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