report 335
Ayoub-94
exp2.docxCalifornia State University of Northridge Lab Experiment #2 Static and Dynamic Response of Temperature Sensors Osvaldo “Ozzy“ Arvizu ME 335L M-W 3:30 PM Dr. George Youseff 04/27/2011
Abstract:
Two types of temperature sensors were analyzed find their time constant. The two sensors were a thermocouple and thermistor. The time constant for both was found experimentally by using labview. It was found that for the thermistor the time constant was 0.057 and 0.162 while it was being heated in water. As for the thermocouple had a time constant of 0.200.
Description of work:
In order to first calibrate both the thermistor and the thermocouple a labview program was written to acquire different voltage readings that change for both as the temp changes. The voltage was taken by putting both probes in a beaker of water as the temperature went from a freezing point to boiling point. The points that were taken were later plotted to obtain the calibration curves for the thermistor and the thermocouple. The curve of each of the sensors will later be used to calculate the time constant of each of the sensors.
A new Labview program was written to find the time constant of both the thermistor and thermocouple. The program would take the calibration curve of each and incorporate into the program. The curve of each is used in the program to convert the voltage that each sensor takes and then convert it into a temperature reading. The temperature reading for each is then taken and subtracted for each other and then the natural log of the difference is taken of both. The program also incorporates a sampling rate and a number samples taken. The sampling rate controls how samples per time are taken and the number of samples are how many samples are taken.
Once the data was collected excel was used to find the time constant of each of the sensors. The data was then plotted ln (Δt) vs. time.
Results and Discussion:
The data that was obtained through the calibration process is as noted below. It is listed for both sensors with their corresponding temperatures and voltages.
The noted data above was plotted in excel and a trend line was applied to each. They were graphed using temperature vs. voltage. The graph for these is illustrated below in figure 1 with their respected trend lines.
Figure 1.
The higher accuracy of the data the better the results will come out to be doing to the linear relationship of the voltage conversion into Celsius.
Once the calibration has been established a total of 10 transient runs will be taken (5 runs for the thermocouple and 5 for the thermistor). When there is a certain sensor targeted for a transient run the other will be the control and remain out of the boiling water. The sensor that is targeted will be placed in boiling water, pull out and let cool down to ambient temperature. This will be done while there is data being taken. The data for each run will be placed in excel and then plotted. The data will be plotted using ln (Δt) vs. time. This will be done for all 10 transient runs. Below is figure 2 and illustrated is the graph for the first run. Note that the first 5 runs were done with the thermistor being the tested sensor and the thermocouple being the control.
Figure 2. Thermistor removed from water.
Since the trendline was taken for each of the samples and it behaved close to a linear line the slope was used to find the time constant. The time constant is taken from the slope of the trendline. The time constant is the absolute value of the slope, which comes out to 0.0568 ln(Δt)/sec. For the remaining 4 runs the data graph are located in the appendix.
Just as done with the first 5 runs the sensors will switch roles. The thermistor will be the control and the thermocouple will be the targeted sensor. The graph of the first run is illustrated below in figure 3.
Figure 3. Thermocouple removed from water.
Just as for the previous 5 runs the absolute value of the slope divided by 1 will be the time constant of the run. The time constant of this run was 0.21 ln(Δt)/sec. The graph of the next 4 runs can be found in the appendix.
Once the data for the 10 transient runs has been accounted for then a table each of the 10 runs can be made. From the data collected and the graph plotted from each, an average and a standard deviation were taken for both. The tables are illustrated below presented the information on both. The table has also place the uncertainty value of each. The uncertainty has a value of 95%.
|
Runs |
Time Constant |
Uncertainty |
|
1 |
0.056774496 |
0.000747659 |
|
2 |
0.056715629 |
0.000843223 |
|
3 |
0.05694682 |
0.000773013 |
|
4 |
0.055231837 |
0.001186892 |
|
5 |
0.057005038 |
0.00127264 |
|
ave/standev |
0.056534764 |
0.00073803 |
Table 1. Thermistor cooling to ambient temp.
|
Runs |
Time Constant |
Uncertainty |
|
1 |
0.207818308 |
0.015018936 |
|
2 |
0.170991862 |
0.019713208 |
|
3 |
0.201330665 |
0.013971371 |
|
4 |
0.201264694 |
0.015696142 |
|
5 |
0.219213538 |
0.02007623 |
|
ave/standev |
0.200123813 |
0.017853932 |
Table 2. Thermocouple cooling to ambient temp.
The next step required only the thermistor. It’s purpose was to find the time constant of the thermistor as it went from ambient temperture to boiling. This was done a total of 3 times and just as before 3 graphs and table with their average and uncertainties were made. The table below illustrates.
|
Runs |
Time Constant |
Uncertainty |
|
1 |
0.162132922 |
0.000920014 |
|
2 |
0.147909726 |
0.001648642 |
|
3 |
0.150495955 |
0.001251979 |
|
ave/stdev |
0.153512868 |
0.000364792 |
Table 3. Thermistor from ambient to boiling water.
Conclusion:
The time constant was very similar because the calibration curve for both was very linear. This made it possible to achieve very good results. The results from the thermistor were 0.057 for the boiling to ambient and 0.162 for the ambient to boiling. The difference between them although they were the same sensor is that the reaction due to the heat being put in it has more energy then that of the energy of the ambient temperature.
The time constant result for the thermocouple was 0.200. This compared to that of the thermistor was slower. They have the same capabilities but different working ranges. A thermistor has a faster reaction time but the thermocouple has a higher range.
Appendix:
Figures 4 thru 7 illustrate runs 2 thru 5 of thermistor from boiling point to ambient temperature.
Figure 4.
Figure 5.
Figure 6
Figure 7.
Figures 8 thru 11 illustrate graphs for runs 2 thru 5 of thermocouple form boiling water to ambient temp.
Figure 8.
Figure 9.
Figure 10.
Figure 11.
Figure 12 thru 14 illustrates runs 1 thru 3 of the thermistor from ambient temperature to boiling water.
Figure 12.
Figure 13.
Figure 14.
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 4.3056999999999999 4.3060200000000002 4.2527999999999997 4.1880899999999945 4.1134099999999956 4.0477299999999996 3.9757499999999966 3.9077000000000002 3.8390299999999966 3.7652900000000002 3.6862300000000001 3.6383800000000002 3.55843 3.51058 3.4367199999999976 3.3794499999999941 3.3372699999999966 3.2814399999999999 3.2427100000000002 3.1774300000000002 3.1055300000000003 3.0944599999999975 2.9949300000000001 2.9582799999999976 2.9250699999999976 2.8434699999999986 2.7965599999999986 2.76 17100000000003 2.7032300000000014 2.6362699999999957 2.5833900000000014 2.5113099999999986 2.4741499999999976 2.4055499999999976 2.3725699999999956 2.3031700000000002 2.2642900000000004 2.20661 2.1558699999999966 1.97343 2.0575000000000001 2.0224399999999987 1.9483900000000001 1.8437599999999998 1.8294299999999988 1.7229599999999998 1.70678 1.6173500000000001 1.5287199999999999 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 4.3255299999999943 4.3210499999999996 4.3066200000000006 4.2531099999999986 4.1908199999999951 4.1134099999999956 4.0430099999999998 3.9744699999999966 3.8940399999999986 3.8258799999999966 3.7626900000000001 3.6918699999999967 3.6336399999999998 3.5526599999999942 3.5099300000000002 3.4489800000000002 3.3901499999999967 3.3276399999999997 3.2712499999999975 3.2151100000000001 3.1603800000000013 3.11957 3.0475000000000003 3.0072399999999999 2.952449999999994 2.9275300000000013 2.8447499999999986 2.7701300000000013 2.80348 2.7196899999999986 2.64269 2.6282300000000003 2.5611200000000003 2.5113099999999986 2.4530599999999976 2.4116599999999941 2.3851499999999977 2.2429000000000001 2.2896900000000002 2.20661 2.1374300000000002 2.1611700000000003 2.02535 2.0224399999999987 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 4.3087400000000002 4.3036000000000003 4.2486400000000026 4.1757400000000002 4.0929799999999945 4.0287099999999976 3.9587399999999997 3.8959099999999967 3.80959 3.7394599999999967 3.6541800000000002 3.6071700000000013 3.54623 3.4722499999999941 3.4207100000000001 3.3717999999999986 3.3146499999999941 3.2609600000000003 3.1978 3.1517900000000001 3.1005100000000003 3.0389300000000001 2.9938199999999986 2.9382699999999966 2.8944799999999966 2.8486899999999986 2.7841700000000014 2.7502800000000001 2.6911200000000002 2.6475100000000014 2.5833900000000014 2.5471400000000002 2.4891800000000002 2.49857 2.3471100000000003 2.2781000000000002 2.2665700000000002 2.20661 2.0967999999999987 tc in ht2 1.2 1.4 1.6 1.8 2 2.2000000000000002 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4 4.2 4.4000000000000004 4.5999999999999996 4.8 5 5.2 5.4 5.6 5.8 6 6.2 6.4 6.6 6.8 7 7. 2 7.4 4.3311099999999998 4.3176999999999977 4.2474400000000001 4.1479999999999944 4.0611099999999976 3.9994999999999976 3.9413300000000002 3.8874200000000001 3.8299599999999976 3.7710599999999976 3.7238300000000013 3.6702499999999967 3.63462 3.5946099999999985 3.5425800000000001 3.5274399999999999 3.4890300000000001 3.4583200000000001 3.4404300000000001 3.4244300000000001 3.3916299999999966 3.3717399999999986 3.3569599999999942 3.3522199999999955 3.3435100000000002 3.3128499999999939 3.3103799999999977 3.2887900000000014 3.2837100000000015 3.2862499999999986 3.2641200000000015 3.2476500000000001 1 1.2 1.4 1.6 1.8 2 2.2000000000000002 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4 4.2 4.4000000000000004 4.5999999999999996 4.8 5 5.2 5.4 5.6 5.8 6 6.2 6.4 6.6 6.8 7 4.3233799999999976 4.3245699999999943 4.3200899999999951 4.2912300000000014 4.2097200000000008 4.1469299999999976 4.0634399999999946 4.0247699999999975 3.9543599999999985 3.9057200000000001 3.8493200000000001 3.7971600000000003 3.74586 3.70627 3.65347 3.6166399999999976 3.5939999999999999 3.54061 3.5094399999999997 3.4604599999999985 3.4207800000000002 3.41337 3.3686499999999966 3.3371399999999998 3.3185799999999976 3.3079000000000001 3.2795000000000001 3.2954699999999986 3.2537600000000002 3.2415000000000003 3.2290800000000002 1.2 1.4 1.6 1.8 2 2.2000000000000002 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4 4.2 4.4000000000000004 4.5999999999999996 4.8 5 5.2 5.4 5.6 5.8 6 6.2 6.4 6.6 6.8 7 4.3197999999999999 4.3179899999999929 4.2753900000000007 4.1989599999999943 4.1419299999999986 4.0676899999999945 4.0251599999999943 3.9543599999999985 3.9007200000000002 3.8440399999999997 3.7895600000000003 3.73786 3.6917900000000001 3.64114 3.6013900000000003 3.5503499999999986 3.5221399999999998 3.46889 3.44834 3.4244300000000001 3.3763899999999976 3.3569599999999942 3.3458999999999977 3.3371399999999998 3.3045999999999998 3.2693000000000003 3.2537600000000002 3.2441500000000003 3.2589200000000003 3.2120099999999976 0.60000000000000009 0.8 1 1.2 1.4 1.6 1.8 2 2.2000000000000002 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4 4.2 4.4000000000000004 4.5999999999999996 4.8 5 4.3191899999999945 4.3146799999999956 4.3179899999999929 4.2390400000000028 4.1256999999999966 4.0638199999999944 3.9933000000000001 3.9241200000000003 3.8772099999999976 3.8299599999999976 3.7798499999999966 3.7335700000000003 3.6850399999999999 3.6540399999999997 3.6304499999999966 3.5827999999999998 3.5548699999999975 3.5333999999999999 3.5194799999999966 3.4917699999999976 3.4554899999999966 3.4419 3.4346499999999955 2 2.1 2.2000000000000002 2.2999999999999998 2.4 2.5 2.6 2.7 2.8 2.9 3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 4.0999999999999996 4.2 4.3 4.4000000000000004 4.5 4.5999999999999996 4.7 4.8 4.9000000000000004 5 5.0999999999999996 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 8 8.1 8.2000000000000011 8.3000000000000007 8.4 8.5 8.6 8.7000000000000011 8.8000000000000007 8.9 9 9.1 9.2000000000000011 9.3000000000000007 9.4 9.5 9.6 9.7000000000000011 9.8000000000000007 9.9 4.0713000000000026 4.0639799999999946 4.0499900000000002 4.03261 4.0258199999999951 4.0002200000000006 3.98529 3.9705499999999976 3.9581900000000001 3.9408799999999986 3.9245999999999999 3.9053200000000001 3.8957799999999976 3.87452 3.8518699999999941 3.8049200000000001 3.8164099999999941 3.8004599999999966 3.7857900000000013 3.7719200000000002 3.7547200000000003 3.7499800000000003 3.7210100000000002 3.7034400000000001 3.67706 3.6742300000000001 3.6470500000000001 3.6459100000000002 3.6088399999999998 3.60765 3.58108 3.5608499999999985 3.5531600000000001 3.53498 3.5310699999999966 3.5077600000000002 3.4969299999999977 3.4727999999999986 3.46089 3.4387499999999975 3.4183399999999997 3.4117099999999976 3.3937599999999977 3.3792999999999966 3.3754799999999956 3.3505799999999986 3.3314799999999956 3.32748 3.2761499999999986 3.2795399999999999 3.26247 3.2512399999999997 3.2407400000000002 3.21035 3.20946 3.1696399999999998 3.1753300000000002 3.1360099999999975 3.1592599999999966 3.1262399999999997 3.1032700000000002 3.0859900000000002 3.0777399999999999 3.0642100000000001 3.0321899999999986 3.0224099999999976 3.00475 3.0091900000000003 2.9776599999999975 2.9462599999999965 2.9498199999999986 2.9308099999999966 2.8978799999999967 2.8879200000000003 2.896659999999994 2.8625699999999976 2.8365599999999955 2.8457599999999976 2.815249999999994 2.81393 0 0.2 0.4 0.60000000000000009 0.8 1 1.2 1.4 1.6 1.8 2 2.2000000000000002 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4 4.2 4.4000000000000004 4.5999999999999996 4.8 5 5.2 5.4 5.6 5.8 6 6.2 6.4 6.6 6.8 7 7.2 7.4 7.6 7.8 8 8.2000000000000011 8.4 8.6 8.8000000000000007 9 9.2000000000000011 9.4 9.6 9.8000000000000007 10 10.199999999999999 10.4 10.6 10.8 11 11.2 11.4 11.6 11.8 12 12.2 12.4 12.6 12.8 13 13.2 13.4 13.6 13.8 14 14.2 14.4 14.6 14.8 15 15.2 15.4 15.6 15.8 16 16.2 16.399999999999999 16.600000000000001 16.8 17 17.2 17.399999999999999 17.600000000000001 17.8 18 18.2 18.399999999999999 18.600000000000001 18.8 19 19.2 19.399999999999999 19.600000000000001 19.8 4.299260000000003 4.3059599999999945 4.29406 4.2776800000000001 4.2440600000000002 4.2209099999999946 4.1811799999999986 4.1515599999999946 4.1184799999999946 4.0827499999999999 4.0401600000000002 4.00474 3.9764899999999956 3.94177 3.8911799999999976 3.8698699999999966 3.8316399999999966 3.8114799999999955 3.7651800000000013 3.7521 3.7106499999999967 3.6 667999999999998 3.6364799999999966 3.61192 3.5892200000000001 3.5493200000000003 3.5178199999999986 3.4825399999999997 3.4566699999999941 3.4057599999999986 3.3816099999999976 3.3560899999999956 3.32748 3.2980100000000001 3.2486100000000002 3.2265700000000002 3.1874400000000001 3.1781600000000001 3.1515900000000001 3.1133500000000001 3.0620699999999985 3.0673800000000013 3.0213399999999999 2.9776599999999975 2.95336 2.9522099999999956 2.9053399999999998 2.88043 2.8600499999999967 2.8326799999999941 2.7907800000000003 2.7527999999999997 2.7118599999999966 2.7208399999999999 2.74281 2.6471900000000015 2.5606200000000001 2.6082300000000003 2.5813800000000002 2.4906199999999976 2.5450599999999985 2.4603800000000002 2.4449100000000 001 2.4351499999999966 2.3805000000000001 2.3226899999999966 2.2959000000000001 2.3293200000000001 2.1959599999999986 2.1935100000000003 2.2085300000000014 2.1784599999999976 2.1181000000000001 2.0935300000000003 2.0823900000000002 2.0482 1.9313899999999999 2.0128099999999955 1.91503 2.00691 1.92177 1.8711100000000001 1.81416 1.83955 1.8502700000000001 1.82161 1.7499499999999988 1.7769999999999988 1.73421 1.7578899999999988 1.71028 1.71028 1.6644700000000001 1.62984 1.68984 1.5613999999999988 1.4879399999999987 1.4464899999999998 1.48295 1.33466 0 0.2 0.4 0.60000000000000009 0.8 1 1.2 1.4 1.6 1.8 2 2.2000000000000002 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4 4.2 4.4000000000000004 4.5999999999999996 4.8 5 5.2 5.4 5.6 5.8 6 6.2 6.4 6.6 6.8 7 7.2 7.4 7.6 7.8 8 8.2000000000000011 8.4 8.6 8.8000000000000007 9 9.2000000000000011 9.4 9.6 9.8000000000000007 10 10.199999999999999 10.4 10.6 10.8 11 11.2 11.4 11.6 11.8 12 12.2 12.4 12.6 12.8 13 13.2 13.4 13.6 13.8 14 14.2 14.4 14.6 14.8 15 4.2556000000000003 4.2476000000000003 4.2195900000000002 4.1825499999999955 4.152979999 9999941 4.1210399999999945 4.0770400000000002 4.0456900000000005 4.0137299999999998 3.97776 3.9347599999999976 3.9147999999999987 3.8787399999999987 3.8480799999999986 3.8094899999999976 3.77915 3.7499800000000003 3.7012200000000002 3.6719399999999998 3.6417800000000002 3.6149300000000002 3.58297 3.55253 3.5184699999999975 3.4887200000000003 3.4580599999999966 3.4161199999999976 3.4161799999999976 3.37473 3.3346899999999966 3.3144899999999966 3.2880000000000011 3.2477500000000004 3.23549 3.2003800000000013 3.1697200000000003 3.1467900000000002 3.1043400000000001 3.0525799999999985 3.02678 3.0279300000000013 2.98455 2.9580399999999987 2.9199899999999985 2.8854599999999966 2.8392399999999967 2.82737000 00000002 2.836659999999994 2.79494 2.7571200000000013 2.7384300000000001 2.6922999999999977 2.71794 2.6423700000000001 2.6098499999999967 2.5762299999999976 2.5676900000000002 2.5127199999999985 2.4980499999999966 2.4680300000000002 2.4449100000000001 2.4212399999999987 2.3887800000000001 2.2496 2.2959000000000001 2.2936800000000002 2.2590300000000001 2.2207500000000002 2.1910499999999966 2.1707399999999999 2.1394899999999986 2.1288499999999986 2.0962399999999985 2.0625300000000002 2.0482 1.9915
Calibration
Thermalcouple 1.24 1.28 1.3800000000000001 1.48 1.59 1.6800000000000002 1.77 1.8800000000000001 1.9600000000000002 16.5 20 30 40 50 60 70 80 90 Thermister 4.28 3.77 3.66 3.4 3.1 2.79 2.6 2.3199999999999976 2 1.78 -3 16.5 20 30 40 50 60 70 80 90Voltage (v)
Temperature (c)
ln (ΔT) vs time
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 4.3102499999999999 4.2730500000000013 4.2126799999999998 4.1491499999999997 4.0816800000000004 4.0060600000000006 3.9335200000000001 3.8661999999999987 3.8000699999999976 3.7437300000000016 3.6823100000000002 3.6192899999999977 3.5500799999999986 3.4936699999999976 3.4374799999999985 3.3810199999999986 3.3187099999999976 3.2746599999999986 3.2223000000000002 3.1679800000000014 3.1045500000000001 3.04217 2.9802200000000001 2.9287000000000001 2.9347699999999985 2.85778 2.8102399999999976 2.7431000000000014 2.7017600000000002 2.6101800000000002 2.5935900000000003 2.5383399999999998 2.4741499999999976 2.4336199999999986 2.35358 2.2758499999999966 2.2431000000000014 2.1662300000000001 2.10242 2.0661399999999999 2.0747 1.9224300000000001 1.8957899999999999 1.8076999999999988Time (s)
ln(ΔT)
ln (ΔT) vs time
Thermacouple in Hot Water 1.6 1.8 2 2.2000000000000002 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4 4.2 4.4000000000000004 4.5999999999999996 4.8 5 5.2 5.4 5.6 5.8 6 6.2 6.4 6.6 4.3325799999999957 4.2653099999999986 4.1945399999999911 4.1198499999999996 4.0699799999999966 4.0283600000000002 3.9953599999999976 3.92455 3.8602799999999986 3.8011900000000001 3.7426499999999976 3.7012499999999986 3.6505200000000002 3.6244499999999986 3.5908699999999976 3.5516099999999966 3.5353300000000001 3.4702599999999966 3.4490399999999997 3.4118599999999941 3.3870499999999986 3.3701599999999976 3.3442799999999986 3.3322999999999956 3.3144499999999941 3.2987900000000003Time (seconds)
ln (Δ T)
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 4.3111600000000001 4.3063200000000004 4.2768000000000024 4.2216300000000002 4.1494999999999997 4.0869600000000004 4.0146099999999976 3.9440300000000001 3.8862399999999986 3.81752 3.7521999999999998 3.6935600000000002 3.6312699999999967 3.58874 3.5099300000000002 3.4645900000000003 3.39317 3.3121799999999966 3.2814399999999999 3.21238 3.17835 3.1125799999999986 3.0591900000000001 3.0072399999999999 2.9571300000000003 2.9043800000000002 2.81013 2.8007 2.7016300 000000002 2.6926099999999966 2.6411300000000013 2.5645100000000003 2.5329599999999965 2.4588899999999976 2.4136299999999986 2.3471100000000003 2.4057200000000001 2.2642900000000004 2.20661 2.12677 2.09138 2.0997300000000001 2.0633500000000002 1.83647 1.8437599999999998 1.7229599999999998 1.7350099999999988 1.6862700000000002 1.5138899999999988TemperatureThermalcoupleThermister
-31.034.28
16.51.243.77
201.283.66
301.383.4
401.483.1
501.592.79
601.682.6
701.772.32
801.882
901.961.78
9621.69
