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 with temperature (which is almost ALL physical properties) can be used as thermometers. 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.

Response of the Skin to Objects of Different Temperature

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 ^°F or 0 ^°C. There will be another pan of water at a temperature much warmer than room temperature – around 100 ^°F. The third pan will be at room temperature. Each will have thermometers so that you can accurately determine the true temperature. Place one hand in the hot water and the other in the ice water for about 20 seconds. Then place both hands into the room temperature water. Comment on the temperature sensed by each hand.

Calibration of an Electronic Temperature Sensor

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 we will prefer to use the uncalibrated data to learn how the raw data (a voltage) is turned into a useful temperature value.

Experimental steps:

• Open the PHY 184 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.
• Practice using the program by taking a set of data, then using 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.
• 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 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 thermometer and then find the mean and standard deviation of the data from the probe.  Record the values. 
• Repeat the process for boiling water.  Be sure to remove both probe and thermometer when you are finished.
• If the probe is linear, we should be able to use the straight line between the two points to find in between temperatures from the voltage measurement. Make a graph in your notebook (not on the computer) of probe voltage vs. temperature. The x-axis should cover the range -10 to 110 ºC. Plot the two data points you have measured and draw a straight line between them. Find the equation of this line. Your equation should be of the form:

V = B + M*T

where M is the slope of the line and B is the y-intercept.

• 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 graph to estimate the temperature of the room.  Check your estimate with the mercury thermometer. Does this measurement support our assumption that the temperature probe is a linear sensor?   Explain why or why not.  This graph is called a calibration graph. It allows us to find the temperature of an object by measuring a voltage with the temperature probe.
• Now that we have a useful sensor, let's take a set of data with it that we could not easily do using a mercury thermometer. 
• Set the experiment to collect data for 50 seconds.  To do this, go to the Experiment menu and select Data Collection.
• Start with a half-filled cup of warm water. 
• Place the temperature probe into the cup and stir slowly. 
• Start the experiment and drop a piece of ice into the cup. 
• Continue stirring for the duration of the experiment. 
• Now we need to convert your voltages into temperatures. We could do this one point at a time using the calibration graph. However, it is much easier to let the computer do it for us. Solve your equation for temperature. Create a new column that is the temperature corresponding to your raw data for each point.  (Under the Data menu select New Calculated Column, then put in your equation for temperature.) Change your graph so it shows the temperature on the vertical axis. Print your graph.
• Think about how many measurements you could accurately make during the 50 seconds using the mercury thermometer. Which method yields the better data? Why?