Of all the physical properties, it is temperature, which is being measured most often.

1. Temperature 1.1 Introduction Of all the physical properties, it is temperature, which is being measured most often. Even the measurement of other physical properties,e.g. pressure, flow, level,, often requires a compensation for the effects of temperature. Thus, when measuring such properties, very often a simultaneous measurement of temperature is being required. The following principles can be used in order to measure temperature: a) Mechanical Thermometers: - Liquid Expansion Thermometers - Solid Expansion Thermometers b) Electrical Thermometers: - Resistance Temperature Devices (RTDs) - Thermistors (NTCs, PTCs) - Thermocouples (TCs) - Semiconductor Sensors c) Remote Sensing of Temperature - Wien s Displacement Law - Stefan-Bolzmann s Law In this lecture-series, we will study RTDs, TCs, and remote sensing of temperature. RTDs have two main advantages: - they can measure temperature very precisely - they are suitable for measuring temperatures between -200 + 850 C For these two reasons, RTDs should be the preferred way of measuring temperature within this temperature range. TCs can be used to measure temperatures of up to 1800 C. Although TCs can also be used (and often are being used) to measure much smaller temperatures, for example between 0 C and say 100 C, this is not advisable. At these temperatures, the produced thermo-voltage is rather small, and hence susceptible to interference such as electrical noise. The advantage of TCs is that they are able to measure high temperatures. For example temperatures above 850 C (where RTDs cannot be used). TCs should only be used for measuring such high temperatures. There, they work great. Remote sensing of temperature is a great way of measuring temperature where the sensor cannot be in physical contact with the object of interest. The distance between the object and the sensor does not matter. In fact, this distance can be extremely large. However, some key advice must be kept in mind in order to make this measurement reliable. 1

1.2 Mechanical Thermometers: Liquid- Expansion- Thermometers: Solid- Expansion- Thermometers: - e.g. bimetals: - amplification of the expansion-effect, By using a spiral design of the bimetal: Mechanical thermometers seem to be obsolete for scientific or industrial applications. Today, electrical thermometers can measure temperature much more accurate. Moreover, with electrical thermometers we can log temperature automatically into computer files. However, in industrial applications, mechanical thermometers are still being used. In addition to comfortable electrical thermometers. The main reason is that these mechanical thermometers serve as backup devices. For example, if the electrical power fails, any fancy electrical thermometer becomes useless. In such a scenario, one still needs to know the temperature of certain processes. A robust spiral-wound mechanical thermometer provides peace of mind. 2

1.3. Resistance Temperature Devices (RTDs) 1.3.1 Basics The measurement principle of RTDs is based on the property of metals to exhibit a higher electrical resistance as the temperature increases: This principle is valid for all metals. Of importance are: Platinum, Nickel (and Copper) RTD-Labeling: - - The most important RTD-material is Platinum. Because: - Pt is chemically very inert and stable (e.g.: it does not corrode easily) - the temperature-resistance-correlation for Pt is linear between 0 und 100 C - Pt as a wide temperature range: -220 +850 C for Pt ( -60 +150 C for Ni ) 3

1.3.2 Platinum RTDs a) Norms In principle, any bare metal can be used in order to serve as an RTD. However, RTDs manufactured out of Platinum have gained importance by far. RTDs made out of Pt are used most often, because of the various advantages that Pt offers. RTDs made out of Pt are standardized in the following norms: DIN 60751 (DE) EN 60751 / IEC 751 (EU) These norms describe and standardize certain properties of Pt-RTDs. Such us: - correlation-formulas - correlation-tables - classes of uncertainty of the manufactured resistance values - recommended amounts of the needed excitation current - recommended test procedures For example, these norms contain the correlation table for Pt100 sensors. For details, please refer to the publications of these norms. The next page contains this very table. It correlates a certain resistance of a Pt100 to the corresponding temperature. This table, by the way, was calculated by using the correlation-formula, which is also specified in the norm. By the way: It is an interesting detail that the specs of a Pt-RTD manufactured in the US do not match the specs of a Pt-RTD that was manufactured in the EU. A Pt-RTD manufactured in the US is slightly more sensitive compared to its European counterpart. As a consequence, a Pt-RTD bought from a US-company cannot be read out by using the correlation function that is valid in Europe. Or else, the result will be slightly off. And vice versa. 4

Pt100 Correlation-Table (DIN EN 60751) The table contains the values of resistance of a Pt100 sensor in Ohm. The corresponding temperature can be calculated by adding the row-temperature (in steps of ten degrees) with the corresponding column-temperature (in steps of two degrees) Examples: For ϑ = 12 C: For ϑ = - 34 C: row ϑ = 10 C, column + 2 C row ϑ = -30 C, column 4 C RPt100 = 104,68 Ω RPt100 = 86,64 Ω 5

b) Uncertainty-Classes The norm IEC-751 defines two uncertainty-classes for Pt100 sensors: class-a and class-b. These classes pertain to the uncertainty of the manufactured resistance of Pt100 sensors. However. Rather than specifying this uncertainty in the unit of resistance (Ohm), it is being translated into the corresponding uncertainty of temperature (in units of degree Celsius). Class-A defines an uncertainty of ± 0.15 C @ 0 C. Class-B defines an uncertainty of ± 0.30 C @ 0 C. As temperature increases, so will this uncertainty. For details, refer to the norm IEC-751. In addition to these two classes, manufacturer of Pt100 sensors offer various other uncertainty classes. For example: Class-(1/3)-B. This class means an uncertainty of ± 0.10 C @ 0 C. Class-(1/10)-B. This class means an uncertainty of ± 0.03 C @ 0 C. Class-2B. This class means an uncertainty of ± 0.60 C @ 0 C. Class-5B. This class means an uncertainty of ± 1.5 C @ 0 C. When purchasing a Pt100 temperature sensor, the uncertainty class typically needs to be chosen. Which class should be chosen? Obviously the answer to this question depends on the application. A smaller uncertainty range gives better measurement accuracy. But such sensors are more somewhat more expensive. And vice versa. In industrial applications, class-b is mostly being used. Because, this range of measurement uncertainty can often be tolerated. Consider an industrial application. In a production line, temperatures between 0 200 C can occur. In such a case, even a class-2-b sensor should suffice. Imagine, on the other hand, you had a baby, 4 month old. And your baby develops a fever late at night. Your fever thermometer, if it contained a Pt100 sensor, cannot possible have a class-2-b sensor. An uncertainty of the measurement of ± 0.6 C would be completely unacceptable in this application. You trust your thermometer that it measures the temperature as exactly as 0.1 C, don t you? Because, you base treatment decisions on this very measurement. In some applications, accuracy matters a lot. 6

c) Wiring There are two prevailing ways of connecting RTD-sensors: - with two wires ( abbreviated: Ω2 ) - with four wires ( abbreviated: Ω4 ) Ω2 Configuration: When an RTD-sensor is connected to its readout-electronics with two wires (Ω2) only, a measurement error can occur. This error depends on the length of the connecting wire. Because, the resistance of the connecting wires are erroneously added to the resistance of the RTD-sensor. With the result that the true temperature at the RTD-sensor is being measured too high. So, this type of measurement error is systematic. An example shall illustrate the problem: For a typical wire resistance of 20 mω/m (milli-ohm per meter), the error in the temperature measurement due to the resistance of the connecting wire will be approximately 0.05 C per meter wire length. The unit meter, which appears in the value of typical wire resistance, refers to the total length of the connecting wire. Imagine, your readout electronics is located just one meter away from your sensor. If you connect the RTD-sensor directly with the readout electronics with two wires only (Ω2), you have one meter of wire leading from the readout electronics towards the RTD-sensor, and one additional meter of wire leading from the RTD-sensor back towards the readout electronics. So, the total length of connecting wire equals two meters. In this case, you would determine the temperature at the RTD-sensor too high by 0.1 C. An error of such small magnitude might be tolerable for many applications. It remains small, because the length of the connecting wire is fairly short. Thus, the error, which is introduced with an Ω2- configuration, may be neglected if the total length of the connecting wire remains rather short. Imaging, in contrast, the following application: The temperature of a large electrical power generator, located at a power station, is to be measured with an RTD-sensor. The readout electronics for this sensor is stored in a shielding box, mounted to the wall of the power station hall. The 2-wire-cable that connects the sensor with its readout electronics runs from the box through the hall to the generator, totaling in length 50 meters. So, this is an Ω2 wiring configuration, and the total wire length equals 2 50 m = 100 m. Thus, the temperature of the generator will be measured too high by approximately 5 C. And this measurement error may be way too high in order to be tolerated. Ω4 Configuration: When an RTD-sensor is connected to its readout electronics with four wires (Ω4), this measurement error will simply not occur! For reasons, please consult the literature. So, the Ω4-configuration has enormous advantage versus the Ω2-configuration. The only drawback is that connecting an RTD-sensor with four wires is slightly more expensive in comparison to a connection with two wires only. However, this slight disadvantage can often be taken considering the enormous advantage. 7

Homework: Find a thermometer, which uses the principle of an RTD. Preferably, the sensor itself should be a Pt100. You can find and present a suitable sensor alone. However, in this case the needed readout-electronics is still missing. You can also find a device, which reads a Pt100. And which also displays the corresponding temperature. This would constitute an entire measurement setup, ready to be used. Search the internet. For example, you can go to the websites of suitable vendors of electronics or of lab equipment. At their main websites, one typically finds a search field. Simply search for RTD or for Pt100. Or, at the left side of the website, navigate to temperature and then RTD, for example. Candidate vendors are: Omega: Cole-Parmer: Greisinger: Fluke: Minco: Jumo: Farnell: Reichelt: Vernier: Newark: Mouser: Conrad: www.omega.com www.coleparmer.com www.greisinger.de www.fluke.com www.minco.com www.jumo.de www.farnell.de www.reichelt.de www.vernier.com www.newark.com www.mouser.com www.conrad.de Send me by email: - a picture of the chosen sensor or device - who is the vendor (i.e., where can it be ordered) - how much does it cost? 8

Problems: 1) Given is a Pt100 temperature sensor of class B. The sensor is connected to its readout-device in an Ω2-Configuration. The distance between the sensor and its readout-device equals 5 m. What is the measurement uncertainty of this sensor at 0 C? 2) Given is a Pt100 temperature sensor of class 5B. The sensor is connected to its readout-device in an Ω2-Configuration. The distance between the sensor and its readout-device equals 90 m. What is the measurement uncertainty of this sensor at 0 C? 3) Given is a Pt100 temperature sensor of class B. The sensor is connected to its readout-device in an Ω4-Configuration. The distance between the sensor and its readout-device equals 200 m. What is the measurement uncertainty of this sensor at 0 C? 4) The manufacturer of thermometers wants to produce a new fever-thermometer. This application calls for a measurement uncertainty that is smaller than ± 0.05 C. Is this uncertainty achievable with a Pt100 sensor? If yes, how? 5) The resistance of a Pt100 sensor equals 172.91 Ω. What is the temperature of this sensor? (Use the R-ϑ-Correlation table for Pt100 sensors at page 5 of this handout). 9

Appendix Uncertainty-Classes (nice to know): In order to explain this topic some more detailed, consider a Pt100 sensor. The name tells us that this sensor has a resistance of 100 Ω at a temperature of 0 C. So much is theory. In practice, the manufacturer of RTDs cannot guaranty that the resistance-value of the RTD is exactly 100.00 Ω at 0 C. Rather, the R-value might be slightly off. Somewhat higher, or somewhat lower. For example, if you were to buy a certain Pt100 sensor in a store, and you measured its resistance at 0 C, you might find out that R is, for example, 100.11 Ω. Or, 99.91 Ω. Or the like. With R = 100.11 Ω, you would measure the temperature (which in truth is 0.00 C) slightly too high. With R = 99.91 Ω, you would measure the temperature (which in truth is 0.00 C) slightly too low. Say, you bought a certain Pt100. And say, its resistance happened to be 100.11 Ω at 0.00 C. This resistance corresponds to a temperature of 0.285 C. Imagine, you would create a water bath, which has a temperature of exactly 0.00 C. For example, a bath with cold water and chunks of ice swimming in it will have a temperature of pretty exactly 0.00 C. So we know the true temperature of this water bath. If you would now try to measure this very temperature with a Pt100, which happens to have a resistance of 100.11 Ω at 0.00 C, you would measure 0.285 C. In other words, you would measure the true temperature wrong by 0.285 C. If such a measurement error can be tolerated or not remains to be determined by the user. It might. Or it might not. If you would now repeat this measurement again and again, say 100 times, you would 100 times measure a resistance of about 100.11 Ω at 0.00 C. So, this type of measurement error is systematic. 100.11 Ω is the resistance of this very Pt100 sensor at 0.00 C. It will not change much (neglecting possible long term drifts at this time). You would measure the true temperature slightly too high by 0.285 C again and again. Assume, you bought another Pt100 sensor, and you might discover that its resistance equals, for example, 99.91 Ω at 0 C. Conducting the water bath experiment again, you would end up measuring the true temperature of the water (which is 0.00 C) slightly too low. You would measure -0.22 C, instead of the true 0.00 C. Measuring with error again. If you would repeat the ice-water bath experiment with this second Pt100 sensor 100 times, you would determine the temperature of the water bath too low by -0.22 C 100 times. Because, this error is systematic to the specific sensor that was being used. If you know bought a third Pt100, it might turn out to exhibit a resistance of 100.07 Ω at 0.00 C, for example. And so on. The manufacturer simply cannot guarantee exact values. They produce these sensors with a certain range of resistance-uncertainty. And we have to live with this uncertainty. What manufacturers do provide, however, are limits. Limits, that no sensor of a certain class will exceed. Per se, these are limits of the resistance value, which the produced sensors will not exceed. For example: for the uncertainty-class-b, the limit of the resistance at 0 C for a Pt100 sensor is defined as ± 0.12 Ω. This means that a manufacturer guaranties that the resistance of a produced Pt100 sensor will not exceed 100.12 Ω, nor that it will fall below 99.88 Ω, at 0 C. We must live with the 10

uncertainty that the produced sensor may have any value within this range. But, we are guaranteed, that this range will not be exceeded. However, specifying the range of uncertainty in Ohms does not tell us much, does it? For this reason, the norm IEC-751 translates this uncertainty of the resistance value of Pt100 sensors into an uncertainty of temperature. By using the specified correlation formula. In the example of the class-b, the uncertainty of measurement equals ± 0.30 C @ 0 C. So, is this type of measurement error systematic, or is it stochastic (as the ± sign might imply)? If we consider a specific Pt100 sensor, the measurement error based on the inaccuracy of the sensorresistance is systematic. For this very sensor, this measurement error will always be the same. You could even correct for it, if you calibrated this sensor. However, if we consider many manufactured Pt100 sensors, this type of measurement error is stochastic. Even worse, we do not know, how this inaccuracy is being distributed. The manufacturer won t tell us. But, we are guaranteed the limits, which are not being exceeded. So, we have to live with this uncertainty. 11