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