It is a bit difficult to take reading. 2 Partial immersion:during calibration,a definite amount of liquid column is immersed in the measured liquid with the remaining portion at a definite temperature. 15 16/47 8.2.2 Liquid-in-Glass Thermometers Full-immersion Partial-immersion thermometer thermometer Auxiliary thermometer (Bulb at n/2) al=70℉ 200 200 80° 80 175 175 50 Correct immersion mork on thermometer Correction兰 Correction 0.00009501200-80l=0.54℉ 0.00009(50){70-80)=-0.045℉ Figure 8.4 Total-and Partial-Immersion Thermometers
Mercury is the most common liquid utilized at intermediate(中等的) and high temperatures. Freezing point of -38℉(−38.9℃), upper limit of 1000℉(537.8℃). Other liquids and their lowest measurable temperature: ▬ Alcohol(酒精), -80℉(−38.9℃) ▬ Toluol(甲苯), -130℉(−90℃) ▬ Pentane(戊烷), -330℉(−201.1℃) ▬ Mixture of propane(丙烷 ) and propylene(丙烯), -360℉(−217.8℃) Two types: ① Total immersion: during calibration, the liquid column is completely immersed in the measured liquid. It is a bit difficult to take reading. ② Partial immersion: during calibration, a definite amount of liquid column is immersed in the measured liquid with the remaining portion at a definite temperature. 8.2.2 Liquid-in-Glass Thermometers 15 15/47 8.2.2 Liquid-in-Glass Thermometers Figure 8.4 Total- and Partial- Immersion Thermometers 16/47
17147 8.2.2 Liquid-in-Glass Thermometers Reading corrections: correction =0.00009n(tcal-tact),F (8.5) where n:number of scale degrees equivalent to emergent stem length,F. For partial immersed thermometer: tcal:air temperature at calibration,F tact:air temperature at use,F(from auxiliary thermometer) For total immersed thermometer: tcal:main-thermometer reading,F tact:auxiliary-thermometer reading,F Accuracy depends on instrument quality,temperature range,and type of immersion. -Total immersed thermometer is inherently more accurate than partial immersed thermometer.It can be as accurate as 0.04F in the range of 32-212F. -Error in partial immersed thermometer may be several times larger. 8.2.3 Pressure Thermometers 18/47 Pressure sensor Bulb Capillary cop Instrument case- Figure 8.5 Pressure Thermometer Consists of a sensitive bulb,an interconnecting capillary tube,and a pressure- measuring device such as Bourden tube,.bellows(波纹管)，or diaphragm(膜片)
Reading corrections: (5.8 ，℉ (࢚ࢉࢇ࢚ − ࢇࢉ࢚ ૢ . = ࢚ࢉࢋ࢘࢘ࢉ where n: number of scale degrees equivalent to emergent stem length, ℉。 − For partial immersed thermometer: ݐ :air temperature at calibration, ℉ ݐ௧: air temperature at use, ℉ (from auxiliary thermometer) − For total immersed thermometer: ݐ :main-thermometer reading, ℉ ݐ௧: auxiliary-thermometer reading, ℉ Accuracy depends on instrument quality, temperature range, and type of immersion. ▬ Total immersed thermometer is inherently more accurate than partial immersed thermometer. It can be as accurate as 0.04℉ in the range of 32-212℉. ▬ Error in partial immersed thermometer may be several times larger. 8.2.2 Liquid-in-Glass Thermometers 17/47 8.2.3 Pressure Thermometers Figure 8.5 Pressure Thermometer Consists of a sensitive bulb, an interconnecting capillary tube, and a pressuremeasuring device such as Bourden tube, bellows(波纹管), or diaphragm(膜片). 18/47
19/47 8.3 Thermoelectric Sensors (Thermocouples) If two wires of different materials A&B are connected in a circuit with one junction at temperature T and the other at T2,then an infinite-resistance voltmeter detects an electromotive force E,or if an ammeter is connected,a current I is measured. Thermojunction A Thermojunction 8 B Voltmeter Ammeter Thermocouple Figure 8.8a The Principle of Thermocouple ◆The thermoelectric emf(热电a动势，EMF=electromotive force)is actually an effect distributed along the length of each single metal wire and exists even if the wire is not connected to anything. The magnitude of E depends on a material property called the Absolute Seebeck Coefficient(绝对塞贝克系数)o and the distribution of temperature along the wire. 20/47 8.3 Thermoelectric Sensors (Thermocouples) Bare wire Bare wire Insulated Grounded butt welded beaded junction junction Fig.8.8b Basic Types of Thermocouple Junctions Thermocouple joining method:welding,soldering,and merely pressing.Welding is he most widely used method. Different joining methods gives same voltage but different current due to different contact resistance at joint
If two wires of different materials A & B are connected in a circuit with one junction at temperature T1 and the other at T2, then an infinite-resistance voltmeter detects an electromotive force E, or if an ammeter is connected, a current I is measured. 8.3 Thermoelectric Sensors (Thermocouples) Figure 8.8a The Principle of Thermocouple The thermoelectric emf (热电动势, EMF=electromotive force) is actually an effect distributed along the length of each single metal wire and exists even if the wire is not connected to anything. The magnitude of ܧఙ depends on a material property called the Absolute Seebeck Coefficient(绝对塞贝克系数) σ and the distribution of temperature along the wire. 19/47 Fig. 8.8b Basic Types of Thermocouple Junctions 8.3 Thermoelectric Sensors (Thermocouples) 20/47 Thermocouple joining method: welding, soldering, and merely pressing. Welding is he most widely used method. Different joining methods gives same voltage but different current due to different contact resistance at joint