Chapter 5 Temperature Measurement 5.1 Liquid in Glass Thermometer 5.2 Bimetallic Strip Thermometer 5.3 Resistance Thermometer and Thermistor 5.4 Thermocouple 充液玻璃温度计 双金属温度计 电阻温度计和热敏电阻 热电偶

Because temperature is such an important variable in many engineering systems, an engineer should be familiar with the basic methods of measuring it. Temperature sensors appear in buildings, chemical process plants, engines, transportation vehicles, appliances, computers, and many other devices that require monitoring and control of temperature. 建筑物、化学工艺厂、发动机、运输车辆、设备、计算机

Since many physical phenomena depend on temperature, we can use this dependence to indirectly measure temperature by measuring quantities such as pressure, volume, electrical resistance, and strain and then convert the value using the physical relationship between the quantity and temperature. 压力、体积、电阻和应变

The following subsections introduce common devices used for measuring temperature. The emphasis is on thermocouples and resistance devices, since they are used for more than 80% of temperature measurement in industry. Some sensors for temperature monitoring are mentioned for completeness. 重点介绍的是热力偶和电阻设备，因为它们在工业中的应用占80%以上。

Temperature measuring instruments can be divided into two groups, electrical and non-electrical: Non- electrical methods (1) Liquid, vapor pressure and gas temperature (2) Bimetal strip thermometers (3) Refractory cones, paints and crayon. （1）流体、蒸汽压和气体温度计 （2）双金属温度计 （3）耐火锥、涂漆、蜡化等方法。

(4) Electrical resistance pyrometers (5) Thermocouple pyrometers (6） Electrical methods 电阻高温计 (4) Electrical resistance pyrometers (5) Thermocouple pyrometers (6） （i）Total radiation pyrometers (ii) Photoelectric pyrometers (iii) Optical pyrometers. 热电偶高温计 全辐射高温计 光电高温计 光学高温计

5.1 Liquid in Glass Thermometer 充液玻璃温度计 5.1 Liquid in Glass Thermometer Mercury is usually used in glass thermometers although other liquids, such as alcohol and pentane, which have lower freezing temperatures than mercury and do not cause contamination through breakage, are also used. 尽管与水银（汞）相比，酒精和戊烷凝固点更低，且破损后不引起污染，但玻璃温度计中常采用水银

Increase in temperature causes the liquid to expand and rise up the stem. When measuring temperature above the boiling point of mercury (357℃ at atmospheric pressure) the space above the liquid is filled with nitrogen under pressure (Fig.5.1),thus raising the boiling point and allowing temperatures up to 510℃ to be measured. 测量温度高于标准大气压下汞的沸点时（357°），将液体上部空间填满氮气，压力增大时，汞的沸点也增大，可测量温度最多可高达510°

When taking measurements in a liquid, the depth of immersion is important, as it can result in different measurements. 当测量液体温度时，浸入深度很重要，因为深度不同所测得结果也不相同。 Since readings are taken visually and there can be a meniscus at the top of the liquid, measurements must be take carefully and consistently. 由于液体上部为弯液面，为准确测量数据，应该小心操作。

Range variation is provided for by incorporating a small cavity above the bulb which the mercury has to fill before rising up the stem. 在玻璃泡上留有一空间，当汞柱上升时必须先填满该空间，使量程可变。

Liquid in glass thermometers have considerable heat capacity and do not respond quickly to rapid changes of temperature; and glass which has been heated and then cooled does not immediately return to its original volume, thus tending to produce a low reading, although for many purposes this discrepancy is of little importance. 很高的热容量

5.2 Bimetallic Strip Thermometer 双金属温度计 5.2 Bimetallic Strip Thermometer Another nonelectrical temperature-measuring device used in simple control system is the bimetallic strip. As illustrated in Fig.5.2,

由两层或多层具有不同热膨胀系数的金属组成，这些金属层通过焊接紧密结合在一起。 it is composed of two or more metal layers having different coefficients of thermal expansion firmly boned together by welding. 由两层或多层具有不同热膨胀系数的金属组成，这些金属层通过焊接紧密结合在一起。 When the strip in heated or cooled, differential expansion or contraction occurs the strip to bend. This is due to the difference in the thermal expansion of the two metal layers. The deflection δ can be related to the temperature of the strip. 变形量δ与温度相关

Bimetallic strips are used in household and industrial thermostats where the mechanical motion of the strip makes or breaks an electrical contact to turn a heating or cooling system on or off. 双金属温度计既可家用又可用于工业场合，温度计金属片的机械运动使得电触头接触或断开进而打开或关闭一加热或冷却系统。

Many switching devices, such as those in oven thermostats, electric irons and car winker lamps, operate on this principle. 烤箱控制器、熨斗、汽车方向指示灯 They are also used as temperature sensors or as compensators for ambient temperature change in liquid in metal, vapor pressure and gas expansion thermometers, in aneroid barometers, and as balance wheel compensators in some watches. 通常用于温度传感器或金属中、蒸汽压中、气体膨胀温度计、无液气压计中任意温度改变补偿器或用作钟表中的平衡轮

Spiral bimetal strip thermometers Fig. 5 Spiral bimetal strip thermometers Fig.5.3 are widely used for measuring ambient and oven temperatures and clip-on types are available for checking the temperature of hot water pipes. 图5.3所示的螺旋形双金属温度计广泛用于测量环境温度和烤箱温度，夹式结构使其很容易确定热水管温度。

The essential characteristics of these thermometers are: Inexpensive: often used instead of liquid in glass thermometers. Compact: the volume of metal used in the protective sheath is small and thus of low thermal capacity, reducing lag. Robust: good resistance to mechanical shock owing to freely floating spindle.

Close linearity throughout the temperature range. Range of applications: low temperature -30 to 200℃; high temperature, 0 to 550℃. Accuracy: (low temperature) 1% of scale range; (high temperature) 2% of scale range. Stem diameters as small as 4mm are available.

5.3 Resistance Thermometer and Thermistor 电阻温度计和热敏电阻 5.3 Resistance Thermometer and Thermistor A resistance thermometer for temperature measurement is constructed of metallic wire wound around a ceramic or glass core and hermetically sealed. 由绕陶瓷和玻璃芯的金属丝组成 气密封的

The resistance of the metallic wire increases with temperature. The resistance of the metallic wire increases with temperature in the range -100 to +800℃. The general relationship between the resistance RTΩof a metal element and temperature T ℃ is a power series of the form 幂指数形式

Which is usually approximated by the following linear expression: (5.1) Which is usually approximated by the following linear expression: (5.2) Where T0 is a reference temperature, R0 is the resistance at the reference temperature and α, β and γ are the calibration constants. The sensitivity (dR/dT) is R0α (see Eq.5.2). The reference temperature is usually the ice point of water (0℃).

Fig.5.4 shows the variation in the ratio RT/R0 with temperature for the metals platinum, copper and nickel. 铂、铜和镍 Although relatively expensive, platinum is usually chosen for industrial resistance thermometers; cheaper metals, notably nickel and copper; are used for less demanding applications.

Platinum is preferred because it is chemically inert, has linear and repeatable resistance-temperature characteristics, can be used over a wide temperature range (-200 to +800℃) and in many types of environment. 优先采用铂是因为其化学惰性（不起化学反应），线性以及可重复性电阻-温度特性，其使用温度范围很广，为-200到800°，用于很多场合。

Resistive temperature elements made from semiconductor materials are known as thermistors. The most commonly used type is prepared from oxides of the iron group of transition metal elements such as chromium, manganese, iron, cobalt and nickel. The resistance of these elements decreases with temperature, in other words there is a negative temperature coefficient (N.T.C.), in a highly non-linear way. 通常由铬、锰、铁、钴、镍等两种或两种以上的金属氧化物制备而成。

Figure 5.5 shows typical thermistor resistance-temperature characteristics which can be described by the relationship Where T0 is a reference temperature, R0 the resistance at the reference temperature, and β is a calibration constant called the characteristic temperature of material.

A well-calibrated thermistor can be accurate to within 0 A well-calibrated thermistor can be accurate to within 0.01℃ or better, which is better than typical RTD (Resistance Temperature Detector )accuracies. 灵敏度比电阻式温度计高 However, thermistors have much narrower operating ranges than RTDs.

Thermistors are usually in the form of either beads, rods or discs; bead thermistors are enclosed in glass envelopes. 热敏电阻通常有珠状、柱状和垫圈形等几种形式，珠状热敏电阻通常封装在玻璃外壳中。 A typical N.T.C. thermistor has a resistance of 12KΩ at 25℃ (298K), falling to 0.95KΩ at 100℃. The manufacturer’s tolerance limits on the above figures are ± 840Ω, at 25℃ and ± 5 percent, i.e. ± 47.5Ω, at 100℃; which is far wider than for metal elements.

The element time constant is 19 sec in air, 3sec in oil and the self heating effect is 1℃ rise for every 7mW of electrical power. Thermistors with positive temperature coefficient (P.T.C) are also available; the resistance of a typical element increases from 100Ω at -55℃ to 10kΩ at 120℃. 自热效应为每7毫瓦升高1° 正温度系数热敏电阻

5.4 Thermocouple 热电偶 5.4.1 basic conception If two wires of different materials A and B are connected in a circuit as shown in Fig.5.6, with one junction at temperature T1 and the other at T2, then an infinite-resistance voltmeter detects an electromotive force V or if ammeter is connected, a current I is measured. 如图5.6，把由不同材料A和B制成的电线组成一电路，在结合点处一端温度为T1，另一端温度为T2,用伏特计检测时能测出两结合点之间有一电压，当用一电流计检测时能测出两结合点之间有电流流过。

The magnitude of the voltage V depends on the materials and temperatures. The current I is simply V divided by the total resistance of the circuit, including the ammeter resistance. 电压幅值与材料及温度有关，电流值可将电压值除以总电阻值(包含电流计自身的电阻)得到。

Because an electrical circuit must form a closed loop, thermoelectric junctions occur in pairs, resulting in what is called a thermocouple. The thermocouple voltage is directly proportional to the junction temperature difference: 由于形成电流回路时，结构中两个结合点，所以叫热电偶。 (5.5) Where α is called the Seebeck coefficient. 西伯克系数

热电偶测温的基本原理：是把两种不同成分的材质导体（称为热电偶丝材或热电极）组成闭合回路，当结合点两端的温度不同，存在温度梯度时，回路中就会有电流通过，此时两端就存在电动势——热电动势，这就是所谓的西伯克效应。

As we will see later in this section, the relationship between voltage and temperature difference is not exactly linear. However, over a small temperature range, α is nearly constant. 后面会介绍到其实电压与温度的差值并不是一线性关系，只是在温度很小的范围内近似取常数。

Secondary thermoelectric effects, known as the Peltier and Thompson effects, are associated with current flow in the thermocouple circuit, but these are usually negligible in measurement systems when compared with the Seebeck effect. 热电效应还伴随有珀尔帖效应和汤普森效应（电流流过不同导体的界面时，将从外界吸收热量或向外界放出热量的现象），它们与流经热电偶电路的电流有关，与西伯克效应相比时在测试系统中经常可以忽略不计。

However, when the current is large in a thermocouple circuit, these other effects become significant. The Peltier effect relates the current flow to heat flow into one junction and out of the other. This effect forms the basis of a thermoelectric refrigerator. 但是，若在热电偶电路中的电流值很大，珀尔帖效应和汤普森效应就会很明显，不能被忽略。珀尔帖效应将电流流动时在一个结合点吸热和在另一个结合点放热联系起来。

珀尔帖效应与西伯克效应都是温差电效应，二者有密切联系。事实上，它们互为反效应，一个说是电偶中有温差存在时会产生电动势（西伯克效应）；一个说电偶中有电流通过时会产生温差（珀尔帖效应）。珀尔帖效应是热电冰箱的工作基础。 热电偶说白了就是一种感温元件，可以直接测量温度的现场仪表，并把温度信号转换为热电动势信号。

5.4.2 Laws of thermocouples In analyzing various types of thermocouple circuits that arise in practice, certain “laws of thermocouples” known for many years are useful. These laws can all be derived from the basic relation (Eq.5.5), but we here simply state them without proof. Law of leadwire temperature Law of intermediate leadwire metals Law of intermediate junction metals Law of intermediate metals Law of intermediate temperatures

1 Law of leadwire temperature 导线温度定律 1 Law of leadwire temperature The thermoelectric voltage due to two junctions in a circuit consisting of two different conducting metals depends only on the junction temperatures T1 and T2. As illustrated in Fig.5.7, the temperature environment of the leads away from the junctions (T3, T4, T5) does not influence the measured voltage. Therefore, we need not be concerned about shielding the leadwires from environmental conditions.

2 Law of intermediate leadwire metals 中间导线金属定律 2 Law of intermediate leadwire metals As illustrated in Fig.5.8, a third metal C introduced in the circuit constituting the thermocouple has no influence on the resulting voltage as long as the temperatures of the two new junctions (A-C and C-A) are the same (T3=T4). As a consequence of this law, a voltage measurement device that creates two new junctions can be inserted into the thermocouple circuit without altering the resulting voltage.

3 Law of intermediate junction metals 结合点处中间金属定律 3 Law of intermediate junction metals As illustrated in Fig.5.9, if a third metal is introduced within a junction creating two new junctions (A-C and C-B), the measured voltage will not be affected as long as the two new junctions are at the same temperature(T1=T3). Therefore although soldered or brazed joints introduce thermojunctions, they have on resulting effect on the measured voltage. If T1 ≠ T3 the effective temperature at C is the average of the two temperatures

4 Law of intermediate metals 中间金属定律 As illustrated in Fig.5.10, the voltage produced by two metals A and B is the same as the sum of the voltages produced by each metal (A and B) relative to a third mental C: This result supports the use of a standard reference metal (e.g., platinum) to be used as a basis to calibrate all other metals.

5 Law of intermediate temperatures 中间温度定律 Junction pairs at T1 and T3 produce the same voltage as two sets of junction pairs spanning the same temperature range (T1 to T2 and T2 to T3,); therefore, as illustrated in Fig.5.11, This result supports the use of a reference junction to allow accurate measurement of an unknown temperature based on a fixed reference temperature (described below).

These laws are of great importance in the practical application of thermocouples. The first states that the lead wires connecting the two junctions may be safely exposed to an unknown and/or a varying temperature environment without affecting the voltage produced.

Laws 2 and 3 make it possible to insert a voltage-measuring device into the circuit to actually measure the emf rather than just talking about its existence. That is, the metal C represents the internal circuit (usually all copper in precise instruments) between the instrument binding posts. The instrument can be connected in two ways, as known in Fig.5.8 and 5.9. Law 3 also shows that thermocouple junctions may be soldered or brazed (thereby introducing a third metal) without affecting the readings.

Law 4 shows that all possible pairs of metals need not be calibrated since the individual metals can each be paired with one standard (platinum is used) and calibrated. Any other combinations then can be calculated; calibration is not necessary.

In considering the fifth law, we should note that, in using a thermocouple to measure an unknown temperature, the temperature of one of the thermojunctions (called the reference junction) must be known by some independent means. A voltage measurement then allows us to get the temperature of the other (measuring) junction from calibration tables.

5.4.3 Common thermocouples Thermocouples formed by welding, soldering, or merely pressing the two materials together give identical voltage. If current is allowed to flow; the currents may be different since the contact resistance differs for the various joining methods. Ready- made thermocouple pairs are, of course, available in a wide range of materials and wire sizes.

While many material exhibit the thermoelectric effect to some degree, only a small number of pairs are in wide use. They are platinum/rhodium, Chromel/Alumel, copper/constantan, and iron/constantan. Each pair exhibits a combination of properties that suit it to a practical class of applications. Since the thermoelectric effect is somewhat nonlinear, the sensitivity varies with temperature. The maximum sensitivity of any of the above pairs is about 60μV/°C for copper/constantan at 350°C. Platinum/platinum-rhodium is the least sensitive: about 6 μV/°C between 0 and 100°C platinum/rhodium 铂/铑 platinum/rhodium 铂/铑 platinum/rhodium 铂/铑 Chromel/Alumel 镍铬合金/镍铝金 Chromel/Alumel 镍铬合金/镍铝金 Chromel/Alumel 镍铬合金/镍铝金 Constantan 康铜 Constantan 康铜

The accuracy of the common thermocouples may be stated in two different ways. If you utilize standard thermocouple wire (which is not individually calibrated by the manufacturer) and make up a thermocouple to be used without calibration, you are relying on the wire manufacturer’s quality control to limit deviations from the published calibration tables. These tables give the average characteristics, not those of a particular batch of wire.

Platinum/platinum-rhodium is the most accurate; error is of the order of ±0.25 percent of reading. Copper/constantan gives±0.5 percent or ±1.5°F (whichever is larger) between -75 and 200°F and ±0.75 percent between 200 and 700°F. Chromel/Alumel gives ±5°F (32 to 660°F) and ±0.75 percent (660 to 2300°F). Iron/constantan has ±66 μV below 500 °F and ±1.0 percent from 500 to 1500 °F.

If higher accuracies are needed, the individual thermocouple may be calibrated. An indication of the achievable accuracy is available from National Bureau of Standards (of U.S.A) listings of the results they will guarantee. At the actual calibration points, the error ranges from 0.05 to 0.5℃. Interpolated points are less accurate: 0.1 to 1.0℃, except platinum/platinum-rhodium at 1450 °F,2.0 to 3.0°C. The realization of this potential accuracy in applying such calibrated thermocouples to practical temperature measurement is, of course, dependent on the application conditions and is rarely possible.

If higher accuracies are needed, the individual thermocouple may be calibrated. An indication of the achievable accuracy is available from National Bureau of Standards (of U.S.A) listings of the results they will guarantee. At the actual calibration points, the error ranges from 0.05 to 0.5℃. Interpolated points are less accurate: 0.1 to 1.0℃, except platinum/platinum-rhodium at 1450 °F,2.0 to 3.0°C. The realization of this potential accuracy in applying such calibrated thermocouples to practical temperature measurement is, of course, dependent on the application conditions and is rarely possible.

platinum/platinum-rhodium thermocouples are employed mainly in the range 0 to 1500℃. The main features of this combination are its chemical inertness and stability at high temperatures in oxidizing atmospheres. Chromel/Alumel couples are useful over the range -200 to +1300℃. Copper/constantan is used at temperatures as low as -200℃; its upper limit is about 350℃ because of the oxidation of copper above this range. Iron/constantan is the most widely utilized used thermocouple for industrial applications and covers the range -150 to +1000℃. It is usable in oxidizing atmospheres to about 760℃ and reducing atmospheres to 1000℃.

The six most commonly used thermocouple metal pairs are denoted by the letters E,J,K,R,S, and T. The 0℃ reference junction calibration for each of the types is nonlinear and can be approximated with a polynomial. Where V is the thermoelectric voltage measured in volts and T is the measuring junction temperature in℃, assuming a 0℃ reference.

The meals in the junction pair, the thermoelectric polarity, the commonly used color code, the operating range, the accuracy, and the polynomial order and coefficients are shown for each type in Table 5.1.

Fig 5.12 shows the sensitivity curves for some commercially available thermocouple pairs. Even though we use a ninth-order polynomial to represent the temperature voltage relation, providing an extremely close fit, the relationship is close to linear as predicted by the Seeback effect.

A standard configuration for thermocouple measurements is shown in Fig A standard configuration for thermocouple measurements is shown in Fig.5.13. It consists of wires of two metals, A and B, attached to a voltage-measuring device with terminals made of metal C. The reference junction is used to establish a temperature reference for one of the junctions to ensure accurate temperature measurements at the other junction relative to the reference. A convenient reference temperature is 0 °C since this temperature can be accurately established and maintained with a distilled water ice bath ( i.e., an ice-water mixture).

If the terminals of the voltage measuring device are at the same temperature, the law of intermediate leadwire metals ensures that the measuring device terminal metal C has no effect on the measurement. For a given pair of the thermocouple metals and a reference temperature, a standard reference table can be compiled for converting voltage measurements to temperatures.

An important alternative to using an ice bath is a semiconductor reference, which electrically establishes the reference temperature based on solid state physics principles. These reference devices are usually included in thermocouple instrumentation to eliminate the need for an external reference temperature.

Fig.5.14 illustrates a two-reference junction configuration, which allows independent choice of the leadwire metal. Copper is a good choice, since copper leadwires are inexpensive and no junctions are introduced at the voltmeter connections, which are usually copper.

热电堆 Fig.5.15 illustrates the configuration for a thermopile, which combines N pairs of junctions, resulting in a voltage N times that of a single pair. In the example shown in the figure, the multiplication factor would be 3. If the measuring junctions (at T) are the different temperatures, the output would represent the average of these temperatures.