Static and Dynamic Response of a Temperature Sensor
In this experiment you will calibrate and experimentally determine the time constant of a common type of temperature sensor. As shown in class, we would expect a temperature sensor to act as a first order system because a first order differential equation (based on the energy equation) governs its transient behavior. This experiment will allow you to assess whether the first order model properly describes the transient behavior of a thermistor. The thermistor sensor actually consists of two different thermistor elements. Thermistors have a non-linear resistance change with respect to temperature; however, this sensor is designed so that the two thermistor elements can be connected to a simple resistor network and provide an output voltage which varies in a linear way with temperature. The calibration constants (slope and intercept) which convert the voltage to temperature will be determined during this experiment. Procedure 1) Open LabView and access the “vi” file that you used in Experiment #1 for calibration. It will probably be easier to modify this file for use in this experiment, although you can start from scratch if you wish. The vi file must be able to read the thermistor output on channel 7 and output it to the screen. 2) Prepare an icewater bath in a beaker for use as a calibration reference. 3) The next step is to collect data to calibrate the thermistor, using a thermometer as the calibration standard. First, put both the thermistor and thermometer in the ice bath and wait about 30 seconds for thermal equilibrium to be achieved. Now run your LabView file and note the voltage reading which corresponds to zero degrees Celsius (i.e. write them down, you will need these later). The sampling rate and duration are not critical here, but you may want to scan a few values to get a sense of the average reading. Also note the thermometer reading – it is expected to read zero degrees, but if it does not the difference will give a sense as to how accurate our standard actually is. 4) Dump out the ice and fill the beaker with tap water. Repeat Step 3 while putting the thermistor and temperature in the room temperature water. 5) Now put the beaker on the hot plate and turn it on. You will record the voltage and temperature several times while the water is being heated to boiling. The purpose is to collect enough points to get a good linear plot between temperature and voltage over the 0 to 100 degree range. Stir the water slightly before recording each reading to achieve a more uniform water temperature in the beaker. 6) Minimize LabView and open EXCEL. Enter the calibration data into a worksheet and plot temperature versus voltage for the thermistor. Find the slope and intercept of the line and make a note of these values. Save the worksheet for future reference. 7) You will now have to modify your LabView file once again to accommodate the measurement of the time constant. (The file used for the second half of Experiment #1 can be used.) You will need to provide digital controls on the front panel for the slope and intercept derived in Step #6, and wire these appropriately so that the voltage value from channel 7 is converted to temperature. It is helpful to connect the temperature value to an indicator on the front panel, so these values can be monitored and checked for accuracy. You will use the thermometer to measure ambient temperature. This value can be entered into a digital control on the front panel. Then, modify the wiring diagram so that the difference in temperatures (thermistor – ambient) is calculated, followed by taking the absolute value and then the natural log. This ln(T) output should be sent to a Waveform Chart (within the For Loop structure). You should also send the ln(T) values and the time values to a Build Array icon, and then send the array to a spreadsheet file. The chart output of ln(T) on the LabView front panel is used to make a visual check of the proper data behavior – it should be linear with a negative slope when the temperature transient is being observed. You should check your calibration by entering the slope and intercept on the front panel and running the file with the thermistor in ambient air, and verifying that the temperature output reads appropriate values. 8) You will need to collect six good transient runs for the thermistor under two different conditions (giving a total of 12 runs). First, test the thermistor by heating it in water (60oC or higher) and then allowing it to cool in the ambient air. You will need to experiment with the sampling frequency and the duration (number of points) in order to get good data. Now, a word or two of explanation is given as to what “good data” means. First, as noted, it is necessary to get six “good” runs for each condition. The purpose of the multiple runs is to allow for statistical comparisons. The ln(T) plots that LabView will show should be fairly linear if the data is “good”. Generally, good data will be collected if: a) you remove the thermistor from the hot water approximately two seconds after clicking the “Run” arrow in LabView, and then hold it still, away from the heat source, for the duration of the run; b) the run duration is chosen to be long enough so that the sensor has time to cool by at least 30 degrees C; and c) the sampling frequency is chosen so that the run consists of 50 to 100 data points in the linear region. Make sure that you choose your file names so that you don’t overwrite your previous runs and you can easily identify them later. 9) The second condition is to test the thermistor by cooling it in ice water, and then exposing it to ambient air. Once again the goal is to get six good runs for statistical purposes. 10) After the data collection is complete, you are ready to analyze the EXCEL files containing the ln(T) and time values for each run. The following procedure should be used for each data file. Make an XY scatter plot of ln(T) versus time, showing only the data points (i.e. no lines connecting the points). This plot should look like the one that appeared on the screen during the data collection; i.e. it should be linear, at least over most of the range. Non-linear behavior may be seen at the beginning, during the thermistor removal, and possibly at the end, if the thermistor temperature reached values close to ambient temperature. You will have to decide what range of data best represents the cooling (or heating) process, and then perform a least squares regression calculation using the LINEST function. (It is advantageous to use LINEST because it gives us an uncertainty value for the slope.) From the slope and its uncertainty, calculate the time constant and its uncertainty for each set of data. For each data set, produce a plot which shows the data (ln(T) vs time) and the linear fit with its equation. 11) Your results and discussion should address the following points a) present the calibration results for the thermistor. Were the results linear as expected? b) then, as noted in Step #10, find the time constant and its uncertainty based on the least squares analysis for each data set (this will yield six separate values for time constant and uncertainty for the thermistor, for both cooling and heating conditions). Show representative plots for the heating and cooling conditions in the results section – the remainder of the plots can be put in the appendix. c) next, using the six time constant values for each condition, calculate the average time constant and the sample standard deviation of the six values. Note that the standard deviation of the mean, multiplied by the appropriate value of the t-factor, can be used to estimate the 95% uncertainty in the average time constant value. d) compare the uncertainties found in Step #10b with the uncertainty determined from Step #10c. These values represent two different approaches to evaluating the uncertainty in time constant. Are the values from Step #10b similar to each other? Are they smaller or larger than the value from Step #10c? Does the comparison match your expectations? e) Compare the time constants for the heating and cooling conditions. Would we expect them to be the same? Do they appear to be the same, within experimental error?