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PHYSICS COURSE NAME LAB 11 THERMOCOUPLES Lab format: This lab is performed with a lab kit. Relationship to theory: This lab corresponds to the study of the thermocouple effect, linear regression / least squares fitting and Newton’s Law of Cooling. OBJECTIVES To construct thermocouple junctions To perform temperature measurements using thermocouples To apply least squares fitting to data obtained To observe Newton’s Law of Cooling EQUIPMENT/SUPPLY LIST Copper/constantan wire (approx. 6 m) – to be supplied in lab kit Cable ties – to be supplied in lab kit (or use alternatives such as rubber bands or electrical tape) Solder – to be supplied in lab kit Soldering iron Wire cutter/stripper Multimeter Ice water Boilng water INTRODUCTION Thermocouples: When two dissimilar metals are connected together so that a wire made of one metal is attached at each end to a wire made of the other metal (see Fig. 3), there is a resulting voltage difference across the ends that depends linearly on the temperature difference between the two junctions (and types of metals used). This is called a thermocouple. The thermocouple can be used to measure temperature differences and if the temperature at one junction is well determined, the thermocouple can be used to measure the temperature at the second junction. Newton’s Law of Cooling: Newton’s Law of Cooling is a differential equation whose solution describes the temperature of an object as a function of time. It is also expressed as the rate of conductive heat transfer in thermal physics (see, for example, Urone et al., ch.14). This law states that if the difference T = Tobj - Tsur Creative Commons Attribution 3.0 Unported License 1 PHYSICS COURSE NAME LAB 11 between the temperature of an object Tobj and the temperature of its surroundings Tsur is not too great, the time rate of change of T is proportional to T itself. In equation form, this is statement looks like 𝑑 (∆𝑇) 𝑑𝑡 = −𝐴 ∆𝑇 where A is a constant. [1] The solution to this differential equation has the form ∆𝑇(𝑡) = ∆𝑇𝑜 𝑒 −𝐴𝑡 where To is the value of T at t = 0. [2] Thus T decreases exponentially toward zero, or we can say that Tobj approaches Tsur asymptotically. Physically, we can expect rapid cooling initially, but as the object cools down, the rate of cooling becomes very slow. From a measurement point of view, because the thermocouple is a device that measures temperature differences (i.e. T rather than Tobj ), it is well suited for observing Newton’s Law of Cooling. Further, we could determine the coefficient A in Equation [2] using linear regression – however, Equation [2] is not linear. Equation [2] can be linearised by taking the logarithm of both sides, such that it becomes 𝑙𝑛 ∆𝑇(𝑡) = −𝐴𝑡 + 𝑙𝑛∆𝑇𝑜 [2A] From a data analysis point of view, Equation [2A] is an equation of a straight line with slope –A. We can graph the data points and use least squares fitting [Bevington and Robinson 2003] on ln T vs. t to determine A. WARNINGS Be careful of boiling hot water: burn hazard PROCEDURE Part I: Constructing a simple thermocouple Using an appropriate tool, cut one piece of constantan wire, approximately 40 cm long. Using an appropriate tool, cut two pieces of copper wire, each approximately 40 cm long. Using an appropriate tool, strip the insulation from the both ends of all three pieces of wire. Ideally, about 1.5 cm of metal should be exposed at each end. (See Figure 1) Creative Commons Attribution 3.0 Unported License 2 PHYSICS COURSE NAME LAB 11 Figure 1 – Stripped wires Figure 2 – Soldered wire connection Connect one of the copper wires to the constantan wire by twisting the ends together. (See Figure 2. This will be referred to as a junction.) Ensure a lasting good connection by soldering this connection (see Appendix 6 about soldering.) Make another junction at the other end of the constantan wire by twisting and soldering the second copper wire to it. You have now constructed a thermocouple. (See Figure 3) Figure 3 – Thermocouple constructed Connect the two loose copper wire ends to the voltage inputs of the multimeter. Set the multimeter to read DC voltages at its most sensitive setting. The meter should read very nearly zero volts. You are now ready to test the thermocouple. (See Figure 4) Creative Commons Attribution 3.0 Unported License 3 PHYSICS COURSE NAME LAB 11 Figure 4 – Thermocouple ready for testing You can go straight to the most extreme reading your thermocouple will give by immersing one junction in boiling hot water (~100 oC) and the other junction in ice water (~0 oC) such that there is ~100 oC difference between the two junctions. Record the thermocouple voltage. This would normally be a very small voltage, typically a few millivolts, and the typical multimeter would only register one non-zero digit (i.e. one significant figure). Question: is this reading enough to tell that your thermocouple is working? (Try taking the junctions in and out of the water.) Question: is your equipment giving you precise enough readings to allow you to study the changes in the thermocouple output as the hot water cools to room temperature? Part II: Constructing a thermocouple probe We can extract greater output from a thermocouple probe by using, not one, but several pairs of junctions connected in series. We will refer to this as a probe, to distinguish it from a single junction. Construct a probe by joining ten pairs of junctions in series (Figure 5) and bundling the ten probe junctions together and the ten reference junctions together (Figure 6). The bundles shown in Figure 6 are secured using cable ties. They can also be secured using alternatives such as electrical tape or rubber bands. At each bundle, we need to ensure that the junctions do not touch and make electrical contact with each other, which would defeat the purpose of connecting them in series. Test the probe in the same manner as we tested the single pair thermocouple using ice water and boiling water. The output should be roughly ten times the value obtained for a single pair. (If the output is smaller, it is likely some of the junctions are touching each other. If the output is zero, one or more junctions are disconnected.) Creative Commons Attribution 3.0 Unported License 4 PHYSICS COURSE NAME LAB 11 Figure 5 – Ten junctions in series Figure 6 – Bundled junctions Part III: Cooling curve of a cup of hot water We can use the new probe to observe the cooling of a hot cup of water. [Note – these are not really temperature measurements as we are not taking steps to calibrate the thermocouple. How might we perform such a calibration? Discuss.] Desired is the widest range of temperatures practically achievable. To this end, we start by pouring hot water into a cup straight from a boiling kettle. An ice-bath will be used again for reference (Figure 7). Figure 7 – Thermocouple probe in use. The ceramic mug contains hot water and the glass bowl contains ice water. Our observations will consist mainly of a data table with time and thermocouple voltage. Rather than measuring the voltage at regular time increments, we will measure the time every time the voltmeter shows a new, lower value. [Why is this a preferred approach? Discuss.] Creative Commons Attribution 3.0 Unported License 5 PHYSICS COURSE NAME LAB 11 Start a run and continue until the water in the cup approaches room temperature enough that temperatures changes becomes so slow that the thermocouple output remains unchanged for several minutes at a time. Repeat at least two more runs to ensure consistency. ANALYSIS AND/OR QUESTIONS For each run, plot a graph of the probe voltage V vs. time t. Recalling that the voltage is a linear function of temperature, we expect from Equation [2] that this graph will show a curve representing logarithmic decay. For a quantitative analysis, now plot graphs of ln V vs. t for each run. Equation [2A] predicts a straight line with slope –A. Using linear least squares fitting, determine the cooling constant A. Discussion: Were the cooling constants the same or similar for your runs? What could we do to observe very different cooling rates purposefully? In other words, what simple changes could be made to our experiment that changes the cooling rates? Support your hypotheses with theory, and perhaps new data. REFERENCES Urone, P., Hinrichs, R., Dirks, K., and Sharma, M., 2014. College Physics. OpenStax-CNX, March 7, 2014. http://cnx.org/content/col11406/1.8/. Bevington, P.R., and Robinson, D.K., (2003), Data Reduction and Error Analysis for the Physical Sciences, 3rd Ed., McGraw-Hill, New York. Original introduction by Jill Lang, KPU. Activity developed for remote delivery by T. Sato under the Remote Science Labs for Second Year Physics Project (2012 – 2013) funded by BCcampus. Creative Commons Attribution 3.0 Unported License 6