Thermometer Trials

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We set out to put the new Dexter Industries Thermometers  through trials.  How accurate is it?  How quickly does it respond to temperature changes?  What kind of resolution do we get with it?  Just how good is the thermometer?

First, Brian Davis wrote a great blog entry about the Lego thermometers and a really nice analysis of their performance.  His entry gives a great baseline for comparison of the hardware already on the market . . .  

The thermometer couldn’t be easier to setup for experiments.  The thermometer plugs directly into the NXT, and with the software download for NXT-G or Labview, it’s ready to roll.  
We whipped out the hotplate and lab stand, and set it up by suspending the thermometers above the beaker.  The protected thermometer’s stainless steel probe is about 15 cm or 6” long, which allows us to submerge it almost 5” into a medium.  For trials comparing the open thermometer to the protected thermometer, we kept both sensors close by tying them together.  In the name of science, we submerged the very tip of the open thermistor in the water to get quick, accurate readings.  Note: submerging the open thermometer this is not recommended and will permanently damage the sensor if you’re not careful!

For most of the experiments, we used water . . . it cools with ice cubes and heats on a hotplate.  It also offers a pretty even temperature throughout the beaker it’s in.  But we wanted to test the thermometer through a larger range of temperatures, above boiling point, to determine how it behaves.  So past about 80 Celsius, we switched to oil as a heating medium.  We always used a stirbar to keep the liquid the same temperature throughout (no thermal pockets or temperature gradients).  In the accuracy experiments, we checked our accuracy with a mercury thermometer.  The mercury thermometer gives a precision of about 0.5 Degrees C.

Depending on the experiment, we used either Labview software, or NXT-G software.  Labview supports floating point calculations and can return a more precise measurement.  NXT-G is quicker and easier, but the 1.0 software can only return integers. 
Data:  You can download a spreadsheet of the complete trial data here
Accuracy:  To test accuracy, we compared results against another lab thermometer.
First, we know that a lot of ice in a little bit of water is close to zero degrees Celsius.  So we lined up 9 thermometers to test over a number of instruments.  We dipped the thermometers into both ice water and room temperature water and compared the value to the mercury thermometer.  We did trials in both NXT-G and Labview.  

 In NXT-G, the average delta, or error, was -0.28 C.  In Labview, the average error was about -0.498. 

Response Time:
Response time is an important factor for a thermometer: ideally you would want to know instantly what the temperature of a solution is.  Thermometer readings often lag behind the actual temperature of the solution.  A typical benchmark is the time it takes a thermometer to reach 90% of the solution’s temperature. 
To measure the response time, we let both thermometers come to equilibrium with the room air and then quickly submerged them in ice water.  We used Labview to get a higher precision; response times would be the same using NXT-G, but not as apparent from the data.
The graph illustrates the different response times of the open thermometer (in yellow) and the protected thermometer (in blue).  The response times were:

Open:           26.7 S  (90%) 
Protected:   50.4 Seconds  (90%)

Resolution:  How precise can we be?  We went about calculating resolution in two ways: theoretical and experimental.  Because of the nature of the thermomister in the thermometers, the resolution varies over the range of measured temperatures.  The thermometer should become more precise in the middle (higher resolution), between 0 C and 100 C, and begin to lose resolution outside that range. 

Theoretical Resolution:  we used the parameters given by the thermistor manufacturer to calculate the resistance in the thermistor for each degree Celsius between -50 and 150 C.  The resistance was calculated the way the NXT would.  The limitation is the 10 bit processor in the NXT: it can only handle integers.  So the resistance value was rounded up and then calculated into a NXT Raw Value (0-1023 the raw value that NXT returns for analog measurements).  The resolution was calculated by taking the difference between each measurement (ie the difference in the raw reading between -50 and -49) and inverting it.  The results for the full spectrum are here:

Experimental Resolution:  using Labview software, we measured resolution in a similar way by heating ice water up to about 80 C, and then heating oil from about 70 C up to 150 C.   We recorded the temperatures.  Then we went ahead and sorted:  what we want is the change between temperature readings.  Each time the thermometer reading went up, how much did it go up by?
The average resolution between each measurement between 0 Celsius and about 45 Celisus is less than 0.1 Degree Celsius.  A few of the deltas show the thermometer jumping, but is probably more the result of small eddies of temperature hitting the thermometer.
Between 45 C and 100 C our resolution stays below 0.5 Degrees C.  After 100 C, the resolution drops from 0.5 C to 2 C, losing accuracy. 
Overlaying the theoretical and experimental data, we can see that the experimental closely tracks the theoretical calculations.  Click on the image the right to see a larger image. 

Room for Improvement:

While the analog thermometers are reasonably accurate for work between 0 and 100 Celsius, at the edges of this range, it becomes less precise.  What can we do about it?

The thermistor manufacturer guarantees an accuracy of +/-0.5 Degress Celsius.  The limitation seems to be the analog-to-digital converter in the NXT hardware . . .  so . . .
We’re going digital.  Over the next few weeks, we’ll be working on a digital sensor that communicates via IIC with the NXT.  Look for a more precise set of thermometers from Dexter Industries in the next month!

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