**Calibration of a Temperature Sensor**

**Introduction:**

Thermometry is the measurement of the temperature of an object or system. Our skin has a sense of temperature, but it is not very reliable. After exposure to a given temperature for a sufficient amount of time our skin (or our brain) tends to have that temperature feel normal.

Any physical property that varies consistently with temperature (which is almost ALL physical properties) can be used as a thermometer. It is desirable to have a nice, linear behavior of the thermometric property on the temperature. In many cases this is not possible, unless one is willing to change thermometers often.

In the upcoming labs we will be using conventional liquid-in-glass thermometers and electronic temperature sensors. Today we will confirm the inappropriateness of using our sense of temperature for quantitative (or even qualitative) measurements and investigate how to calibrate an uncalibrated electronic temperature sensor to make useful measurements.

There will be three pans of water located in the lab. One will be a mixture of ice and
water and its temperature will be about 32 ^{0}F or 0 ^{0}C. There
will be another pan of water at a temperature much warmer than room temperature, perhaps
100 to 120 ^{0}F. The third pan will be at room temperature. Each group will have
a liquid-in-glass thermometer so that you can accurately determine the true temperature
of the pail. Record the temperature of each pail gently using the
thermometer as a stirring rod. Then place one hand in
the hot water and the other in the ice water for about 30 seconds (or as long as you can
stand). Then quickly place both hands into the room temperature water. Pay
careful attention to the temperature that each hand feels. Comment on your
observations.

There are many kinds of thermometers. Some are more familiar than others - liquid-in-glass being the most common type. The LabPro that we used frequently last semester can be equipped with a sensor that measures changes in temperature - i.e., a temperature probe. The probes can be calibrated directly in temperature, but today we will prefer to use the uncalibrated data to learn how the raw data is turned into a useful temperature value.

Experimental steps:

- Put some water into the small beaker and place it on the electric hot plate to begin heating.
- Open the PHY 174 folder on the computer desktop. Start Logger Pro by double clicking the "Temperature Probe" icon. The program will be set up to take 10 readings per second for 10 seconds, yielding 100 different readings of the raw temperature data. The units of the raw data (RD) are volts (V).
- Practice Using the Program. Take a set of data, then use the STATISTICS function to calculate the mean and standard deviation of the 100 data points. The best estimate of the value is the mean ± the standard deviation.
- Use the liquid-in-glass thermometer to measure the air temperature.
Estimate the value to 0.1
^{o}C and record it in your notebook. Take a set of data with the sensor in about the same location as the thermometer was. Record the mean and standard deviation to 3 or 4 decimal places. - Place the temperature probe and the ordinary thermometer in a cup of ice and water. Do not let either rest against the cup. Stir slowly with the temperature probe for about a minute. Take a set of data. If the line is not horizontal, then stir some more and take another set. Once your graph is a horizontal line, record the temperature of the liquid-in-glass thermometer and then calculate the mean and standard deviation of the data. Record these values as in the step above.
- Repeat the process for boiling water on the electric hot plate. Remember to allow a minute of stirring before taking the data with LabPro. If your standard deviation is substantially greater than with the ice water, keep stirring and take another set. Record your values as described in the previous step.
- Be sure to remove
both probe and thermometer when you are finished. (
*Be sure to keep adding water to the beaker on the hot plate until you are finished. Then turn the hot plate off and unplug it)* - If the probe is linear, we should be able to calculate the straight line between the two points (ice water and boiling water) and find the equation of the line relating the data values to the temperature. Calculate the equation of the line that connects the two points on a graph of raw data (RD) versus Celsius temperature (T). Your equation should be of the form RD = m*T + b, where m is the slope of the line and b is the y-intercept. Watch units carefully as you calculate m and b.
- A calibration equation lets us find T if we know RD, so it should be in the form of T equals an expression with RD in it. Take the equation you just found and and isolate T on the left side of the equation. Your result should look like

T = B + M*RD

where M and B are constants that would be the slope and y-intercept if we had plotted a new graph with T on the vertical axis and RD on the horizontal. Write the equation in your book with the appropriate numerical values for M and B

(i.e. it should be something like T = 6.543 * RD +1.234 -- use your numbers and include units).

- Now you want do a quick check to see if the sensor is linear. Start the program "Graphical Analysis" (do not close Logger Pro) and
make a
graph of T versus RD using your equation from the previous step.
- Rename Column X to be RD with units of V.
- First we need to put in some RD values by hand. Choose a minimum value of RD of about 90% of RD for the ice water mixture and a maximum value of RD of about 110% of the RD value for the boiling water which will make graph cover temperatures from about-10 to 110 șC. Choose 8 or 9 additional points more or less evenly spaced between these two.
- Now select New calculated column from the Data menu. Label the column Temperature
and put in the equation you just found
*(omit the T=)*. On your graph, click on the vertical axis label and change it to Temperature (a straight line should now be on your graph). This is graph is called a calibration graph. If you measure a voltage with the temperature probe, you can use the graph to find the corresponding temperature.

- Do a linear fit to the equation in your GA plot and confirm that the equation in your fit is the same as you entered.
- Next, allow your temperature probe to come to room temperature. Take a set of data, calculate the mean and standard deviation, and then use your GA graph to estimate the temperature of the room by finding the temperature on the GA plot that is roughly your mean value of RD. Check your estimate with the liquid-in-glass thermometer. Does this measurement support our assumption that the temperature probe is a linear sensor? Explain. (Think about how you would know if the sensor was not linear.)
- Now that we have a useful sensor, let's take a set of data with it that we could not easily do using a liquid-in-glass thermometer. Set the experiment to collect data for 50 seconds. To do this, go to the Experiment menu and select Data Collection. Once completed perform the following steps:
- Start with a half-filled cup of warm water.
- Place the temperature probe into the cup and stir slowly for about a minute.
- Start the experiment and, and after about 10 seconds, drop a piece of ice into the cup.
- Continue stirring for the duration of the experiment.
- Calculate a new column that is the temperature corresponding to your raw data for each
point.
*(The procedure to make the new column is the same as you have already done in Graphical Analysis.)* - Look at the values of the temperature that you calculated. If they look reasonable, print a plot of your graph and include it in your lab report. If the data does not look reasonable, ask your instructor.
- Think about how many measurements you could accurately make during the 50 seconds using the liquid-in-glass thermometer. Which method yields the better data? Why?
- Empty your cups and beakers, dry your thermometer and temperature probe with a paper towel, and close Logger Pro.
- Spend a few minutes reflecting on the trustworthiness of sensed temperatures, and the process of calibrating a linear sensor. While you may think that you have 'proved' that the sensor is more accurate that is not the case - you have not done any real checks of the accuracy other than when you used the GA graph earlier to compare the temp probe to the liquid-in-glass thermometer at room temperature.