1 PART A : MAKING THE DIGITAL THERMOMETER 1. There are three parts to this exercise, which takes two 3-hour laboratory sessions.

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1 1 PART A : MAKING THE DIGITAL THERMOMETER 1 October 24, 2016 Digital Thermometry Experiment designed by Peter Crew, Navot Arad and Dr Alston J. Misquitta There are three parts to this exercise, which takes two 3-hour laboratory sessions. In part A you make and calibrate a direct-reading digital thermometer usable over the range C. In part B you automate the data acquisition using an Arduino. In part C you use this thermometer to investigate the rate at which various liquids cool. There are few instructions provided for part C instead you are given a copy of a published study of this topic, and asked to repeat the procedures and check the conclusions for yourself. You must write a short formal report on this exercise, using the published paper as a model. Details of this report will be provided in the lectures and on the module QM+ page. Because the calibration of the thermometer is very sensitive to any changes in its electrical circuit, you should do parts A, B and C on successive days, Monday/Tuesday or Thursday/Friday. Your circuit will be left undisturbed on the bench between the two sessions. Plan your experiment well as you will require at least 1h30m to record the data needed for part C. Making the thermometer requires you to use and understand some of the electrical circuits covered in experiment 1, which you must have completed before starting this 1 Part A : Making the digital thermometer 1.1 Introduction The temperature sensor is a semiconductor diode whose resistance varies with temperature. The diode is used as one arm of a Wheatstone bridge circuit, which will therefore only balance at one temperature. The off-balance voltage is measured with a digital multimeter (DMM) and adjusted with a potential divider to give a direct digital reading, in mv, of the temperature in degrees Celsius. There are three separate tasks: 1. measure the properties of the diode related to its temperature dependence; 2. set up and adjust the Wheatstone bridge circuit; 3. use a potential divider to adjust, calibrate and check the performance of your thermometer. You should allocate at most an hour to each of these tasks (including tabulating and plotting data), so as to complete part A in the first afternoon. 1.2 Diode characteristics Diodes are electrical devices which allow current to pass in only one direction, the forward direction. In the reverse direction they have a high resistance, and so can act as one-way switches. The symbol for a diode

2 1 PART A : MAKING THE DIGITAL THERMOMETER 2 Figure 1: Characteristics of a diode. The relationship between voltage and current is non-linear. We will use the diode in the forward-bias mode, past its knee region. Note the change of scale on the negative y-axis: the reverse-bias current is a few orders of magnitude smaller than the forward-bias current. There is an error in the figure: the reverse-bias current is measured in micro amperes (µa) and not milli amperes (ma). We use silicon-based diodes in this laboratory. Figure taken from diode/diode_3.html is with the arrowhead indicating the forward direction, so a voltage applied thus + causes current to flow; the diode is then said to be forward biased. To make a diode, a semiconducting material (silicon in this case) is doped with an impurity in order to give a deficit of electrons, hence excess positive charge, in one region, and another impurity to give an excess of electrons, hence excess negative charge, in an adjacent region. The boundary between the regions is the junction. So the diodes you use here are called silicon pn junction diodes. The diodes themselves are small, the size of a match head; the one you use has been encased in insulating mastic with only its two electrical leads left exposed. The diode does not obey Ohm s law since the current I is not proportional to the voltage V. The relation between I and V is called the characteristic and is shown schematically in fig. 1. In the forward-bias regime that is the low-resistance mode of the diode the characteristic has the theoretical form: I = I S (exp (ev/kt ) 1), (1.1) where, e is the electronic charge, k is Boltzmann s constant, T is temperature measured in degrees Kelvin, and I S is the reversed-biased current. This characteristic is displayed in fig. 1. It is strikingly non-linear, but also has an explicit dependence on the temperature. If the current is kept constant then a change in temperature will be accompanied by a compensating change in voltage. Thus as T changes the resistance of the diode, that is the ratio R = V/I, also changes. In this experiment we will work with the diode in its forward-bias regime, just passed the knee region. We will also limit the current flowing through the diode to be around 1mA. We can determine the characteristic of the diode using the circuit shown in fig. 2. All we need do is vary the current flowing through the diode using the 10kΩ potentiometer (adjustable resistance) and measure the voltage across the diode as a function of this current. However we will not perform this measurement in this experiment. This is mainly for lack of sufficient time. Instead, we have chosen the components used in the next section to allow us to operate the diode in its forward-bias regime with a current of around 1mA flowing through it. We know from eq. (1.1) that as the temperature changes, the current flowing through the diode will change. Before moving on to the next section you need to determine just how much the voltage across the diode will change in response to change in the temperature. One summer s day when

3 1 PART A : MAKING THE DIGITAL THERMOMETER 3 +5V 680 Ω A I 10 kω V V 0 V Figure 2: Circuit diagram to measure the characteristic of a diode. The voltage provided to the circuit is varied using the potentiometer. The current flowing through the diode, I, and the voltage across it, V, are measured and the forward-bias characteristic of the diode may be determined. However, as mentioned in the main text, you will not be determining the characteristic of the diode in this experiment! +5V 4.7 kω 200 Ω A V V 4.7 kω B 620 Ω 0V Figure 3: Wheatstone bridge circuit. The DMM is connected across nodes A and B. the temperature in the lab was 28 C the voltage across the diode was measured to be 607mV and current 1mA. Using this data, answer the following: What is the resistance of the diode at this current and voltage? Use the characteristic equation given to calculate what voltage change will compensate for a temperature change of 1 C. You should find that the voltage change is very small. It is this small voltage change that we seek to measure. We will need these pieces of information in determining the values of the resistors used in the circuits shown below. 1.3 The Wheatstone bridge circuit You may like to review the Wheatstone bridge circuit by referring to the lab script for Experiment 2 before continuing. While you are getting on to the steps below, consider the following questions: why do you think we are using a Wheatstone bridge to read out the voltage change across the diode? Why can we not read it out directly using a DMM? Surely the latter would be the simpler way, would it not? Or does the Wheatstone bridge

4 1 PART A : MAKING THE DIGITAL THERMOMETER 4 have properties that make it superior to a direct reading? If so, what might these be? Get into a discussion with the laboratory demonstrators or research this yourself. HINTS: What does the balance-point allow you to do? How large an effect are you trying to measure? (see result of the last section) Would noise in the circuit allow you to measure this? Where might the noise arise from? Consider how a small fluctuation in the supplied voltage would effect a direct reading across the diode. What effect would this fluctuation have on the balance point of the Wheatstone bridge? Step 1 Construct the bridge circuit of fig. 3. The leads on the small blue multi-turn variable resistor (helipot) are easily broken do not stretch them! We can easily place an upper bound on the current that will flow through the two arms of the bridge circuit by assuming that this circuit can be approximated by the two 4.7kΩ resistors. In other words by assuming that the other resistors and diode have zero resistance. The two 4.7kΩ resistors in parallel present a combined resistance of 2.35kΩ, allowing a current of no more than 5V/2350Ω. This corresponds to a current of about 2mA to flow through the two arms of the bridge. At balance this will be divided equally between the arms, giving the desired 1mA current through the diode. You should have calculated a diode resistance of several hundred ohms at this current; the 200Ω helipot is adjusted to this value to balance the bridge Step 2 We wish to balance the bridge at 0 C (so as to get a reading of zero at this temperature), so place the diode in a beaker of melting ice. There should be both ice and water in this mixture! Set the DMM to the 200mV range, connect it across the outputs AB of the bridge, and adjust the 200Ω helipot until the DMM reads zero. This is a tricky adjustment that is very sensitive to small movements of the helipot. At balance the DMM may still be fluctuating a few tenths of a mv on either side of zero Step 3 Take the diode out of the ice bath and see whether the DMM voltage increases or decreases as the diode warms up. If it decreases, reverse the meter connections to A and B so that the digital reading will be positive for temperatures above 0 C. 1.4 Calibration of the thermometer Your calculation of the voltage change accompanying a 1 C temperature rise should suggest that at 100 C the DMM will register well over 100mV. To get a direct reading of temperature we need to reduce this using a potential divider, preferably one with a high input resistance so that it does not overly disturb the currents flowing in the bridge circuit. A resistance of 10kΩ should be sufficient. Replace the DMM across the output AB by the 10kΩ helipot, and connect the DMM itself across the centre and an outside terminal of the helipot this is shown in fig. 4. Place the diode in boiling water and adjust this helipot until the DMM registers 100mV. Then check that the reading is still zero when the diode is in melting ice, making small adjustments to the 200Ω helipot if necessary. Repeat the sequence until readings of 0mV and 100mV are obtained at 0 C and 100 C, respectively. The hot water cools quickly so you may only reach a temperature of C. In this case you should adjust the helipot such that the DMM registers in mv the temperature of the water in degrees Centigrade. You now have a direct reading digital thermometer!

5 2 PART B : AUTOMATED DATA ACQUISITION 5 +5V 4.7 kω 4.7 kω A B 200 Ω 620 Ω 0V C 10 kω DMM V A Figure 4: Final circuit for digital thermometer. This is a modification of the circuit shown in fig. 3. Here, instead of the DMM across nodes A and B, we have introduced the 10kΩ potentiometer that, when calibrated, allows us to read-out the temperature using the DMM that is now connected across it. In automation step of this experiment this DMM will be replaced by an Arduino Uno via an amplifier stage. Note that the two nodes labeled A are equivalent. Finally, check and correct the calibration against the alcohol-in-glass thermometer. Adjust your digital thermometer when the two thermometers are placed side by side in melting ice and boiling water. Then record the readings when they are both placed in water at some intermediate temperatures, say about 70 C, 60 C, 50 C, 40 C, and 30 C. You do not need these exactly temperatures, just try to get close to these values. Try to estimate the glass thermometer reading to one-fifth of a degree, and comment in your report on the agreement between the two temperature scales. Make sure you have enough of data from the previous step so as to determine the accuracy of the digital thermometer. Remember that you have calibrated it against the glass thermometer, which itself will have a read-out uncertainty. 2 Part B : Automated data acquisition IMPORTANT: You should have made and calibrated your diode thermometer before coming to this section. Make sure you have done this and check to see that your thermometer is accurate before attempting to use it. [The Arduino program for this experiment is provided at the end of the assignment and is available online as for reference]. You should now have a working digital thermometer. In the next section (Part C) you will need to record cooling data for four different fluids. This takes time and is tedious, so here you will build an automatic data acquisition system for your thermometer. The idea is simple: rather than use a digital multimeter (DMM) to read out the voltage, and hence the temperature, we will use the Analogue to Digital converters (ADC) on the Arduino to read the potential difference across the 10kΩ potentiometer. In principle this is a simple step: all that needs to be done is to connect Arduino pins A0 and A1 (the A indicates that

6 2 PART B : AUTOMATED DATA ACQUISITION 6 these are analogue pins, that is, they are able to read an analogue signal like a voltage, and convert it to a digital signal) to the points where the DMM currently is (nodes A and C in fig. 4). The difference in the readings will then be proportional to the potential difference. This does not work well as the ADCs on the Arduino convert a voltage range of 0V to 5V to a value from 0 to 1023 (as the ADCs are 10bit converters and 10bits corresponds to a range of values from 0 to = 1023). However, the voltage we expect across the 10kΩ potentiometer is only in the range 0mV to 100mV. This range would utilize only values 0 to 20 (= /5) on the ADC. This small range of values would give us very large uncertainties, something we need to avoid. 2.1 Op-Amps One solution to this problem is to amplify the signal by a factor of 50 as that would convert the 0mV to 100mV range we expect across the 10kΩ potentiometer to 0V to 5V, which would fully utilise the range on the Arduino. We have constructed the amplifiers for you using two sets of operational amplifiers. There are two op-amps in each of the black chips in shown in fig. 5. We use operational amplifiers, or op-amps, as they can amplify signals with a minimal input current. The input resistance of an op-amp is typically a few MΩ, like the DMMs you have used in the Electrical experiment. Additionally, the amplification characteristic is usually fairly linear which is ideal for a good amplifier. You will not be building the amplifier as you will not have the time to do so. Instead, we will supply you with the pre-built amplifier shown in fig. 5. Figure 5: Image of the pre-built op-amp amplifier with input and output pins indicated. The variable potentiometer can be used to fine tune the amplification to be A = 50. The voltage difference across nodes A and C in fig. 4 is the bridge voltage that is is amplified and output is between the output at A0 and the common ground. For thisscanned to work by CamScanner all parts of the circuits should share a common ground. Connections: Connect the power (5V and ground) to the amplifier. Connect the two bridge inputs (nodes A and C in fig. ckt:digital-thermometer) to the points marked bridge. You will need to experiment with the order of these connections. It will work one way and not the other.

7 2 PART B : AUTOMATED DATA ACQUISITION 7 Before connecting the Arduino, check to see that the amplifier works. To do this, connect a second DMM at the outputs A0 and Ground (this is the common ground of the circuit) of the amplifier. Power it up. Check the voltage at the output. Is it nearly 50 times the input voltage? If yes, your circuit is functional. If not, check your connections. Adjust the potentiometer on the amplifier to make the gain almost exactly A = 50. Note the uncertainty on the gain. 2.2 Amplifier and Arduino Once you are sure that the amplifier works (That is, the second DMM between the A0 output of the amplifier and ground shows a voltage that is 50 times the voltage across the bridge.), you can proceed to connect the Arduino Uno to the circuit. Essentially, the Arduino will take the place of the second DMM you have connected across points A0 and the Ground. With a suitable program, it will record the voltage at specified time intervals. A schematic view of the Arduino Uno is shown in fig. 6. The Arduino gets its power from the computer via the USB cable, so no additional power is needed. But it needs to be grounded to the common ground for it to be able to read voltages. This is why you needed to pass the ground to the Arduino. Figure 6: Bread-board view of the Arduino. You will use only the Ground and pin A0. We will not use pin A1 in this experiment. Connections: Connect ouput A0 of the amplifier to pin A0 on the Arduino. Connect ground output of the amplifier to any of the Ground pins on the Arduino. Connect the Arduino Uno to the computer using the USB cable. You do not need to disconnect the second DMM. It can serve as a useful check on the readings of the Arduino. Once this is done, upload the program (listed below, but please use the version on the SCM Wiki page) to the Arduino. The program will cause the Arduino to record temperatures in Celsius every 30sec. It works continuously and so the reset button on the Arduino needs to be pressed to re-start it. Data will be displayed on the serial monitor. Ask a demonstrator for help if you are unsure of how to start the serial monitor. Before relying on the data recorded by the Arduino make sure it is recording the correct temperature (i.e.,

8 3 COFFEE COOLING : PART C 8 check the output against the reading on the alcohol thermometer). Once you are satisfied it is, proceed to part C of this experiment. The Arduino will display readings on the Serial Monitor (on the computer screen). You may cut-and-paste these readings into a file for your records Reflection What are the sources of error in this setup? What do you expect the uncertainty on the temperature readings to be? Is the uncertainty limited by the thermometer? Or the calibration step? Or the amplifier? Or the Arduino? What will be the random and systematic errors? Is the amplification of the amplifier really A = 50? How would you test this? If it is not 50, what effect would the error in the amplification have on your results? Consider these questions (and others you may have) while you proceed with Part C of this experiment. 3 Coffee cooling : Part C HINT: You should have built your calibrated thermometer and got the automated data acquisition with the Arduino working before coming to this section. Additionally, please read the paper the Rees and Viney before you start this part of the experiment. Rees and Viney found that black and white coffee cooled at different rates, and sought to explain this. We are not asking you to attempt an explanation, but to repeat some of Rees and Viney s measurements and comment on whether your results agree with theirs and if not, what differences you find. You should be able to make the measurements and draw the graphs in one laboratory period you may also have time to make some of the additional checks mentioned by Rees and Viney. We suggest that, after checking that your thermometer still records the ice and boiling points correctly, you measure the cooling curves of: 200 ml of plain water, brought to the boil and poured into the china mug. Black coffee made by adding 200 ml of water to a level teaspoon of granules in the mug. White coffee made by adding 20 ml of cold milk to a freshly-made mug of black coffee (200 ml again), stirring, and pouring out 20 ml to leave 200 ml. Do not re-boil the coffee. Black coffee made by adding 20 ml of cold water to a freshly-made mug of black coffee (200 ml again), stirring, and pouring out 20 ml to leave 200 ml. Do not re-boil the coffee. Can you say why the fourth procedure might be informative? Use the digital thermometer to record the ambient room temperature. 3.1 Writing your report The report must include: 1. A title. 2. Author s name and affiliation.

9 4 APPENDIX 9 3. An abstract, which is a brief summary of a few lines including results but not too detailed. 4. A short introduction what are you describing, and why did you do it? 5. A brief summary of the theory (you can refer to other publications for this, e.g. It is shown by Rees and Viney (1) that... ). It is unacceptable to copy verbatim from the paper. You should present your results in your own words. Do not include theoretical details that are not relevant to your experiment, especially if you do not fully understand them. When you refer to the paper by Rees and Viney you should cite it appropriately. 6. A brief description of your digital thermometer. 7. A brief description of how you used the Arduino to automate the data collection. 8. A brief description of what you did and measured. 9. A summary of the results, together with calculated quantities. Show raw data as graphs (much more informative than tables which you will not have the space to include), while derived quantities (such as time constants) can conveniently be tabulated. Use log rather than linear plots where appropriate. 10. A discussion of the significance of the results, including any uncertainties due to measurement precision (errors) and whether or not differences found are meaningful. 11. A short conclusion. 12. A list of references with name(s) of author(s), journal name and volume number or book title and publisher, page number(s), and date. 4 Appendix 4.1 Other Information Larger versions of the circuits used can be found on the SCM Wiki page where the Arduino program needed to take the readings may also be found. A listing of the program is also provided in sec The Dual Op-Amp pin diagram The pin diagram for the Dual Op-Amp (TSS922IN or equivalent) used in the amplifier is shown in fig. 7.

10 4 APPENDIX , TS922A Pin diagrams Pin diagrams Figure 1. Pin connections (top view) Figure 7: Pin diagram for the TS922IN dual op-amp. Figure 2. Pinout for Flip-Chip package (top view) OUT2 -IN2 +IN2 - + VVCC+ + VGND CC OUT1 -IN1 +IN1

11 4 APPENDIX The Arduino program This will read out the temperature to the serial monitor in degrees Celsius. Readings are printed out every 30sec. To smooth-out random fluctuations, readings are averaged for 1 sec. This program is listed here for reference only. Please use the version from the SCM Wiki page! /* OpAmp Thermometer written by : Navot Arad, Queen Mary University of London */ int InputPin = 0; // A0 is the amplified signal pin float temp = 0; // variable to store data from pin A0 float AmpVoltage = 0; // Use float to convert data from A0 to voltage float G = 50.0; // Amplification factor float scaleg = 0; float conversion = 0; // Conversion rate to degrees float average = 0; void setup () // Only runs once after board is reset { Serial. begin (9600) ; // Rate at which data is sent to serial monitor Serial. println (" Time Temperature "); // Sends everything inside " " as a string to the serial monitor } void loop () // Runs continuously on repeat { // average temperature over first second for ( int i = 0; i < 100; i ++) { temp = analogread ( InputPin ); // Read data from the input pin ( A0 ) on a 10 bit scale scaleg = G + (( temp ) * 1.5 * ) ; conversion = (1023 * scaleg ) /50; // conversion factor AmpVoltage = temp *(100.0/ conversion ); // Converts signal to temperature average = average + AmpVoltage ; delay (10) ; } } Serial. print ( millis () /1000) ; // Sends value stored on AmpVoltage // to serial monitor and starts new line Serial. print (" "); average = average /100; Serial. println ( average,1) ; average = 0; delay (29000) ; // 29 second delay before loop runs again