I. Introduction and Objectives

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1 Calibration and Measurement of Temperatures using K, T-Type Thermocouples, and a Thermistor Ben Sandoval 1 8/28/2013 Five K and five T type thermocouples were calibrated using ice water, a hot bath (boiling water), and a boiling liquid nitrogen bath. These reference temperatures allowed for the calibration of the thermocouples at different temperature gradients. The thermistor was calibrated in the ice bath and the boiling water. These measurements were used to determine the accuracy and precision of each type of thermometric device. Fig. 5 and Fig. 10 give the relative accuracy of each device, while Fig. 3, Fig. 6, and Fig. 8 show the specific accuracy and precision. K-Type thermocouples were also attached to a hot plate in various locations and steady state and transient temperature conditions. These measurements were plotted overtime (Fig. 11) to determine the appearance of a steady state curve and the most accurate placement of a K-Type Thermocouple (the placement of K-Type #6). R = electrical resistance in ohms T = temperature in Kelvin I = sensing current, 10µA A = Eq 1 coefficient, 1.032E-3 B = Eq 1 coefficient, 2.387E-4 C = Eq 1 coefficient, 1.597E-7 S a = Seebeck coefficient material a S b = Seebeck coefficient material b (T 1 - T 2 ) = Temperature gradient Nomenclature I. Introduction and Objectives 1 Mechanical Engineering Student, Fulton School of Engineering at Arizona State University, ID: Fall 2013

2 In order to experimentally measure temperature, two requirements must be met. 1) The sensor (or system) must have thermometric properties, varying predictably with temperature, and 2) A calibration curve that relates the thermometric readings to a known temperature scale. The two types of temperature sensors used in this experiment were thermistors and thermocouples. Thermistors are considered semiconductors and have an electrical resistance that varies significantly based on the temperature. A thermocouple is made of two different metals that when joined, produce a small current when exposed to temperature differentials. Specifically, K type (chromel alumel) and T type (copper-constantan) thermocouples were used. The purpose of this experiment was to obtain calibration data for the two types of thermocouples and the thermistor, with the objective of using this information to assess the precision and accuracy of the temperature sensing technologies. The Steinhart-Hart equation [1] (Eq 1, used to convert thermistor temperature readings (originally in kohms) into degrees Celsius. Eq. 2 [2] was applied to the data before analysis in order to convert the readings of the thermocouples into degrees Celsius. Eq. 3 was applied to each data set in order to determine the accuracy of each thermometric device. Thermocouples are of interest in many engineering and testing applications due to their durability, low cost, simplicity, accuracy (which was the factor focused on in this experiment) and finally reproducibility. Equations 1 T = A + Bln(R) + Cln(R) 3 Eq. 1 V out = (S a - S b )(T 1 - T 2 ) Eq. 2 Eq. 3 II. Experimental Setup and Procedure 2 Fall 2013

3 First, K and T type thermocouples were made by spot welding one end of the two different metals together, while still leaving the other end unattached. The spot welder (Fig. 1, a) was used to complete this task for each of the thermocouples. The open ends of these thermocouples (five K, five T-type) were then placed in specific slots on the isothermal terminal block (Fig. 1, b). This terminal block was then placed in the LabVIEW data acquisition system (Fig. 1, c) and a computer running the LabVIEW program (Fig. 1, d) was used to capture and record the corresponding readings from each thermocouple and plot them in real time. In order to calibrate the thermistor, measurements were taken by connecting it to a multimeter and measuring the resistance as it was submerged in an ice bath (Fig. 2, far left, known to be at 0 C) and boiling water (Fig. 2, 2nd from the left, boiling point calculation was based off of laboratory conditions, theoretically calculated at C). Three resistance measurements were taken at each calibration point. The same tests (cold bath, hot bath) were performed using the thermocouples, but in this case LabView was used to capture the calibration data. For the K type thermocouple, additional calibration data was taken by submerging it in boiling liquid nitrogen (Fig. 2, 3rd from the left, know to be C). Similarly, three measurements were taken for each sensor at each calibration point. Figure 2. The above photographs shows multiple thermal systems with known temperatures that were used to calibrate the sensors. Finally, measurements were taken by exposing each of the five K type thermocouples to transient and steady state temperatures of the hot plate (Fig. 2, far right). Each thermocouple was placed at a different depth on the hot plate, with #1 being on the surface and #10 at a depth of roughly 0.5cm. A continuous sample was taken starting from the time that the hot plate was cool, then turning it on and waiting until it reached a steady state temperature. III. Results and Discussion 3 Fall 2013

4 For the first part of the experiment, each thermocouple (five K-Type, five T-Type) was placed in the ice bath and five readings were recorded. This was repeated three times. For each reading set (total of 15) the average off the readings (5 total for each thermocouple type) were calculated, along with their standard deviation (Eq. 3) which was used to determine the relative accuracy of each sample. Three readings were taken with the Thermistor. The chart below (Fig. 3) is a brief summary of the results, more clearly depicted by the graph in Fig. 4. Figure 3. This chart is a brief summary of data collected from three different thermometric devices (T, K-Type Thermocouples, and a Thermistor.) At some points during the experiment, there were rogue data points. The columns with the Corrected Data label are the result when this rogue data was removed. All readings are in degrees Celsius. Figure 4. The above graph shows the the temperature readings for each of the three thermometric devices (T, K-Type Thermocouples and a Thermistor). For the thermocouples, each bar represents the average of the five readings taken with the stacked bar representing the standard deviation (Eq. 3). For the thermistor, each bar represents one measurement with the stacked bar representing the deviation between the three measurements. Upon looking at Fig. 4 and eyeballing the standard deviation, then comparing this with the overall findings listed in Fig. 3, it is clear that the T-Type Thermocouple is the least precise, with the highest deviation between the sensors (0.894 degrees Celsius,) and as well the least accurate with an average temperature reading of 4.11 degrees Celsius in the ice bath of known temperature (0 degrees Celsius.) 4 Fall 2013

5 The thermistor is the second most precise with a deviation of 0.79 degrees Celsius and the most accurate of the three sensors with an average temperature of 2.23 degrees Celsius in the ice bath. Finally, the K-Type Thermocouple was the most precise with an adjusted standard deviation of 0.48 degrees Celsius and the second most accurate with an average reading of 3.38 degrees Celsius. The precision and accuracy findings of all of the ice bath calibration tests are listed below in Fig. 5. Thermistor T-Type Thermocouple K-Type Thermocouple Accuracy Precision Figure 5. The table above summarizes the precision and accuracy of each thermometric device tested in an ice bath. 1 is the most accurate or precise, and 3 is the least. For the second part of the experiment, each thermocouple (five K-Type, five T-Type) was placed in the boiling nitrogen and five readings were recorded. This was repeated three times. For each reading set (total of 15) the average off the readings (5 total for each thermocouple type) were calculated, along with their standard deviation (Eq. 3) which was used to determine the relative accuracy of each sample. The chart below (Fig. 6) is a brief summary of the results, more clearly depicted by the graph in Fig. 7. Figure 6. The above chart is a brief summary of data collected from two different thermometric devices (T, K- Type Thermocouples.) At some points during the experiment, there were rogue data points. The columns with the Corrected Data label are the result when this rogue data was removed. All readings are in degrees Celsius. Figure 7. The above graph shows the the temperature readings for the two thermometric devices (T, K-Type Thermocouples.) Each bar represents the average of the five readings taken with the stacked bar representing the standard deviation (Eq. 3). Looking at Fig. 7 and referencing the summary data from Fig. 6 as verification, it is clear to see that the T-Type Thermocouple is the most precise with an adjusted standard deviation of 0.50 degrees Celsius and the most accurate 5 Fall 2013

6 with an average temperature reading of degrees Celsius in the boiling nitrogen (know to be at degrees Celsius). The K-Type Thermocouple is the second most precise (standard deviation of 1.72 degrees Celsius) and the second most accurate with an average reading of degrees Celsius in the boiling nitrogen. For the third part of the experiment, each thermocouple (five K-Type, five T-Type) was placed in the boiling water and five readings were recorded. This was repeated three times. For each reading set (total of 15) the average off the readings (5 total for each thermocouple type) were calculated, along with their standard deviation (Eq. 3) which was used to determine the relative accuracy of each sample. Three readings were taken with the Thermistor. The chart below (Fig. 3) is a brief summary of the results, more clearly depicted by the graph in Fig. 4. Figure 8. This chart is a brief summary of data collected from three different thermometric devices (T, K-Type Thermocouples, and a Thermistor) when they were submerged in boiling water. Occasionally there were rogue data points. The columns with the Corrected Data label are the result when this rogue data was removed. All readings are in degrees Celsius. Figure 9. The above graph shows the the temperature readings for each of the three thermometric devices (T, K-Type Thermocouples and a Thermistor) when submerged in liquid nitrogen. For the thermocouples, each bar represents the average of the five readings taken with the stacked bar representing the standard deviation (Eq. 3). For the thermistor, each bar represents one measurement with the stacked bar representing the deviation between the three measurements. 6 Fall 2013

7 Upon reviewing Fig. 8 and Fig. 9, it is clear that the T-Type Thermocouple is the most accurate with an average temperature reading of degrees Celsius (in water with a known boiling point of degrees Celsius), and the second most precise with an adjusted standard deviation of 1.72 degrees Celsius. The K-Type Thermocouple is the second most accurate with an average temperature reading of degrees Celsius and the most precise with a standard deviation of 0.41 degrees Celsius. The Thermistor is the least accurate and precise of the three with an average temperature reading of degrees Celsius and a standard deviation of 1.82 degrees Celsius. The precision and accuracy findings of all of the ice bath calibration tests are listed below Thermistor T-Type Thermocouple K-Type Thermocouple Accuracy Precision Figure 10. The table above summarizes the precision and accuracy of each thermometric device tested in boiling water. 1 is the most accurate or precise, and 3 is the least. Finally, the graph below (Fig. 11) shows the temperature measurements of the K-Type Thermocouples over a period of time as it was exposed to steady state and transient conditions. Figure 11. The graph above shows the temperature readings of the five K-Type thermocouples vs time on a hot plate. The standard deviation of the set of lines is located near the lower (0-20 degrees Celsius) part of the graph. 7 Fall 2013

8 After further review of the graph in Fig. 11, it becomes clear that the hot plate reaches steady state when the slopes of the lines become zero. This occurs at the beginning of the test (from roughly seconds) and towards the very end of the trial (from roughly seconds). The K-Type Thermocouple that appears to give the most accurate measurement of the plate temperature appears to be #6, which follows the average of the other four thermocouples very closely. On a side note, it quickly became obvious that as the hot plate increased in temperature, the deviation of the K-Type Thermocouple measurements increased significantly. Q and A 1. The reading of average reading of the T-Type thermocouple was 4.11 degrees Celsius in the ice bath, the average reading of the T-Type thermocouple in the liquid nitrogen was degrees Celsius (0.4 higher than the known), and average in the hot bath was degrees Celsius (.3 degrees above the calculated boiling point of water. Setting the differences of the Seebeck coefficients (S a S b ) equal to 41µV/K and applying the Eq. 1, the corresponding temperatures are a) -76, 0.0, 198.7, degrees Celsius. b) , 32.0, 387.9, and degrees Celsius. 2. The average reading of the K-Type thermocouple in the ice bath was 3.6 degrees Celsius, in the liquid nitrogen, (1.9 above the reference), and in boiling water, 99 degrees Celsius (0.5 above the reference.) Applying these calibrations along with Eq. 1 yields a) -22.0, -5.6, (no calibration applied), and 100 degrees Celsius. 3. If the ice bath reference was allowed to increase, it would decrease the temperature gradient from 45 degrees Celsius (45 0 degrees Celsius) to 39 (45-6) degrees Celsius. This would decrease the voltage from 1.845mV to 1.599mV. The magnitude of the error introduced is 13.3% for both the temperature and voltage. IV. Summary In this experiment, three devices with known thermometric properties were used in order to assess their accuracy and precision. The tests used to assess this were common bath temperatures used in a laboratory. These baths included: ice, boiling liquid nitrogen, boiling water, and direct contact with a hot plate. These tests made it very clear the accuracy of each device at the different positions. At extreme temperature differentials, the thermocouples were clearly more accurate at larger temperature differentials (such as the boiling water and the liquid nitrogen) while the thermistor was more accurate at moderate temperatures like those simulated by the ice bath. In this experiment, it seemed that excess sensors were used and excess data was collected than would actually be needed in the calibration of various sensors. I think that an acceptable number of sensors to run this trial would be three K-Type and three T-Type thermocouples, with ten total samples taken at each temperature. This would increase the processing time of the calibration data, without much loss to the accuracy of experimental data. References [1] J. S. Steinhart and S. R. Hart, Calibration curves for thermistors, Deep Sea Research 15, 4, (1968) [2] Kerlin, Thomas W. Practical Thermocouple Thermometry. Research Triangle Pa: International Society of Automation, Print. Appendix Throughout the report, the methodology of all calculations was described in detail, along with the equations used listed in the Experimental Setup and Procedure section (II). 8 Fall 2013