Chapter 6 Temperature Measurement (Revision 2.0, 1/12/2009)

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1 Chapter 6 emperature Measurement (Revision 2.0, /2/2009). Introduction his Chapter looks that various methods of temperature measurement. Historically, there are two temperature measurement scales: he Celsius (of which the absolute range is the Kelvin scale) and the Fahrenheit (of which the absolute range is the Rankine scale). here are three principal methods of measuring temperature: temperature measurement by mechanical effects, temperature measurement by electrical effects; and temperature measurement by radiation effects. 2. Mechanical Effects Measuring temperature by mechanical effects is based on the fact that materials expand as their temperature increases. here are number of applications of this method. 2. Liquid-in-glass thermometer he liquid-in-glass thermometer is one of the most widely used devices in measuring temperature used in every-day use. It is based on the principle of the expansion of a liquid (such as mercury or alcohol) in a capillary glass tube. he rise of the fluid in the glass tube can be read off against a scale that indicated the temperature. An example of such a device is shown in Figure. he liquid is stored in a reservoir to provide enough fluid to fill the capillary tube. A safety bulb is provided at the top of the capillary tube to protect against the breakage of the glass in case of excessive expansion of the fluid. Safety bulb Proper depth of immersion Capillary tube emperature sensing bulb Fluid to be measured Figure : Diagram showing an example of a liquid-in-glass thermometer. It is worth mentioning the temperature indication on such a device is affected not only by the expansion of the fluid but also by the expansion of the glass Copyright held by the author 2009: Dr. Lutfi R. Al-Sharif Page of 22

2 (in effect the rise in the fluid level depends on the difference between the expansion of the fluid and the expansion of the glass). In order to overcome this problem, manufacturers will alter the scale in order to take this effect into consideration based on a certain immersion level of the device. A mark will then be shown on the capillary tube showing the correct point of immersion that makes the scale correct (as shown in Figure ). he most widely used fluids are mercury and alcohol. Mercury has the disadvantage that is freezes at C so it cannot measure temperature below this value. Alcohol has a high coefficient of expansion (which is desirable to increase the sensitivity of the device) but is limited to measuring lower temperatures. he Mercury-in-glass device can used to measure temperature up to 35 C. If the space is filled with Nitrogen, then this can be increased to 538 C. 2.2 Bimetallic Strip Another mechanically based method exploits the fact that different metals have different thermal coefficients of expansion. If two strips of different metals are bonded together, then as the temperature rises from that at which they were bonded, one strip will elongate more than the other strip and the whole unit will bend with a certain radius of curvature. If one end of the device is fixed then the other end will move as the temperature changes. he following formula can be used to calculate the radius of curvature of the bonded strip as follows: Where: t 3 r = 6 2 ( + m) + ( + m n) ( α α ) ( ) ( + m) m 2 + m n t is the combined thickness (in m) m is the ratio of thickness of the two strips (dimensionless) n ratio of the moduli of elasticity of the two strips (dimensionless) α is the lower coefficient of expansion (in units of K - ) α 2 is the higher coefficient of expansion (in units of K - ) is the temperature at which the radius of curvature is required ( C) 0 is the initial bonding temperature ( C) Some examples of materials used in bimetallic strips are shown below: hermal coefficient of Modulus of elasticity Material expansion (K - ) (GPa) Invar.7x Yellow Brass 2.02x Stainless steel.6x he bimetallic strip is used widely in room thermostat devices and in electric water heaters (for controlling the temperature). Copyright held by the author 2009: Dr. Lutfi R. Al-Sharif Page 2 of 22

3 2.3 Fluid expansion hermometers hese devices work on the principle that a fluid will expand when heated. But if the volume on the container is fixed this will lead to an increase in pressure. If this pressure is measured, it could be used as an indication of the increase in temperature. A block diagram of such a system is shown in Figure 2 below. It shows a container with a fluid in it connected to a Bourdon pressure gauge using a capillary tube. he tube can be up to 60 m long. tube emperature Vapour Bourdon Pressure Gauge Liquid Figure 2: Diagram showing a fluid expansion thermometer. his device in effect converts the temperature into an expansion, the expansion into pressure and the pressure into a displacement (in the pressure gauge). he device has a low cost, is stable in operation and is widely used in industrial applications. It can provide an accuracy of around ± C. he dynamic response of the device depends on the volume of the bulb and the characteristics of the tube connecting it to the pressure gauge. 3. emperature Measurement by Electrical Effects here are six methods that can be used to measure temperature by electrical effects. hese are discussed in more detail in this section. 3. Resistance emperature Detector (RD) Whenever a metallic material is heated its resistivity will change. Most metals have a positive temperature coefficient (PC). his is due to the fact that metals in general have sufficient electrical carriers. So an increase in temperature will lead to an increase in the collisions between the carriers, thus increasing the resistivity of the material. A resistance temperature detector (RD) is a device that is used to detect the temperature change as a change in its resistance. he coefficient of temperature changes is calculated as follows: α = R R 2 R ( ) 2 Copyright held by the author 2009: Dr. Lutfi R. Al-Sharif Page 3 of 22

4 he unit of are K - (or more clearly can be thought of as Ω Ω - K - ). In effect it represents a percentage change in resistance (or resistivity) for every one degree change in temperature. For example Nickel has a value of equal to K - which means that its resistivity (or resistance) will increase by 0.67% for every one degree kelvin increase in temperature. A linear relationship is assumed between resistance and temperature and this is shown graphically in Figure 3. his linearity is only valid provided that it is applied over a narrow temperature range. R 2 Resistance R 2 emperature Figure 3: Approximate relationship between resistance and temperature for the RD. he coefficient is shown below for various materials. able : hermal coefficient of resistance for various materials. Material α (Ω Ω - K - ) Nickel ungsten Platinum Manganin ± Carbon Semiconductors to +0.4 For wider temperature variations the linearity is no longer valid, and a nonlinear model has to be used. 2 ( + a + b ) R = R0 Where a and b are constants that depend on the material. It is important to protect the wire element from moisture coming into contact with it and from mechanical stresses, as both of these disturbances would change the value of the resistance. Copyright held by the author 2009: Dr. Lutfi R. Al-Sharif Page 4 of 22

5 In practice an RD is built by winding a wire around a glass or ceramic bobbin (former) and then sealing it with molten glass. he molten glass protects the wire element from moisture, but it introduces stresses into the material caused by temperature variations (i.e., strain gauge effect). A RD is usually installed within a dc bridge. As opposed to the use of four strain gauges in the case of force or strain measurements, only one element is used within a bridge for temperature measurements. As this element might be installed far away from the bridge, an error develops caused by the lead wires connecting the temperature sensor to the bridge. his requires socalled lead-wire compensation. A number of methods are available including the three wire Siemens method, the Callender 4 wire method, and the floating wire method. Practical problems in the use of RD s are:. he error caused by the leads. 2. Its bulky size that slows down its speed of response and thus increases its time constant. 3. Its fragile construction (as it contains glass). 4. he risk of self heating (I 2 R effects) when placed in the bridge. 3.2 hermistor hermistors, as opposed to RDs, have a negative temperature coefficient of resistance, but are much more sensitive that RD s. heir resistance can be modelled in accordance with the following exponential equation: R = R 0 e β 0 he value of β ranges from 3500 to 4600 K (note that its unit must be K in order to balance the equation above dimensionally). It is worth noting that the equation above can also be expressed in terms of resistivity (rather than resistance) as follows: ρ l R = = R A ρ = ρ e 0 0 e β 0 β 0 ρ0 l = e A β 0 It is worth noting that the slope of this curve is negative (i.e., it has a negative temperature coefficient, NC). he sensitivity at a certain point can be found by differentiating the function above at that point. Copyright held by the author 2009: Dr. Lutfi R. Al-Sharif Page 5 of 22

6 Copyright held by the author 2009: Dr. Lutfi R. Al-Sharif Page 6 of 22 = = e dt d e β ρ ρ ρ ρ β β Example Calculate the sensitivity of a thermistor at =00 C=373 K, if 00 ρ =0 Ω cm=. Ω m and, β=420 K at =00 C Solution Substituting the values in the equation above, gives: K m e. e S C 00 0 Ω = = β = ρ β = he sign of the answer is obviously negative confirming the negative slope of the function and the NC property. A thermistor is usually used as one arm of a dc bridge to detect temperature. he two outputs of the bridge are connected to the inputs of an instrumentation amplifier. A thermistor usually consists of a semiconductor material, and hence cannot withstand high temperatures. It cannot be used for measuring temperatures above 300 C. hermistors for example are used for measuring the temperature inside motor windings, for temperatures up to around 80 C (F class insulation). 3.3 hermoelectric Effects (thermocouple) he third electric method of temperature measurement makes use of the socalled temperature effect. When two different metals are placed against each other, an emf is produced that is a function of the temperature of the junction (Figure 4). he junction is called a thermocouple.

7 θ Material Material 2 + emf - Figure 4: A thermocouple is a junction of two different materials. here are three effects that interact within the thermocouple []:. Seebeck effect: his is the most important effect. It is the fact that a voltage (emf) is produced as a function of the junction temperature. 2. Peltier effect: If a current is drawn from the junction, the original voltage (emf) is altered. 3. homson effect: If a temperature gradient exists along either or both materials, then an addition alteration of the emf takes place. Various types of thermocouples are shown below showing the letter designation and the materials there are made of (starting with the positive material) [2]: able 2: Various thermocouples with their materials. ype E J K N S Material (positive listed first) Chromel-Constantan Iron-Constantan Chromel-Alumel Nicrosil-Nisil Platinum/0% Rhodium-Platinum Copper-Constantan When attempting to measure the voltage from a thermocouple, a practical problem is encountered. When the thermocouple terminals are connected to the voltmeter, for example, they have to be connected via a wire that is a different material that the materials making the thermocouple (most likely the connecting wire is copper). But this in effect creates two new junctions: One between the first material of the thermocouple and the first copper wire; the second between the second material and the other copper wire. his will create an error in the reading of the voltmeter due to the two new thermocouples introduced into the circuit. his can be further complicated by the other two new junctions formed from the copper wires connecting to the voltmeter itself which might have different materials internally. Copyright held by the author 2009: Dr. Lutfi R. Al-Sharif Page 7 of 22

8 θ J Material J2 J3 Material 2 Copper Copper J4 J5 Material 3 Material V/M Figure 5: he five junctions that form when trying to measure the voltage output of a thermocouple by the use of a voltmeter. he full setup is shown in Figure 5. Five junctions are shown. J is intentional, but junctions 2 to 5 are unintentional. Provided J4 and J5 are at the same temperature, their effect will cancel out as they have opposing polarities. his leave J2 and J3 to deal with, as their effect will be to alter the voltage ready by the voltmeter. So the circuit will simplify to that shown in Figure 6 below. θ J Material J2 J3 Material 2 Copper Copper + - V/M Figure 6: the two junctions J4 and J5 can now be removed as they cancel out. In order to further simplify the model above we can use the following two thermocouple laws:. he law of intermediate metals: If a metal is placed between the two materials of the thermocouples, the net voltage is the same if the intermediate metal is removed. his is shown graphically in below. Copyright held by the author 2009: Dr. Lutfi R. Al-Sharif Page 8 of 22

9 θ Material θ Material θ J Material 3 = J3 J2 Material 2 Material 2 Figure 7: the two junctions J4 and J5 can now be removed as they cancel out. By using this law, we can further simplify the circuit as shown below: θ J Material Material 2 J2 Material V/M Figure 8: Using the law of intermediate metals, we can remove the copper from the circuit model. In this setup we call J the hot junction and J2 the reference junction. Obviously the temperature of this junction will affect the final reading of the voltmeter. We next use the law of intermediate temperatures. 2. he law of intermediate temperatures: he voltage produced by the hot junction is equal to the sum of the voltage shown by the voltmeter and the voltage produced by the reference junction. his consequence of this law is that if we can measure the voltage at the voltmeter, add to it the voltage produced by the reference junction (knowing the temperature of the reference junction), then we can use the resultant voltage to infer the temperature of the hot junction. his can be done by the use of tables. For each thermocouple the relationship between the junction temperature and the voltage from it are tabulated, with reference to a Copyright held by the author 2009: Dr. Lutfi R. Al-Sharif Page 9 of 22

10 reference junction of 0 C. he table, by definition shows 0 V for a junction temperature junction of 0 C. Example 2 Assume you are using a K-type thermocouple. he voltmeter is measuring a voltage of 2.5 mv. If you know that the reference junction (i.e., the two connections between the two thermocouple wires and the two Copper terminals) are at room temperature, which is known to be 25 C. What is the temperature of the hot junction, if:. You ignored the error caused by the reference junction? 2. You took the reference junction into consideration? Use the attached K type thermocouple table that provides the value of emf for each temperature in Celsius. Solution If we ignore the reference junction, then we can use the table to find the temperature for a K-type thermocouple when it produces a voltage of 2.5 mv. his gives a temperature of 62 C. However, if we take the reference junction into consideration, then we must first add to the voltage measured the corresponding voltage for the 25 C temperature to the reference junction, which from the table is (using interpolation).000 mv. hus the total voltage for the hot junction is = mv. Using this value in the table again (and also using interpolation) gives a hot junction temperature of 86 C. Note that the answer is no 87 C as would be incorrectly inferred by adding the two temperatures corresponding to the reference junction and the temperature found from the table for the read voltage. his is due the non-linearity in the relationship. Also note that the error from ignoring the reference junction is very large (around 24 C!). One way to overcome the problem of having to know the temperature f the reference junction is use a reference junction that is kept at 0 C. One way of doing this is to immerse the reference junction (in practice two junctions, one for each of the thermocouple terminals) in an ice-water mixture. Such a mixture will remain at 0 C provided:. he ice has not all melted. 2. he pressure is exactly one atmospheric pressure. 3. he water is distilled and saturated with air. Appendix B shows a simple experiment conducted to show how the water/ice mixture stays at a constant temperature until all the ice has melted. In this case the temperature at which it stays constant is not 0 C but 4 C due the imperfections in the conditions required above (e.g., water not distilled, pressure not at atmospheric pressure) in addition to errors in the measuring device (liquid-in-glass thermometer). Copyright held by the author 2009: Dr. Lutfi R. Al-Sharif Page 0 of 22

11 If such an accurate setup is available to keep the reference junction at 0 C, then the temperature that is read on the voltmeter can be directly use to infer the hot junction temperature, without the need for any correction. he following are the problems usually encountered with the use of thermocouples:. Junctions could be formed using high temperatures or faulty soldering. 2. hermocouples could be used outside their applicable temperature range. 3. Faulty reference junction may be employed. 4. Faults in the installation. 5. Wrong type of the thermocouple for the readout instrument (i.e., each readout instrument must be matched to the thermocouple type). hermocouples could also be connected in series to increase the output sensitivity or be used to detect the temperature difference between two objects. hey are then called thermopiles. If an even number of junctions is used, this removes the need for a reference junction. But care must be taken to ensure they are all kept insulated from each other. Parallel connection is also possible; although this presents the problem that they may not equally share the current. 3.4 emperature sensitive semiconductor devices Semiconductor devices can also be used for accurate temperature measurement. hey offer the advantage of a linear output that is already signal conditioned. A widely used example device is the LM35 that is shown in Appendix C. 3.5 Quartz Crystal hermometers he resonant frequency of a quartz crystal is sensitive to its temperature. Provided the correct angle is cut, a very linear relationship is obtained between the frequency and the temperature. his can be used to accurately measure the temperature. Since it relies on frequency measurement, the device is less sensitive to noise pickup in the connecting cables. he device has a sensitivity of around 00 Hz K -, and can measure temperature in the range of -40 to 230 C. 3.6 Liquid Crystal hermography Certain materials exhibit different colours depending on their temperature. hese can be used to indicate temperature changes. Certain esters of cholesterol exhibit this phenomenon. he advantage is that this change is reversible and repeatable, and it can be made to work from 0 C up to several hundred C. Copyright held by the author 2009: Dr. Lutfi R. Al-Sharif Page of 22

12 4. hermal time constant he thermal time constant of a thermocouple will be derived in this section. It is based on the assumption that heat will only be transferred by convection and that none is transferred by radiation. he rate of flow of heat into the thermocouple will lead to a change in its temperature. his can be expressed as follows (note that the left hand side represents the flow of heat into the thermocouple, where it depends on the area, the heat transfer coefficient and the difference in temperature the right hand side is the rise in the temperature of the thermocouple due to the received heat): h A ( ) = m c Where: h is the heat transfer coefficient (W m -2 K - ) A is the surface area of the thermocouple exposed to the surrounding fluid (m 2 ) is the temperature of the surrounding fluid (K) is the temperature of the thermocouple (K) m is the mass of the thermocouple (kg). c is the specific heat capacity of the thermocouple material (J kg - K - ) t is time (s) Rearranging: d dt m c d dt + h A = h A aking Laplace transforms, gives the transfer function: ( s ) Where the time constant is equal to m c s + h A = m c h A and the steady state gain is equal to. his shows that the time constant does not only depend on the characteristics of the thermocouple (h, A and c), but also on the medium (h: the heat transfer coefficient that depends on the fluid surrounding the thermocouple). Compensation can be applied to improve the response of the thermocouple by the use of the RC network shown below. Copyright held by the author 2009: Dr. Lutfi R. Al-Sharif Page 2 of 22

13 R C V i C R V o Figure 9: Dynamic Compensation Network. It can be shown that its response is: F( s ) + τ s = α + α τ s where : τ = R C C R α = R + R C If τ is made to be equal to the time constant of the thermocouple, then the effect of this dynamic compensator is to reduce the time constant by multiplying it by a number that is less than (i.e., α) and reducing the steady state gain by multiplying by α as well. So the dynamic response is speeded up at the expense of steady state gain. 5. Radiation Effects emperature can also be measured by the use of radiation effects. he main advantage of this method is that no contact is required between the measurement device and the object. his is very useful in hazardous environments. hermal radiation is electromagnetic radiation emitted by a body by virtue of its temperature. his should be distinguished from other forms of electromagnetic radiation such as radio waves and X-rays that are not propagated as a result of temperature. It is worth noting that electromagnetic radiation in general does not need a medium for transport. 5. Radiation Pyrometry (Emittance Determination) Any object when subjected to thermal radiation will either absorb some of the energy, reflect some of the energy and transmit some of the energy (transmission is only applicable to transparent objects that will allow the energy to continue to the other side). his can be summarised in the following equation: = α + ρ + τ Where these three parameters are all dimensionless α is the absorptivity ρ is the reflectivity Copyright held by the author 2009: Dr. Lutfi R. Al-Sharif Page 3 of 22

14 τ is the transmissivity (only applicable to transparent objects) For the special case of opaque objects, this reduces to: = α + ρ In other words, the received thermal energy must be either reflected or absorbed. A further special case of this is the case of a perfect black body, that does not reflect any energy (the perfect black body must have a black colour and a rough surface). In this case, the equation further reduces to: = α We shall define the emissive power (E) as the amount of thermal radiation energy emitted by a body per unit area at a certain temperature. he units of E are W m -2. As the black body has the highest emissivity (as it has zero reflectivity) we can compare the emissive power of any body by dividing it by the emissive power of a black body at the same temperature. his parameter is called the emissivity (denoted by ε) and is very important in temperature measurement by radiation effects. ε = It is worth noting that the emissive power of a black body varies with wavelength. Under thermal equilibrium, any thermal energy received by the body will raise its temperature. hus, under thermal equilibrium conditions for an opaque body: ε = E = E E b E E b = α = ρ ( ρ) Eb = ε Eb But the emissive power of a black body at a certain temperature is related to the absolute temperature of the body as follows: E b = σ 4 Where σ is the Stefan Boltzmann constant (5.669x0-8 W m -2 K -4 ) [his should be distinguished from the Boltzmann constant used in calculating the thermal noise from a resistor.37x0-23 J K - ] Combining the last two equations gives us the basis for measuring the temperature of any body by thermal radiation: Copyright held by the author 2009: Dr. Lutfi R. Al-Sharif Page 4 of 22

15 E = ε σ E = ε σ 4 4 So the temperature of a body can be measured by radiation by measuring the emissive power from it and knowing the emissivity. he emissivity is the item that need determining and could lead to an error. he emissivity of a body depends on the following:. Surface finish. 2. Colour. 3. Oxidisation. 4. Aging. 5. Other factors. his method is thus not suitable for measuring the temperature of very shiny and smooth objects (e.g., polished stainless steel). Most of the radiation meters will allow the user to enter the value of emissivity for the object he/she is measuring. he meter usually has a default value of 0.95 for emissivity. Adjustment for material with different emissivities Most radiation thermometers will have an assumed emissivity that is used within the device, usually If the emissivity of the body the temperature of which is being measured has a different emissivity the user can make an adjustment in the reading to account for such a different. he method of adjustment is discussed below. Let us assume the following: E is the emissive power per unit area of the body being measured in units of W m -2 ε def is the emissivity that is assumed within the device (default emissivity) ε act is the emissivity of the object being measured (actual emissivity) σ is the Stefan Boltzmann constant (5.669x0-8 W m -2 K -4 ) ind is the indicated temperature by the device in K act is the actual temperature of the body in K 4 ind E ind = ε def σ 4 = E ind ε def σ E E ε def = ε = ε def σ ε def σ ε act ε 4 act def E ε = ε act σ ε act def But: Copyright held by the author 2009: Dr. Lutfi R. Al-Sharif Page 5 of 22

16 E = ε act σ Substituting in the previous equation gives: 4 act 4 ind = 4 act ε ε act def Or ind act ε = ε act def 4 Rearranging gives the important result: = act ind ε ε def act 4 So by knowing the indicated temperature by the thermometer, the actual emissivity of the body and the default emissivity assumed in the device (usually given in the manual) the actual correct temperature of the body can be found. A list of the emissivities of some common materials can be used for the correction. 5.2 Optical Pyrometry his method is based on the principle that material when heated up to high temperatures will change colours in accordance with the temperature (staring with dark red, then orange and then white). By using a special optical device, a user can adjust the device until a reading can be taken of the colour emitted. his method is only suitable for high temperatures. 6. Comparison of methods Appendix A contains a table from [] that shows a comparison of the various methods with their typical parameters. It is worth noting the following:. he S-type thermocouple is the most resistant to oxidising environments, but has a high cost. 2. he RD is the most accurate device. 3. he thermistor has a good dynamic response. 4. he radiation methods are the only methods that are contact-less. References Copyright held by the author 2009: Dr. Lutfi R. Al-Sharif Page 6 of 22

17 [] Experimental Methods for Engineers, J.P. Holman, 7 th Edition, McGraw Hill International Edition. [2] Measurement & Instrumentation Principles, Alan S. Morris, Elsevier, 200. Copyright held by the author 2009: Dr. Lutfi R. Al-Sharif Page 7 of 22

18 Appendix A: Comparison of different types of temperature measurement devices (adapted from able 8.7 of J.P.Holman, Experimental Methods for Engineers []) Effect Principle Mechanical Device Electrical Applicable emperature Range ( C) Approximate accuracy ( C) ransient Response Cost Comments Liquid in glass Fluid expansion thermometer Bimetallic Strip RD (electrical resistance) Alcohol Mercury Glass filled Mercury Liquid or gas Vapourpressure Bimetallic Strip RD (electrical resistance) -70 to to to to to to to 000 ±0.5 Poor Low ±0.25 Poor Variable ±0.25 Poor Variable ± Poor Low ± Poor Low ±0.25 Poor Low ± Fair to good depending on size of element Readout equipment can be rather expensive for highprecision work Used as inexpensive low cost thermometers. Accuracy of ±0.05 C may be obtained with special calibrated thermometers Widely used for industrial temperature measurements Widely used in simple temperature-control devices Most accurate of all methods Copyright held by the author 2009: Dr. Lutfi R. Al-Sharif Page 8 of 22

19 Effect Principle Device Applicable emperature Range ( C) Approximate accuracy ( C) ransient Response Cost Comments hermistor hermoelectric hermistor -type J-ype K-ype S-ype -70 to to to to to 650 ±0.0 Very good ±0.25 Good, depends on wire size Low, but readout equipment may be rather expensive for highprecision work Low Low Low High Useful for temperature compensation circuits; thermistor beads may be obtained in very small sizes. Superior in reducing atmospheres Resistant to oxidation at high temperatures Low output; most resistant to oxidation at high temperatures; accuracy of ±0.5 may be obtained in carefully controlled conditions Copyright held by the author 2009: Dr. Lutfi R. Al-Sharif Page 9 of 22

20 Effect Principle Device Applicable emperature Range ( C) Approximate accuracy ( C) ransient Response Radiation Cost Comments Optical Pyrometry Radiation Pyrometry Optical Pyrometer Radiation Pyrometer 650 and above -5 and above ±0 Poor Medium ±0.5 at low ranges* Good, depending on type Medium to high Widely used for measurement of industrial furnace temperatures Increased applications resulting from new high precision devices being developed * ±2.5 to 0 at high temperatures; depends on blackbody conditions and type of pyrometer. Copyright held by the author 2009: Dr. Lutfi R. Al-Sharif Page 20 of 22

21 Appendix B: Experimental investigation into the temperature of an ice-water mixture against time compared to water. Figure 0: ime plot of temperature of ice-water mixture. Copyright held by the author 2009: Dr. Lutfi R. Al-Sharif Page 2 of 22

22 Appendix C: Part of a datasheet for a semiconductor type of temperature sensor, LM35. Copyright held by the author 2009: Dr. Lutfi R. Al-Sharif Page 22 of 22