Trial version. Temperature Sensing. How does the temperature sensor work and how can it be used to control the temperature of a refrigerator?

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1 Temperature Sensing How does the temperature sensor work and how can it be used to control the temperature of a refrigerator? Temperature Sensing page: 1 of 13 Contents Initial Problem Statement 2 Narrative 3-11 Notes 12 Appendix 13

2 Temperature Sensing Initial Problem Statement A household refrigerator is a device to keep food products within a fixed temperature range. The temperature should be low enough to preserve the food as long as possible, but not too low that the liquids in the refrigerator freeze. To do this the refrigerator uses a temperature sensor to indicate when to turn on or off the cooling system. How does the temperature sensor work and how can it be used to control the temperature of a refrigerator? Temperature Sensing page: 2 of 13

3 Narrative Introduction Temperature, T Look at the following graph of a temperature measurement made inside a refrigerator. Describe what is happening. What temperature range would be important for a refrigerator? How could you control the device to achieve an appropriate temperature? How could you design the refrigerator to be as efficient as possible? Figure 1. Time, t To prevent the cooling system turning on and off repeatedly, the control logic will usually turn off the cooling when the lowest allowable temperature has been reached and will not turn it back on until the highest allowable temperature has been reached. This means the temperature is controlled within a range rather than at a single value. This method of using different control points is called introducing hysteresis into the system and is very common in many control applications. One possible temperature sensor is the thermistor. This is a device that has a resistance to the flow of electrical current that is temperature dependent. There are two kinds of thermistor, the positive temperature coefficient (PTC) thermistor and the negative temperature coefficient (NTC) thermistor. The response coefficient of a device tells you whether an increase in the input leads to an increase or decrease in the output. Temperature Sensing page: 3 of 13

4 Activity 1 Look at the following two graphs. Which do you think has a positive temperature coefficient and which has a negative temperature coefficient? What do you think positive temperature coefficient and negative temperature coefficient means? Resistance graph (a) Temperature Figure 2. Resistance graph (b) Temperature The most appropriate type of thermistor used for temperature sensing is the NTC thermistor. In all the following text the term thermistor will specifically mean NTC thermistor. Temperature Sensing page: 4 of 13

5 2. The characteristics of a thermistor Thermistors are usually constructed using a semiconductor material. A typical thermistor is shown below. Multimedia Figure 3. The movie Temperature Sensing Video is available to demonstrate the behaviour of a thermistor. The resistance of a thermistor varies with temperature as You may sometimes see this T T R = Re written as where R = R exp T T R is the resistance of the thermistor at the temperature being measured R is the resistance of the thermistor at a calibration temperature T B is a characterising parameter published by the manufacturer See "Calibration" T is the temperature being measured on page 6. T is the calibration temperature used when measuring R T T Note, be very careful when using the expression R = Re as the temperature in this expression is in Kelvin (K), not Celsius. See "The Kelvin temperature scale" on page 7. Temperature Sensing page: 5 of 13

6 Calibration The behaviour of a device such as a thermister depends upon the materials and construction details used in its manufacture. For a given design to be useful it must give repeatable results which are valid over a range of temperatures. The behaviour is characterised by calibrating the design. For the thermistor two characterising values are used at a given calibration temperature. The first characterising value is the resistance, R, at a specified calibration temperature, T. Usually the design is such that R and T are standard. A typical value of R would coincide with a standard resistor value; for example 15 kω, while a typical value of T would coincide with an expected temperature; for example 25 C. The second characterising value is the parameter B. This is determined by how the resistance changes from the resistance at the calibration temperature as the temperature changes from the calibration temperature. Look at the expression that shows how the resistance of a thermistor varies with temperature, R = Re T T What would the resistance, R, be if the measuring temperature, T, is the freezing point of water? (Use R = 15 (Ω), T = 25 ( C) and B = 35.) Is there a problem with the device or the equation? Temperature Sensing page: 6 of 13

7 Activity 2 After production a thermistor is found to have a characteristic resistance, R, of 15 Ω at the characterising temperature, T, of 25 C. A second calibrating measurement is made. It is found that at a temperature, T, of 21 C the resistance, R, is Ω. Calculate the characterising parameter, B. What are the units of B? The Kelvin temperature scale The Kelvin temperature measures the so-called absolute temperature. The temperature of absolute zero is defined as the point at which the motion of atoms due to thermal energy ceases. Its value is determined to be C (although in this resource a value of -273 is used). The average temperature of outer space is 2.73 K. To convert from C to Kelvin, you just add 273 so that C is 273 K and 1 C is 373 K Activity 3 Using the value of B just calculated fill in the following table and plot the results to show how resistance varies with temperature in C over the given range. Use B rounded to the nearest integer, as this is the value that would published by the manufacturer. Convert R in to kilohm to 1 d.p. Verify that the graph fits the definition of an NTC thermistor, i.e. has a negative gradient. T ( C) T (K) R (Ω) Convert R to kω for plotting You could try to share the work out in a group to complete this table, or use a spreadsheet. Temperature Sensing page: 7 of 13

8 Resistance, R (kω) Temperature, T ( C) Activity 4 Figure 4. The thermistor is used in a device to measure the temperature of a room. A resistance of 27 kω is recorded. Use your graph to determine the temperature to the nearest ½ C. Substitute your answer back into the equation R = Re T T and find the corresponding value of R to check for consistency. Temperature Sensing page: 8 of 13

9 3. Using a thermistor in a device When using a thermistor in a practical device it is obviously not convenient for it to report the resistance as you either have to refer that to a conversion table or a graph. Instead the resistance is converted to a temperature which can be displayed directly or used to trigger a control mechanism. Activity 5 Figure 4. Look at the expression relating measured resistance to the temperature: R = Re T T Rearrange this expression to make T the subject of the equation so that a measured resistance will translate directly to a temperature. Temperature Sensing page: 9 of 13

10 Activity 6 You are testing a thermistor to be used in a device to measure the temperature for control purposes. A resistance of kω is recorded. T T B = 374 Figure 5. Use the expression R = Re to determine what the temperature should be. Recall that for the device you have determined that R = 15 ( in kω) T = 298 ( in K) Multimedia A calibrating thermometer determines that the actual temperature is 25 C. If the temperature given by your expression does not agree with the calibration temperature what are the possible explanations? The movie resource Temperature Sensing Video is available to demonstrate the reading of the resistance for this experiment. Temperature Sensing page: 1 of 13

11 4. Calculating the accuracy of the device Most devices are manufactured to within specified tolerances. For calibration instruments these tolerances are usually small so that accurate readings are given. For more general devices however, more relaxed tolerances can be used as long as the impact of these on a design are assessed as being appropriate. Activity 7 The tolerance on the thermistor being used is stated as being ±5%. This is allowed variation of the calibration resistance, R, at the calibration temperature, T. Assuming B is fixed, what is the range of temperatures that could be displayed when the R = kω? What is the accuracy of the thermistor you are using? Activity 8 Assume the calibration thermometer reading of 25. C is correct. Show this value and the expected range of variation due to the tolerance on a number line. Is the calculated reading of 24.5 C consistent with the accuracy of the thermistor? Would this device be suitable for your refrigerator control mechanism? How could you compensate for any bias in the readings due to the manufacturing tolerance? Temperature Sensing page: 11 of 13

12 Notes Semiconductor resistance Semiconductors are materials in which electrons are not usually free to conduct electricity. As the temperature increases it give some electrons enough energy to become available to conduct so a small current flows. Increasing the temperature further makes more electrons available and a larger current flows. If there is a fixed potential across the semiconductor then Ohm s law states that the potential difference, V, the current, I, and the resistance, R, are related as V = IR As the amount of current that can flow increases with increasing temperature, it can be seen that the resistance must fall with increasing temperature. Temperature Sensing page: 12 of 13

13 Appendix mathematical coverage PL objectives Use algebra to solve engineering problems Be able to evaluate expressions. Understand and be able to work with percentages. Change the subject of a formula. Know how to check answers by substitution. Be able to plot data. Be able to draw graphs by constucting a table of values. Be able to construct and use conversion graphs. Be able to extract information from a graph. Solve problems using laws of logarithms. Solve problems involving exponential growth and decay. Temperature Sensing page: 13 of 13