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Measurement of Temperature

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1 Measurement of Temperature
Practical Temperature Measurement Temperature Measurement Presentation Defining and measuring temperature Thermal Time Constant Measurement Errors RTD’s Thermistors I.C. Sensors Thermocouples 1 The website shown near the top of the slide is from the Hewlett Packard Educators Corner and is an interesting and complete document on temperature measurement. I recommend that you read this document and it is included with this presentation in PDF form. Hewlett Packard (the instrument division of HP was spun off into Agilent) also provides an excellent PPT presentation at the 2nd website address shown on the slide. The HP presentation also has an informative commentary with it. It is 1.3 Mbytes in size, so I have not included it, however, it is viewable on the web and you can download it to your computer. Some of the figures and discussion in this presentation will be taken from this document. The basic definition and measurement of temperature will be discussed followed by the concept of a thermal time constant and measurement errors. Then, each of the 4 major types of temperature sensors will be discussed with examples. Transition: First, lets look at the definition of temperature.

2 Defining Temperature A scalar quantity that determines the direction of heat flow between two bodies A statistical measurement A difficult measurement A mostly empirical measurement 2 Temperature is not easily defined. It is a quantity that determines the direction of heat flow between two bodies. It is a statistical measurement, as evidenced by the fact that it is impossible to determine the temperature of a single molecule. When you try to measure temperature accurately, you find that the measurement is difficult to repeat, and that it is influenced by variables such as thermal contact, response time and electrical noise. The Miriam-Webster dictionary, online, shows the definitions displayed on the slide for temperature and for empirical. So, from this, temperature is a relative measurement and must be based on a scale that was made up by humans. Transition: Next is a look at some of the temperature scales used. Temperature: degree of hotness or coldness measured on a definite scale Empirical: originating in or based on observation or experience

3 3 You are all familiar with the Fahrenheit and Centigrade or Celsius scales and have used the Kelvin scale in Physics or Chemistry. The Rankine scale is directly related to Fahrenheit and is of historical interest as is the little known Reaumur scale in which the difference between the freezing and boiling points of water was defined as 80 degrees rather than the 100 degrees as in the Celsius scale that has come into favor. The point of this chart is that Temperature measurements are relative and are defined by a scale. This scale is generally related to the three points shown on the chart, absolute zero, the melting point of ice and the boiling point of water. The temperature of an object depends on how fast the atoms and  molecules which make up the object can oscillate. As an object is cooled, the oscillations of its atoms and molecules slow down. For example, as water cools, the slowing oscillations of the molecules allow the water to freeze into ice. In all materials, a point is eventually reached at which all oscillations are the slowest they can possibly be. The temperature which corresponds to this point is called absolute zero. Note that the oscillations never come to a complete stop, even at absolute zero. Transition: Next is a look at a principle of temperature measurement. The Reaumur temperature scale is named after the French scientist ( ). He proposed his temperature scale, in Reaumur divided the fundamental interval between the ice and steam points of water into 80 degrees, fixing the ice point at 0 Degrees and the steam point at 80 degrees. The reaumur scale, although of historical significance, is no longer in use. Temperature Systems

4 Measuring Temperature
Don't let the measuring device change the temperature of what you're measuring. Response time is a function of Thermal mass (mass of the device e.g large Thermistor vs small Thermistor) Measuring device (type of device e.g. RTD or Thermocouple) The Thermal Time Constant for a thermistor is the time required for a thermistor to change its body temperature by 63.2% of a specific temperature span when the measurements are made under zero-power conditions in thermally stable environments. 4 Some factors in temperature measurement are shown here. The first on is to not let the measuring device change the temperature of what you are measuring. The best example of this is any resistive temperature device such as a Thermistor or RTD. In order to measure the resistance, for instance in a bridge configuration, you must make current flow through the device. Current ALWAYS creates I2R power loss. I2R creates heat, which changes the temperature of what is being measured. So, you must be very careful that the current through the device does not produce enough heat to make the temperature measurement invalid. The response time of a temperature measuring device generally uses a Thermal time constant, which is defined at the bottom of the slide. This is the standard definition of one time constant which is tau in the mathematical expression, exp(-t/tau) and you will measure this in the lab experiments. Since (1-e-1) is .632, this is the standard rising exponential. Transition: Next is a discussion of factors that affect thermal time constants.

5 The dominant factors that affect the T.C. of a thermistor are:
The mass and the thermal mass of the thermistor itself. Custom assemblies and thermal coupling agents that couple the  thermistor to the medium being monitored. Mounting configurations such as a probe assembly or surface mounting. Thermal conductivity of the materials used to assemble the thermistor  in probe housings. The environment that the thermistor will be exposed to and  the heat transfer characteristics of that environment. Typically, gases are less dense than liquids so thermistors have greater time constants when monitoring temperature in a gaseous medium than in a liquid one. 5 Factors that affect the thermal time constant of a temperature sensor are shown here. The size of the device and how it is coupled and mounted to the medium to be measured are all important factors. Thermal conductivity is how well the material conducts heat. Metals are generally good heat conductors and Gold is the best heat conductor, which is one reason it is used for leads in high end microprocessor devices. Gold conducts the internal heat of the high speed device out to the edge of the device where it can be cooled. The environment is critical to the thermal time constant. The example, in brown on the slide, shows what you already know logically, that a thermistor, or other device, will take longer to change temperature in air than in water because the medium of water conducts heat to the device much better than the medium of air. The information on this page is from the website shown near the bottom of the slide. This website has much more information on the companies products. Transition: Next is an example of a thermal time constant using a universal time constant chart. Thermal Time Constant

6 Thermal Time Constant 3τ 1τ 2τ 4τ 5τ
6 The example at the bottom of the slide shows that the universal time constant chart can be used to determine the temperature that would be reached in one time constant when moving a thermistor from a 250C to a 750C environment. You can see that the 250C and 750C are superimposed on the universal time constant chart created in PSpice. So, after 1 time constant, the temperature has risen to 63.2% of the difference between the beginning and ending temperature, which is 56.60C. Transition: Next is a look at temperature errors. 250C Example: A thermistor is placed in an oil bath at 25°C and allowed to reach equilibrium temperature. The thermistor is then rapidly moved to an oil bath at 75°C. The T.C. is the time required for the thermistor to reach 56.6°C (63.2% of the temperature span [difference]). Thermal Time Constant

7 Temperature Errors What is YOUR normal temperature?
Thermometer accuracy, resolution Contact time Thermal mass of thermometer, tongue Human error in reading 95% Confidence interval 7 You must always consider errors in measurements and temperature is no exception. For instance, this information, taken from the HP slides considers taking your body temperature with a thermometer. You know that you should be at 98.60F, but, in reality an individuals normal body temperature may vary slightly from this, so this is not a fixed number, but a Normal distribution. The paper, which can be viewed at the website shown near the bottom of the slide, shows that a recent study shows the actual mean body temperature is The 95% confidence limits, for 130 subjects in this study, extends from to As discussed earlier, this means that 95% of the samples were within that interval and it would make up most of the area under a normal distribution curve. You must always question accuracy and resolution of measurements. In addition, the thermal time constant is critical. For instance, how long does it take to get a good reading of a thermometer under your tongue? This depends on good contact, the size (thermal mass) of the thermometer’s metal tip and its contact with the base of the tongue. You must also question the reading and ensure that if it is taken by a person, that they are well trained in the exact method of reading the thermometer. Transition: Next is a look at the first of 4 basic temperature measurement sensors, the RTD.

8 The Resistance Temperature Detector (RTD)
RTD: Most accurate, Most stable, Fairly linear Expensive (platinum) Slow (relative) Needs I source (changing resistance) Self-heating (don’t change the measurement due to the internal current!) 4-wire measurement (must take the resistance of the leads into account) 8 The resistance temperature detector is the most accurate and stable device, but it is expensive because it is made of Platinum. It is relatively slow because the thermal mass of the platinum resistance must be heated prior to the temperature changing. It needs a current source because you must still use Ohm’s law to measure the change in resistance. It must also use a 4 wire measurement to cancel the resistance of the lead wires. Additional information on RTD’s and other temperature measurement sensors is at the top website shown and the bottom website shown contains information about the product line sold by Minco. Transition: Next is additional discussion of RTD’s.

9 RTDs are among the most precise temperature sensors commercially used
RTDs are among the most precise temperature sensors commercially used. They are based on the positive temperature coefficient of electrical resistance. RTD’s 9 Metals normally have a positive temperature coefficient of resistance, meaning that as the temperature increases, the resistance of the metal increases. Platinum RTD’s are the most common and are used over a wide temperature range as shown on the chart, which is from the website shown just above the chart. Copper and other metals are also used, with Tungsten available for very high temperature applications. Omega is a major manufacturer of sensors and its website is also shown on the slide. The article at the Sensors magazine website shown on the slide provides a detailed look at RTD’s. Transition: Next is a look at the linearity of RTD’s.

10 RTD Linearity R=RRef[1+α(T-TRef)] R=100[1+.00385(70-60)] =103.85 ohms
The graph at the top of the slide shows the relative linearity over a wide temperature range for various metals used in RTD’s. You can see that Platinum is the most linear over a wide temperature range. The base resistance of most platinum RTD’s is 100 ohms as shown in the chart near the bottom of the slide. The standard Temperature Coefficient of Resistance (TCR on the chart) for platinum is This means that for each degree increase in temperature, the resistance increases by degrees. What this really means is that a measurement of temperature using an RTD must be extremely accurate and precise. The formula for using this linear temperature coefficient is the same as the one used in your DC circuits course and is shown in red near the top right of the slide. An example of its use is shown, in blue, on the slide. The example uses a standard 100 ohm platinum RTD with a TCR of The temperature is increased from 600C to 700C. The resistance increases by only 3.85 ohms with this temperature increase, so you must be able to accurately measure this change in resistance. Transition: Next is a look at how to accurately measure these small changes in resistance using a bridge circuit.

11 RTD Measurement To balance the bridge: R1R3=R2R4
DDC RTD Measurement To balance the bridge: R1R3=R2R4 11 The circuit diagrams shown on the left of the slide are taken from the website shown on the upper right. A standard Wheatstone bridge circuit is used for most measurements and the RTD (or other sensor), can be far from the location of the bridge. This means that the resistance of the wires must be taken into account since the change in resistance of the RTD is quite small for a small temperature change. In the 2-Wire circuit, the Wire resistances RL1 and RL2 are added to the RTD resistance and, thus, the RTD resistance is read as higher than its actual resistance by the total wire resistance. A 3 wire RTD circuit also uses a Wheatstone bridge, but the resistance of R3 is increased by RL2+RL3 and the resistance of the RTD is increased by RL1 and RL2. If these leads are all the same length, the resistances of the leads to the RTD and to R3 cancel. Remember, from the text that the balance equation for a bridge is R1R3=R2R4 as shown here. The dissipation constant of a thermistor is defined, in blue, on the slide, but all resistance measurement devices must take this effect into account. The key is to ensure that you are only measuring the change in resistance of the RTD and not the wire resistance. Also, remember to take into account the heating effect of the current through the bridge circuit. The chart near the bottom right shows that increasing the current in an RTD increases the temperature and, thus, low currents must be used in the circuits. Transition: Next is a look at the 4 wire RTD circuit configuration. Dissipation Constant The power in milliwatts required to raise a thermistor 1°C above the surrounding temperature is the dissipation constant.

12 To estimate leadwire error for a 2-wire configuration, multiply the total length of the extension leads by the resistance per foot in the table shown below. Then divide by the sensitivity of the RTD, given in the table below to obtain an error in C°. Example: You are using a 100 platinum RTD with a TCR of and 50 ft. of 22 AWG leadwire. R = 50 ft. x /ft. = 0.825 Approximate error = / = 2.14°C 12 The slide shows a 4 wire configuration, taken from the website at the top of the slide. This 4 wire configuration uses a precision current driver and precision voltage instrument. The 4 wires cancel more effects and should be used for high accuracy sensors, whether RTD or other type. The importance of leadwire resistance can be seen in the Example shown near the bottom of the slide. The 50 feet of #22 AWG (about the size of the lead wires you use for your breadboards) produces over 2 degrees of error in the temperature measurement. Transition: Next is a look at Thermistors. 4-wire circuit

13 Thermistors Advantages: Disadvantages High output Fast
2-wire measurement Disadvantages Very nonlinear Limited range Needs I source Self-heating Fragile NTC Thermistor Shown RT R25 13 The typical Thermistor Resistance/Temperature curve shown on the left of the slide is taken from the website below the graph. Notice that the Thermistor curve can be compared to the linear RTD curve. One of the advantages of the Thermistor is its high output. What this means is that for a relatively small change in temperature, there is a substantial change in resistance of an RTD. As you can see from the graph, for a temperature change of 0 to 10 degrees C, the resistance of the RTD goes from just under 3 times the resistance at 25 degrees C to just under 2 times the resistance. This is a large resistance change when compared to a platinum RTD that would only change about 3.85 ohms with a change of 10 degrees C. Thermistors can be fast because they can be made quite small. Fast is relative, but refers to the Thermal time constant that was discussed earlier. Since there is a large resistance change, simpler 2-wire measurements can be used with Thermistors because the wire resistance is quite small compared with the change in resistance of the Thermistor. The first disadvantage can be readily seen from the graph. It is very nonlinear, so a table or a linearization method would have to be used. Notice that a Negative Temperature Coefficient Thermistor is shown on the graph and this is the most common type used. The negative temperature coefficient refers to the fact that an increase in temperature results in a decrease in resistance, in other words, the slope is negative. Thermistors are generally useable over a more limited range of temperatures, you need a current source and must be careful of self-heating. The Fragility item is relative since we have had all of our Platinum RTD’s broken, but rarely have trouble with the thermistors. However, you must be careful of all of the equipment. Transition: Next is a look at more thermistor characteristics and circuits.

14 Commonly used for sensing air and liquid temperatures in pipes and ducts, and as room temperature sensors.  Unlike RTD's, the temperature-resistance characteristic of a thermistor is non-linear, and cannot be characterized by a single coefficient.   The following is a mathematical expression for thermistor resistance1: R(T) = R0 exp[b (1/T - 1/T0)] Where: R(T) = the resistance at temperature T, in K, R0 = the resistance at reference temperature T0, in K, b = a constant that varies with thermistor composition T = a temperature, in K, T0 = a reference temperature (usually K) Because the lead resistance of most thermistors is very small in comparison to sensor resistance, three and four wire configurations have not evolved.  Otherwise, sensing circuits are very similar to RTD's, using the Wheatstone bridge 14 Manufacturers commonly provide resistance-temperature data in curves, tables or polynomial expressions.  Linearizing the resistance-temperature correlation may be accomplished with analog circuitry, or by the application of mathematics using digital computation. An equation for a thermistor is shown in blue on the slide taken from the website shown near the bottom of the slide. However, this is not necessarily the best equation for a thermistor. Transition: Another equation for a Thermistor is shown on the next slide. 1Beckwith, Thomas G., Roy D. Marangoni, and John H. Lienhard V. Mechanical Measurements. New York: Addison and Wesley, Pp. 673 DDC Thermistors Thermistors

15 15 A different equation for a thermistor Temperature/Resistance curve is shown here as taken from the Omega website shown. Notice that this equation uses natural logarithms rather than an exponentials and is considerable more complex than the equation on the previous slide. Transition: Next is a look at a Thermistor Temperature/Resistance curve. Thermistor Equation

16 Thermistor Curve http://www.workaci.com/pdf/t-19.pdf
16 The data for the curve is shown on the right and is taken from the website shown. The curve was plotted using Excel and is shown on the left of the slide. Transition: Next is a look at how to use the Omega equation discussed on the previous slide. Thermistor Curve

17 Thermistor Circuit The Omega Thermistor equation is:
Eq. Temp 273.15 59.988 The Omega Thermistor equation is: 1/T =A+B*Ln(R)+C*(Ln(R))3 =A+8.903B C =A+6.698B C =A B C To use this equation you write 3 simultaneous eqs. In 3 unknowns and solve. The eqs. Used the values at 0, 50 and 100 Celsius, with the Kelvin values shown on the left. 323.15 The final equation is: 1/T =A+B*Ln(R)+C*(Ln(R))3 with A = 1.472E-3, B=237.5E-6, and C=105.9E-9 17 The Omega Thermistor equation is shown again near the top of the slide. This is solved by using three known values of temperature and resistance from a table or from measurements and solving for a list of temperatures that go with the resistance values. This was done using Excel and the Excel spreadsheet is attached with this presentation for you to download and study. The temperatures that go with each of the resistance values use the final equation that is shown in red near the middle of the slide. These temperatures are very close to the value shown on the left. You should be able to do this calculation using Excel and I recommend downloading the spreadsheet and ensuring that you understand the calculations. Transition: Next is a look at Integrated Circuit Temperature sensors. The resulting temperatures from the equation are shown here and are almost identical to the given values. The resulting graph from the Eq. is indistinguishable From the original graph from the table. 373.15 Thermistor Circuit

18 I.C. Sensors Disadvantages Advantages Limited variety High output
18 Integrated circuit sensors provide either a voltage or current output and are internally linearized. They are relatively inexpensive because they have active devices internal that make it much easier to process the output signal from the sensor. There are a limited number of IC temperature sensors available. The Maxim web site provides the table shown on this slide and shows only 5 different types of output interface. Note that the bottom two items on the slide provide a serial digital interface to the sensor so the information can be connected directly to a microcontroller for processing. The high output shown as an advantage is because there is internal circuitry, like an opamp, and the output voltage or current can be in the mA or Volt range rather than the extremely small outputs of some direct sensors. They are relatively inexpensive, but generally have a limited temperature range due to the internal circuitry. For high temperatures, RTD’s and other devices are generally used. Transition: Next is a look at two available I.C. sensors. Disadvantages Limited variety Limited range Needs V source Self-heating Advantages High output Most linear Inexpensive I.C. Sensors

19 I.C. Sensors LM34: $2.33 from DigiKey AD590: $5.24 from Analog Devices
AD590 (Analog Devices) Current Output – Two Terminal IC Temperature Transducer Produces an output current proportional to absolute temperature. For supply voltages between +4 V and +30 V the device acts as a high impedance, constant current regulator passing 1 µA/K. LM34 (National Semiconductor) The LM34 is a precision integrated-circuit temperature sensor, whose output voltage is linearly proportional to the Fahrenheit temperature. 18 You are familiar with the LM34, which was used in lab and you know that it is very easy to use, just connect a power supply to one pin, ground to another pin and measure the voltage output from the third pin. This voltage output corresponds directly to the temperature in degrees Fahrenheit. The AD590 from Analog Devices outputs a current that is 1 uA per degree kelvin, so it is more difficult to convert to Fahrenheit. As you can see, the cost of both is relatively inexpensive, but not cheap. Transition: Next is a look at AD590 and LM34 circuits.

20 AD590 & LM34 Circuits 20 Circuits from the Analog Devices and the National Semiconductor websites are shown here. Since the AD590 is a current source output, It must have a complete circuit prior to measurement of the output. The circuit shown on the left provides an exact 1kohm resistor at the output of the AD590 so that the voltage measured across the 1kohm resistor is in mV per degree kelvin. The simple LM34 circuit on the right provides a direct voltage output so no resistance is needed to measure the temperature on a DMM. Transition: Next is a look at a circuit to convert the AD590 output into degrees Fahrenheit.

21 Conversion from Kelvin to Fahrenheit
We know that K = 00C = 320F AND K=1000C=2120F so we can write two linear equations in two unknowns. 32 = m + b 212=373.15m + b Solving these for m and b yields: m = 1.8 b = 21 Linear conversion was covered earlier this semester, so it should be relatively straightforward to determine a conversion equation from Kelvin, which is the output of the AD590 temperature sensor to Fahrenheit. First, use the known values of temperature in Kelvin and Fahrenheit to write two linear equations, shown in red. Next, solve these equations for m and b, the slope and axis crossing of the final equation. Then, write the equation. It should now be a simple matter to design an OpAmp circuit to perform the conversion. Transition: Next is the opamp circuit to be able to read the output of an AD590 in Fahrenheit. the linear conversion equation is 0F = 1.8*(0K) –

22 AD590 Conversion to Fahrenheit in mV
+10 volts 180KΩ 180KΩ 100KΩ - AD590 1mV/0K -1mV/0F 1KΩ + 0F = -1.8*(0K) in mvolts 22 Conversion of the AD590 output used to be one of the labs in this course and a simple circuit is used for conversion. The problem is that ALL of the resistors must be EXACT and the input voltage of must also be exact to get an accurate output that is in mV per degree Fahrenheit. This becomes quite challenging and variable resistors must be used and adjusted to get the correct values. The ratio of the two 180 kohm resistors must be one and the ratio of the 180k feedback resistor to the 100k input resistor must be exactly 1.8. Another factor is that the input resistance to the opamp is 100 kohm, so the output of the AD590 sees a 1 kohm resistor in parallel with a 100 kohm resistor, so that the output voltage has a 1% error due to this. Consider this simple circuit and all of the errors that can occur due to different values and you will see that the output in degrees Fahrenheit can be affected in many ways. You must always be careful of input and output impedances and actual resistor values when building or designing circuits. Transition: Next is a look at thermocouples. Use an inverting amplifier to get positive output

23 Thermocouples Advantages: Disadvantages Wide variety Cheap
Wide T. range No self-heating Disadvantages Hard to measure Relative T. only Nonlinear Special connectors 23 Thermocouples are widely used for temperature measurement in industry. They are readily available, inexpensive, can measure a wide temperature range, and measure voltage so there is no self-heating involved. However, thermocouple measurements are tricky and only provide a temperature that is relative to a reference temperature. They are quite nonlinear and require special procedures and connectors. The image on the right is from the Omega website and shows some of its series of thermocouples. Transition: Next is a look at two effects that are related to thermocouple use.

24 Seebeck and Peltier Effects
24 The Seebeck effect is the production of an electric current in a circuit made up of two dissimilar metals that are at different temperatures. The Peltier effect is the production of a temperature gradient at the junction of two dissimilar metals when a current is passed through the junction. As you can see, these two effects are interrelated as was described in the mid 19th century. Transition: Next is a look at Thermocouples. Seebeck and Peltier Effects

25 Seebeck coefficient   in a circuit exhibiting the Seebeck effect, the ratio of the open-circuit voltage to the temperature difference between the hot and cold junctions. 25 This slide is directly from the HP slide show referred to at the beginning of this presentation. If one end of a wire is heated, there is a voltage difference produced between the ends of the wire. So, there is a gradient in voltage along the wire. The voltage is the integral of the non-linear Seebeck coefficient, which is a function of temperature. Transition: Next is how a thermocouple is made. Thermocouples

26 26 Two wires of dissimilar metals joined together make a thermocouple. The voltage at the non-heated end is a complex function of the Seebeck coefficients. If both wires were the same material, there would be no voltage difference between the ends. Remember that the gradient theory stated that heating ONE end of a wire made a voltage difference between the heated end of the wire and the other end. So if both wires were the same, there would be no difference between the end of one wire and the end of the other. Transition: Next is a look at how thermocouple voltage is measured. Thermocouples

27 27 A type J thermocouple is made up of an Iron wire (designated by its Periodic Table designation of Fe) and Constantan (which is an alloy). The Tx junction is at the temperature that must be measured, but having a copper connection to the Iron and the Constantan creates more unknown junctions, so the measurement is useless. Transition: Next is a look at how this voltage can be measured. Thermocouples

28 28 To measure an unknown temperature using a thermocouple, you must have a thermocouple, known as a reference, at a known temperature. The freezing point of water, 00C is a common reference as shown on the slide. Here again is a type J, Constantan-Iron wire thermocouple. So the voltage produced by the unknown temperature is now only a function of that unknown temperature. There are methods of eliminating the reference voltage and you can read the PDF file included with this presentation for more information. Transition: Next is a closer look at thermocouple measurements. Thermocouples

29 29 The curves show the thermocouple Seebeck coefficients for different types of thermocouples. The J and K thermocouples are probably used the the most and you notice that even they are nonlinear. The coefficients are all in uvolts per degree Centigrade, so measurement must be accurate. Thermocouples have tables that show their measurement voltages at all temperatures in their range. Appendix 3 of the text has thermocouple tables for type J, K, T, and S thermocouples. Each table references a 00C reference junction. Transition: Next is a summary of what was covered in this presentation. Thermocouples

30 Summary Defining and measuring temperature Thermal Time Constant
Temperature Errors RTD’s Thermistors I.C. Sensors Thermocouples Next 30 After defining temperature as a relative term defining the flow of heat, some temperature measurement systems were discussed. When measuring temperature, you must realize that this is a difficult measurement and you must look for all of the sources of error that arise. Any temperature measurement depends on a sensor that has a thermal time constant. This time constant is dependant on the mass and composition of the sensor and of the surrounding material. For instance, a thermistor in hot oil will have a faster time constant than the same thermistor in hot air at the same temperature because the oil conducts heat better than air. RTD’s are linear, accurate and used heavily in industry. Because many are made of precious metals, such as platinum, they are expensive. They also require precise measurement because of their generally small temperature coefficient of resistance. Thermistors are inexpensive and highly nonlinear, but have a wide resistance variation with temperatures and do not require the 3 and 4 wire circuits needed in RTD measurements. Integrated circuit sensors are accurate and linear, but there are a limited number available and they function over a limited temperature range. Thermocouples are inexpensive and widely used, but require special measurement techniques. Transition: The next topic will be mechanical sensors.


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