The CRC Handbook of Mechanical Engineering. Chapter 4. Heat and Mass Transfer (776127), страница 45
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Such instruments are normally marked to indicate the external resistance for which they havebeen calibrated. Potentiometric instruments, either manually balanced or automatically balanced, drawno current when in balance, hence can be used with thermocouple loops of any arbitrary resistancewithout error. High-input impedance voltmeters draw very low currents and, except for very highresistance circuits, are not affected by the loop resistance.Thermocouple Theory.
Equation (4.6.1) is the general form describing the EMF generated in a two-wirethermocouple (Moffat, 1962). The same form can be derived from either the free-electron theory ofmetals or from thermodynamic arguments alone: the output of a thermocouple can be described as thesum of a set of terms, one arising in each wire in the circuit.The junctions do not generate the EMF: they are merely electrical connections between the wires.For a two-wire circuit,EMF =òL0e1dTdx +dx0òeL2dTdxdx(4.6.1)wheree1 and e2 = the total thermoelectric power of materials 1 and 2, respectively, mV/C.
The value of e isequal to the sum of the Thomson coefficient and the temperature derivative of the Peltiercoefficient for the material.T = temperature, Cx = distance along the wire, mL = length of the wire, m© 1999 by CRC Press LLC4-185Heat and Mass TransferThis form for expressing the output of a two-wire circuit applies regardless of whether the wires areuniform in composition or not. If a circuit contained four wires (two thermocouple wires and twoextension wires), then Equation (4.6.1) would be written with four terms, one for each length of wire.When the wire is uniform in composition and both wires begin at (To) and both end at (TL) the twoterms can be collected into one integral:EMF =òTLT0(e1 - e 2 ) dT(4.6.2)The EMF–temperature (E–T) tables produced by NIST and others are “solutions” to Equation (4.6.2)and can be used only when the following three conditions are met:1.
The thermoelectric power, e, is not a function of position; i.e., the wires are homogeneous;2. There are only two wires in the circuit;3. Each wire begins at To and ends at TLWhen the circuit consists entirely of pairs of materials, Equation 4.6.2 can be used directly as the basisfor understanding the source of the EMF. As an example, consider the three-pair system shown in Figure4.6.1. For that circuit, Equation (4.6.2) would have three terms: one for each pair. The total EMF generatedby the circuit would be the sum of the EMFs generated in the thermocouple pair and in the extensionwire pair.
The pair of copper wires would not contribute to the net EMF, assuming the two copper wireswere perfectly matched. The EMF contributed by each pair would be proportional to the temperaturedifference from end to end of that pair, as shown in Equation (4.6.3) and (4.6.4).EMF =òT2T1(ecu- e cu ) dT +T3T423òT (e + - e - )LEADS dT + òT (e + - e - )TC dTEMF = 0 + (T 3 - T 2) (e + - e - ) LEADS + (T 4 - T 3) (e + - e - ) TC(4.6.3)(4.6.4)FIGURE 4.6.1 A three-pair circuit.Most thermocouple circuits consist only of pairs of wires and can be understood in terms of these twoequations, but some require a more detailed treatment. A graphical method of analysis is available, basedon Equation (4.6.1).The temperature–EMF calibrations of the more common materials are shown in Figure 4.6.2 derivedfrom NBS Monograph 125 and other sources.
This figure provides the input data for a simple graphicaltechnique for describing the EMF generation in a circuit. Each curve in Figure 4.6.2 represents theoutput which would be derived from a thermocouple made of material X used with platinum when thecold end is held at 0°C and the hot end is held at T.Those elements commonly used as “first names” for thermocouple pairs, i.e., Chromel (ChromelAlumel), iron (-constantan), copper (-constantan), have positive slopes in Figure 4.6.2.The simplest thermocouple circuit for temperature measurement consists of two wires joined togetherat one end (forming the “measuring junction”) with their other ends connected directly to a measuringinstrument, as shown in the upper portion of Figure 4.6.3.
The EMF generation in this circuit isgraphically represented in the lower portion, an E–T diagram, using the data in Figure 4.6.2. The E–T© 1999 by CRC Press LLC4-186Section 4FIGURE 4.6.2 E–T calibrations for several common thermocouple materials.FIGURE 4.6.3 E–T diagram of a thermocouple using an ambient reference.diagram is used for examining the EMF generated in the circuit, to be certain that it arises only fromthe desired thermocouple materials, and that all segments of the circuit are properly connected.
The E–Tdiagram is not used for evaluating the output — that is done using the tables after the circuit has beenshown to be correctly wired.To construct an E–T diagram, first sketch the physical system considered and assign a number to each“point of interest” on that sketch and a temperature. On E–T coordinates, locate point 1 at 0/mV and atits assigned temperature. Then start a line from point 1, moving toward the temperature of point 2, andcopying the shape of the calibration curve of the iron wire (see Figure 4.6.2).
From 2 to 3, use theconstantan calibration curve. The difference in elevation of points 1 and 3 describes the net EMF© 1999 by CRC Press LLCHeat and Mass Transfer4-187generated in the circuit between points 1 and 3, and describes the polarity. When point 3 lies physicallyabove point 1 in the E–T diagram, it is, by convention, electrically negative with respect to point 1.The simple triangular shape shown in Figure 4.6.3 identifies a proper circuit. Any thermocouple circuitwhose E–T diagram is equivalent to that is appropriate for temperature measurement and its EMF maybe interpreted using the conventional tables. Any circuit whose E–T diagram is not equivalent to thepattern circuit should be rewired.Thermocouples generate their signal in response to the temperature difference between the two endsof the loop.
For accurate measurements, the temperature of the “reference junction” must be known.Laboratory users often use an ice bath made from a good-quality Dewar flask or vacuum-insulated bottleof at least 1 pt capacity, as shown in Figure 4.6.4. The flask should be filled with finely crushed ice andthen flooded with water to fill the interstices between the ice particles. The reference thermocouple isinserted into a thin-walled glass tube containing a small amount of silicone oil and submerged six oreight diameters into the ice pack.
The oil assures good thermal contact between the thermocouple junctionand the ice/water mixture. The tube should be sealed at the top to prevent atmospheric moisture fromcondensing inside it, which would cause corrosion when using iron-constantan thermocouples. Figure4.6.5 shows in iron-constantan thermocouple circuit with an ice bath. The individual thermocouple wiresare connected to copper wires in the ice bath, and the two copper wires taken to the voltmeter.
Thelower portion of this figure shows the E–T diagram for this circuit, and proves that the output of thiscircuit is entirely due to the temperature difference from end to end of the iron-constantan loop: the twocopper wires do not contribute to the output.FIGURE 4.6.4 Characteristics of a good ice bath.Calibration.
Thermocouple calibrations are provided by the wire manufacturers to tolerances agreedupon industry-wide, as summarized in Table 4.6.1. These tolerances include two components: theuncertainty in the average slope of the calibration curve of the wire, and the effects of local inhomogeneities in the wire. It is difficult to improve the accuracy of a thermocouple by calibrating it. For a trulysignificant calibration, the thermocouple would have to be exposed to the same temperature duringcalibration, at every point along it, that it would encounter in service. In an oven calibration, most ofthe signal is generated in the material at the mouth of the oven, as could be recognized by consideringthe temperature gradient distribution along the wire.
The material inside the oven contributes little ornothing to the signal.ThermistorsThermistors are electrical resistance temperature transducers whose resistance varies inversely, andexponentially, with temperature. The resistance of a 5000 W thermistor may go down by 200 W for eachdegree C increase in temperature in the vicinity of the initial temperature. Interrogated by a 1.0 mAcurrent source, this yields a signal of 200 mV/°C.
As a consequence of this large signal, thermistorsare frequently used in systems where high sensitivity is required. It is not uncommon to find thermistordata logged to the nearest 0.001°C. This does not mean that the data are accurate to 0.001°C, simply© 1999 by CRC Press LLC4-188Section 4FIGURE 4.6.5 A thermocouple circuit using an ice bath reference, and its E–T diagram.that the data are readable to that precision. A thermistor probe is sensitive to the same environmentalerrors which afflict any immersion sensor: its accuracy depends on its environment.Thermistor probes can be used between –183°C (the oxygen point) and +327°C (the lead point) butmost applications are between –80 and +150°C.
The sensitivity of a thermistor (i.e., the percent changein resistance per degree C change in thermistor temperature) varies markedly with temperature, beinghighest at cryogenic temperatures.Thermistor probes range in size from 0.25-mm spherical beads (glass covered) to 6-mm-diametersteel-jacketed cylinders. Lead wires are proportionately sized. Disks and pad-mounted sensors areavailable in a wide range of shapes, usually representing a custom design “gone commercial.” Asidefrom the unmounted spherical probes and the cylindrical probes, there is nothing standard about theprobe shapes.Calibration. Thermistor probes vary in resistance from a few hundred ohms to megohms. Probe resistance is frequently quoted at 25°C, with no power dissipation in the thermistor.
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