Chapter 8

Temperature

Material from Theory and Design for Mechanical Measurements; Figliola, Third Edition

Temperature Standards

‘“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 will 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. Although the zeroth law of thermodynamics essentially provides the definition of equality of temperature, it provides no means for defining a temperature scale.”

Temperature Standards

‘ A temperature scale provides for three essential aspects of temperature measurement: (1) the definition of the size of the scale increment, (2) fixed reference points for establishing known temperatures (3) a means for interpolating between these fixed temperature points.

1 Temperature Standards

‘The calibration of a temperature measurement device entails not only the establishment of fixed temperature points, but 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.

Temperature Standards

‘Submerge the thermometer in water at the ice point, make a mark on the glass at the height of the column of mercury, and label it 0oC. ‘Submerge the thermometer in boiling water, and mark the level of mercury, and Figliola, 2000 label it 100oC.

Temperature Standards

‘The process of establishing 50oC without a fixed- point calibration is called interpolation. ‘Theory of the behavior of the mercury in the thermometer, or many fixed points for calibration are necessary. ‘Even by the late 18th 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.

2 Temperature

‘Temperature is one of the most commonly measured engineering variables. ‘Thermometry is based on thermal expansion. ‘Most materials exhibit a change in size as a result of a change on temperature. ‘Measure temperature variation through thermal expansion of liquid in glass. ‘Difference in thermal expansion between liquid and glass results in a change in level.

Temperature

‘The modern engineering definition of the temperature scale is provided by a standard called the International Temperature Scale. ‘This standard establishes fixed points for temperature and provides standard procedures and devices for interpolating between fixed points.

Temperature

‘ A liquid-in-glass thermometer measures temperature by virtue of the thermal expansion of liquid. ‘ 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 Figliola, 2000 of the liquid in the stem.

3 Temperature

‘ During calibration, the thermometer is subject to one of three measuring environments: 1. Complete immersion thermometer 2. Total immersion thermometer 3. Partial immersion thermometer

Bi-Metallic Thermometer

‘Based on differential thermal expansion of two metals ‘Two different materials are bonded together ‘At bonding temperature, the metals are straight

Figliola, 2000

Bi-Metallic Thermometer

‘Rc ∝ d / [(C∝)A –(C∝)B](T2 -T1)

‘Rc = radius of curvature

‘C∝ = material thermal expansion coefficient ‘T = temperature ‘d = thickness ‘INVar is common material where o •C∝ = 1.7 * 10-8 m/m C ‘Where steel -5 -5 o •C ∝ = 2*10 to 20*10 m/m C

4 Electrical Resistance Thermometry

‘By physical nature of the conduction of electricity, electrical resistance of a conductor varies with temperature. ‘Two basic classes of sensor – Resistance temperature detectors (RTD) • Electrical conductors – Thermistors • Semiconductors

Electrical Resistance Thermometry

‘The physical basis for the relationship between resistance and temperature is the temperature dependence of the resistivity of the material, ρe. ‘The resistance of a conductor length l and cross-sectional area Ac may be expressed in terms of resistivity: R = Resistance

•R = ρel / Ac ρe = resistivity of material (temp dependent) l = length

Ac = cross-sectional area

Figliola, 2000

‘ The resistance temperature detector (RTD) is constructed by mounting a metal wire on an insulating support structure to eliminate mechanical strain and by encasing the wire to prevent changes in resistance due to sensor’s environment, such as corrosion. ‘ Mechanical strains change a conductor’s resistance and must be eliminated for accurate temperature measurements are to be made.

5 Electrical Resistance Thermometry

• Over small temperature ranges, R = Ro [1 + ∝(T – To)]

•Ro= reference resistance at To ; ∝= coefficient of resistivity.

• Helical coils provide strain relief as the conductor expands and contracts. Platinum is the most popular.

Resistance Measurements

‘Platinum is the most linear over the entire region. Figliola, 2000 ‘Platinum RTD’s are used over a wide range from cryogenic to ≈ 650oC with uncertainty at ± 0.005oC possible

Figliola, 2000

Resistance Measurements

‘The choice of an appropriate resistance measuring device must be made based on the required level of uncertainty in the final temperature measurement. ‘Conventional ohmmeters cause a small current to flow during resistance measurements, creating self-heating in the RTD. – An appreciable temperature change of the sensor may be caused by this current, in effect a loading error.

6 Resistance Measurements

‘Bridge circuits are used to measure the resistance of RTDs, to minimize loading errors, and to provide low uncertainties in measured resistance values. ‘Wheatstone bridge circuits are commonly used for these measurements. – However, the basic Wheatstone bridge circuit does not compensate for the resistance of the leads in measuring resistance of an RTD, which are a major source of error in electrical resistance thermometers.

Bridge Circuits

Figliola, 2000 ‘ Use a wheatstone bridge with conductor length compensation. ‘ Fig. 8.6a is a 3-wire Callender-Griffith bridge circuit.

Leads 1, 2, 3 have resistance r1, r2, r3, where r2 does not affect the circuit, since there is no current through the galvometer at balance conditions.

Bridge Circuits

‘At balanced condition, iG = 0 ‘R1/R2 = R3/RRTD Î R1/R2 = (R3 + r1)/ (RRTD + r3) ‘If R1 = R2, RRTD = R3 + r1 –r3 ‘If r1 balances r3 Î RRTD = R3

‘A 4-wire, shown in Fig. 8.6b is available for low- error, the 3-wire is most common. ‘RTD has a slow response time and may not be suitable in transit conditions.

7 Thermister

‘Thermally sensitive resistors ‘They are ceramic-like semi-conductor devices. Resistance decreases rapidly with decreasing temperature β ranges from 3500 to 4600k β (1/T - 1/To) –R = Roe depending on device material and construction. ‘This equation is valid over limited temperature range, unless β(t) is given. Typically, β is constant for set temperature range.

Thermistor

‘Thermisters are generally used in applications where high sensitivity, ruggedness, or fast response times are necessary. ‘High resistance of thermisters eliminates the lead length compensation issues found in RTD. However, thermisters are not directly interchangeable, due to variation in β and sensitivity to temperature change.

8 Thermoelectric Temperature Measurement

‘The most common temperature sensing and control element is the thermocouple. ‘Consists of two electrical conductors, made of dissimilar materials joined together at a junction. ‘The output is a voltage that is related to the temperature at the junction. ‘The thermoelectric phenomena is a result of simultaneous flow of heat and electricity away from the junction.

Thermoelectric Temperature Measurement

‘If T1 ≠ T2, a finite electric potential emf1 exists whose magnitude depends on ∆T and the difference in materials.

Thermoelectric Temperature Measurement

‘ “In an electrical conductor that is subject to a temperature gradient, there will be both a flow of thermal energy and a flow of electricity. Both of these phenomena are closely tied to the behavior of the free electrons in a metal; it is no coincidence that good electrical conductors are, in general, good thermal conductors. The characteristic behavior of these free electrons in an electrical circuit composed of dissimilar metals results in a useful relationship between temperature and emf.” ‘ Three effects can occur: (1) Seebeck effect, (2) Peltier effect, (3)Thomson effect

9 Seebeck Effect

‘Seebeck effect – generation of voltage potential as a result of temperature difference between two junctions in circuit. It is a fixed and reproducible

relationship between emf and junction temp T1 and T2

‘Seebeck coefficient: ∝AB = [∂(emf) / ∂T]open circuit ‘This is a measure of the rate of change of voltage of the two materials, with respect to temperature, and is the static sensitivity of the open circuit thermocouple.

Seebeck Effect

‘Under ideal conditions, the measured emf of thermocouple is due to Seebeck effect, alone. ‘Should be measured with no current flow through use of high impedance measurement device.

Peltier Effect

‘Peltier Effect: Joule heat = I2R

Figliola, 2000

‘In Peltier effect, heat must be removed at I2R to maintain temperature of conductor. At the junction, extra heat is generated (Peltier heat),which is proportional to I.

10 Peltier Effect

‘The Peltier effect is due to the thermodynamically reversible conversion of energy as a current flows across the junction, in contrast to the irreversible dissipation of energy associated with I2R losses. ‘The proportionality constant is the Peltier

coefficient πAB, and the heat transfer required to maintain a constant temperature is: Qπ = πABI ‘If I ≈ 0, heat ≈ 0

Thompson Effect

‘ The conductor has temperature gradient and potential difference, there is a flow of heat and current. ‘ To maintain constant temperature, an amount of heat must be removed different from I2R.

•Qσ = σI (T1-T2) Figliola, 2000 • σ = Thompson coeff

Figliola, 2000

11 ‘ “The basic thermocouple circuit can be used to measure

the difference between the two temperatures T1 and T2. For practical temperature measurements, one of these junctions becomes a reference junction and is maintained at some known, constant reference temperature. The other junction then becomes the measuring junction, and the emf existing in the circuit for any temperature T1 provides a direct indication of the temperature of the measuring junction.”

Reference Junctions

‘ Thermocouples can be used to measure the temperature difference between two junctions of dissimilar material. One junction at reference temperature, the other at measured temperature. – Ice bath of crushed ice and water is common. Figliola, 2000

Reference Junctions

‘Law of intermediate materials ensures that the extension wires on potentiometer do not effect emf as long as they are at the same temperature. ‘The reference junction must be at a known temperature, be reproducible, and be stable. Ice point 0oC is common, although it is only relatively stable. ‘Electronic reference junctions are available on some measurement devices, which use a thermister to measure local environment temperature (internal compensation).

12 Thermocouple Designations

Figliola, 2000 ‘ Thermocouples are made from many different combinations of materials. ‘ Choice of thermocouple depends on temperature range, application environment, and desired uncertainty level.

Voltage Output

‘ The slope of the curve corresponds to the static sensitivity of the thermocouple circuit. ‘ The output emf voltage of a thermocouple can be interpreted either from conversion tables or by polynomial expressions that are fitted to a particular type of thermocouple. ‘ See Table 8.6, 8.7 Figliola, 2000

Thermocouple Measurement

‘ The Seebeck voltage can be measured at no current flow. If current is flowing in circuit, Thomson and Peltier effects may be experienced. ‘ The ideal is to use either a potentiometer or a high impedance digital voltmeter which results in minimal current flow. ‘ In common applications, a “built-in electronic cold junction compensation” method is used, which employs the use of a thermister. Typical error is 0.5o to 1.5o bias. ‘ Internal polynomial interpolation is often used to convert from voltage to temperature, which introduces a linearization error.

13 Thermocouple Measurement

‘Often gains of 100 to 500 are used to boost the thermo-electric signal to a range detectable by A/D board. ‘Typical use of differential-ended inputs with twisted pair conductors and a 10kΩ to 100kΩ resistor between low input (-) terminal and low-level ground.

Multiple-Junction Thermocouple Circuits

‘More than two junctions can be employed in a thermocouple circuit, and thermocouple circuits can be devised to measure temperature differences or average temperature or to amplify the output voltage of a thermocouple circuit.

Thermopiles

‘“Thermopile” is a term used to describe a multiple-junction thermocouple circuit that is designed to amplify the output of the circuit. ‘Increasing the voltage output may be a key element in reducing the uncertainty in the temperature measurement.

14 ‘This figure shows a thermopile for providing an amplified output signal; in this case, the output voltage would be N times the single thermocouple output, where N is the number of measuring junctions in the circuit. ‘The average output voltage corresponds to the average temperature level sensed by the N junctions.

Thermocouples

‘When spatially averaged temperature is desired, multiple thermocouple junctions can be arranged as shown:

N emf = 1/ N∑(emf)i i=1 N T = 1/ N∑Ti i=1

Data Acquisition Considerations

‘Attention must be given to the cold junction compensation method. ‘The two connection points of the thermocouple to the DAS board form two new thermocouple connections. ‘Use of external cold junction methods between the thermocouple and the board will eliminate this problem, but more frequently, the thermocouple will be connected directly to the board and use built-in electronic cold junction compensation.

15 Data Acquisition Considerations

‘This is usually accomplished by using a separate thermistor sensor, which measures the temperature at the system connection point to determine the cold junction error, and providing an appropriate bias voltage correction either directly or through software. ‘These boards also may use internal polynomial interpolation for converting measured voltage into temperature. ‘This introduces a “linearization” error, which is a function of thermocouple material and temperature range and typically specified with the DAS board.

Data Acquisition Considerations

‘Thermocouple wire pairs should be twisted to reduce noise. ‘A differential-ended connection is preferred between the thermocouple and the DAS board. ‘The thermocouple becomes an isolated voltage source, meaning there is no longer a direct ground path keeping the input within its common mode range. ‘As a consequence, a common complaint is that the measured signal may drift or suddenly jump in the level of its output.

Data Acquisition Considerations

‘This interference behavior is eliminated by placing a 10-kΩ to 100-kΩ resistor between the low terminal of the output and low-level ground. ‘Since most DAS boards use A/D converters having a ± 5V full scale, the signal must be conditioned using an amplifier. ‘Usually, a gain of 100 to 500 is significant. ‘High gain, very low noise amplifiers are important for accurate measurements.

16 Data Acquisition Considerations

‘Thermocouples tend to have long time constant relative to the typical sample rate capabilities of general purpose DAS boards. ‘If temperature measurements show greater then expected fluctuations, high-frequency sampling noise is a likely cause. ‘Slowing down the sample rate or using a smoothing filter are simple solutions. ‘The period of averaging should be on the scale of the time constant of the thermocouple.

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