Lab_3 Final

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Department Of Mechanical And Industrial Engineering Measurement Of Temperature and Sensor Characteristics By Kisei Mano Team 1 1. Kisei Mano 2. Clair Wagner 3. Courage Lahban 4. Elijah Smith Date of Experiment: 5-24-2023 & 5-25-2023 Instructor: B. S. Mani ME343-011, MECHANICAL LAB-1 Summer 2023 1
Table of Contents Cover Page………………………………………………………………………………………………………………………… Page 1 Table of Contents………………………………………………………………………………………………………………. Page 2 Grading Citaria………………………………………………………………………………………………………………….. Page 3 Table of Tables…………………………………………………………………………………………………………………… Page 5 Table of Figures…………………………………………………………………………………………………………………. Page 5 Abstract…………………………………………………………………………………………………………………………….. Page 6 Theoretical Principles..………………………………………………………………………………………………………. Page 7 Experimental methodology……………………………………………………………………………………………... Page12 o Equipment…………………………………………………………………………………………………………. Page 12 o Experimental description…………………………………………………………………………………... Page 16 Data and Result………………………………………………………………………………………………………………. Page 18 Discussion……..………………………………………………………………………………………………………………… Page 27 Conclusion………………………………………………………………………………………………………………………. Page 28 Bibliography……………………………………………………………………………………………………………………. Page 29 Appendix………………………………………………………………………………………………………………………… Page 30 Bonus Points…………………………………………………………………………………………………………………… Page 36 2
MEASUREMENT OF TEMPERATURE AND SENSOR CHARACTERISTICS Grading Criteria for Lab Report 3 (Maximum Possible 50 points + Bonus 15 points ) REVISED 02/28/23 1. General Format ( 20 points = 2.5+7.5+2.5+2.5+5.0 ) Cover page ( 2.5 points ) Grading Criteria Table of Contents (Include Responses for Bonus points, if any, after Conclusion) Abstract Theoretical principles (See details below given separately) Experimental system (See details below given separately) Results and discussions (See details below given separately) Conclusion ( 2.5 points ) Appendices ( 5 points ) Lab manual organization Photocopy of original data Detailed sample calculation Nomenclature used in report 2. Theoretical Principles (7.5 points = 5x1.5 each) Thermocouple (TC) general equation for type K General equation for Resistance Temperature Detector (RTD) General equation for Thermistor (TM) and Determination of β for TM & Sensitivity for RTD & TM Definition and determination of response time for TC 3. Experimental Systems (2.5 points) Schematic diagram of experimental system of each of the above set up Photograph of the system and its key components 4. Results and Discussions ( 30 points = 10.0 + 10.0 + 10.0 ) Calibration of Thermocouple (TC) and TC equations (7.5 points) 3
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Calibration of Thermistor (TM) (7.5 points) Calibration of Resistance Temperature Detector (RTD) and IR (7.5 points) Data acquisition of TC and determination of response time (7.5 points) 5. Bonus: (15 points) Determination of β, direct least square method; Include discussion, logarithmic plot (linearization) Compare the response time of open type and encased type of Thermocouple. Table of Figures 4
Figure # Description Page # 1 Display of the TC module 7 2 Thermocouple Module 12 3 Thermocouple Sensor (exposed type) 12 4 Thermocouple Sensor (underground type) 12 5 Thermistor 13 6 Resistance Temperature Detector (RTD) 14 7 Digital Multimeter 14 8 Inferated Thermometer 15 9 Heat Plate 15 10 Full assembly of thermocouple 16 11 Schematic diagram of using thermistor 16 12 Schematic diagram of using RTD 17 13 Schematic diagram of using response time 17 14 Graph of the thermocouple (open type) Voltage vs Temperature 18 15 Graph of the thermocouple (close type) Voltage vs Temperature 19 16 Resistance vs 1/T Graph for Thermistor 20 17 Thermistor Temperature vs Resistance 21 18 Thermistor ln(R) vs Inverse of Temperature 21 19 RTD Temperature vs Resistance 23 20 Transient Analysis cold to Hot 24 21 Transient Analysis Hot to cold 25 22 Transient Analysis linear cold to Hot 26 Table of Tables Table # Page # 1 18 2 19 3 20 4 22 5 23 6 25 5
Abstract The abstract of this lab was to measure the temperatures of five different types of water in various methods. The group members used six different methods to measure the temperature of the water. For example, there is the thermocouple, resistance thermometer (RTD), thermistor, and infrared thermometer. Also, this experiment made us understand the thermocouple equation, general equation for RTD and TM, determination of β , and determination of the response time. With the help of the Microsoft Excel software, we used the gathered data to obtain the graph. From the graph we were able to understand the error percentage and accuracy of the results. 6
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Theoretical Principles Thermocouple Equation In this method we use a measurement tool called Thermocouple, to measure the temperature of any liquid. From figure 1, we can see that consists of two different metals joined together. When there is a temperature difference between the measurement point (hot junction) and the reference point (cold junction), the thermocouple generates a voltage known as the thermoelectric voltage. From equation 1, we were able to obtain the temperature as T, from the Ninth polynomial. T = a 0 + a 1 x + a 2 x 2 + a 3 x 3 …… .. + a 9 ( x 9 ) (1) 7
Figure 1: Display of the TC module General Equation for RTD In this part of the experiment, we use the device called the Resistance Thermometer Detector, or RTD for short. RTD is a measurement tool for liquid temperature. This utilizes the change in electrical resistance of a metal wire due to its excellent stability, linearity, and wide temperature range. a = R − R 0 R ( T − T 0 ) (2) The equation above explains the linear slope of the temperature coefficient of resistance, where R 0 is the resistance at the temperature T 0 and R is the resistance at the temperature T. This equation is mainly used at the narrow range temperature. 8
R = R 0 ( 1 + aT + bT 2 ) (3) Equation 3 is mainly used for wide temperature range, where a and b are constants, T is temperature, and R0 is resistance. Determination of β From The General equation for Thermistor: In this lab we used the Thermistor general equation and used that to determine the β. The thermistor is a device that is typically made of a semiconductor material used to measure the temperature of liquids. The thermistor we used has a negative temperature coefficient of resister, which means as the temperature increases the resistance decreases. In the equation 4, R 0 represents the electrical resistance at T 0 . Also β characterize as an experimental constant of resistance-temperature curve of the thermistor: R = R 0 e β ∗ ( 1 T − 1 T 0 ) (4) With equation 4 we can obtain the equation 5 β = ln ( R R 0 ) 1 T − 1 T 0 (5) Sensitivity for RTD and Thermistor 9
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The sensitivity for the RTD sensors has high accuracy because it consists of thin filmed metal-glass slurry. The general equation of the RTD is the slope of the sensitivity plot, shown at equation 2. The sensitivity for the thermistor also has high accuracy from the change in resistance, but the only difference is that the graphed data is always nonlinear. The slope of the plot can be determined by the equation below: S = dR dT The R represents the resistance and T stands for temperature. With the combination of the equations 4 and 6, we were able to get the equation 7 below: S = R 0 e ( B ∗ ( 1 T − 1 T 0 ) ) ∗ ( − b T 2 ) (7) Definition and Determination of Response Time for TC In this last method, we used the thermocouple connected to LabQuest Mini (Model 2). This device is a powerful, affordable, and easy- to-use sensor interface for data collection on a computer or a Chromebook. (The Vernier, 2023) With the use of a software program “Lab-View”, we were able to obtain two types of data. The first one is the measurement of 10
the temperature change when the thermocouple dipped from cold to hot. The other one is from hot to cold. The equation below represents as a rate of change in Thermal Energy; τ c represents time constant, m is mass, C is specific heat, A is the area of the junction dissipating heat. heat flux = hA ( T ∝ − T ) = mC ( dT dτ ) τ c = mC hA ( dT dτ ) = hA mC ( T ∝ − T ) T = ∫ hA mC ( T ∝ − T ) dτ After the integration we eventually get the equation () and () below: T = T ∝ + ( T 0 − T ∝ ) e − t τ c () T = e − t τ s () 11
Experiment methodology Equipment and Description: Figure 2: Thermocouple Module Thermocouple Module: This device is used to measure the temperature with the reattach able thermocouple sensor. When this device is plugged into the digital multimeter, we were able to obtain the different temperatures of the water. 12
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Figure 3: Thermocouple Sensor (exposed type) Figure 4: Thermocouple (undergrounded type) Thermocouple Sensor (exposed type K and undergrounded type): There are two types of thermocouples shown above. Figure 3 is the exposed type, which has a fast reaction time because it is in direct contact with water. However, since it’s not protected by the sheath it’s very weak in physical pressure. Figure 4 is the underground type, which is protected by the metallic outer sheath enabling the device to have a wide variety of uses. However, compared to the exposed type it takes a longer time to react in temperature change. 13
Figure 5: Thermistor Thermistor: This is a semi-conductor temperature sensor, which has an input high temperature coefficient of resistance. This explains that the change of resistance responds to the change in temperature. In this experiment we used Negative Temperature Coefficient in collecting data, which means as the temperature increases the resistance of the NTC thermistor decreases. 14
Figure 6: Resistance Temperature Detector (RTD) Resistance Temperature Detector (RTD): This device is used to measure temperature as the electrical resistance of a metal changes. RTDs are known for their high accuracy, stability, and linearity over a wide temperature range. Figure 7: Digital multimeter Digital multimeter : This device can analyze how much power is measured in a certain frequency. In this experiment, we used it mainly to get the data of voltage and resistance. Also, with the combination of the multimeter and Thermocouple Module we were able to get the temperature of the water. 15
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Figure 8: Inferated Thermometer Infrared Thermometer: This is a device that is used to measure temperature without any direct contact with water. Figure 8: Heat Plate Heating Plate : This device can heat up the water to the specific temperature and maintain it for a while. 16
Equipment and Description: 1. Measurement of temperature with the use of Thermocouple: In this experiment, we only measure the voltage and temperatures from five different containers with the use of thermocouple. Figure 9: full assembly of thermocouple 2. Measurement of temperature with the use of Thermistor: In this part of the experiment, we connected the multimeter with thermistor to obtain the temperature and resistance data and change it into graph. 17
Figure 10: schematic diagram of using thermistor 3. Measurement of temperature with the use of RTD: In this experiment, with the use of RTD connected to the digital multimeter. We were able to obtain the different temperature and collected resistance data. Figure 11: Schematics diagram of using RTD 4. Measurement of response time: 18 Combined
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Figure 12: Schematics diagram of the response time In this experiment, we use the two types of the thermocouple to see the temperature change from cold water to hot water and hot water to cold water. Results And Discussion 1. Calibration of Thermocouple (TC) and TC equations Table 1: Thermocouple Data for Open Device Ice Water Ice Water + Room Temp "Room Temp" Water Room Temp + Heated Heated Water Thermocoup le Module (C) -1.6 20.5 22.7 57.9 98.5 Open thermocoupl e (mV) -5.67 -4.8 -0.53 -0.48 -0.87 19 OR
-20 0 20 40 60 80 100 120 -6 -5 -4 -3 -2 -1 0 f(x) = 0.04 x − 4.24 R² = 0.47 Thermocouple Data for Open Device Temperature (C) Voltage (mV) Figure 13: Graph of thermocouple (open type) Voltage vs Temperature Table 2: Thermocouple Data for Close Device Ice Water Ice Water + Room Temp "Room Temp" Water Room Temp + Heated Heated Water Thermocoup le Module (C) -1.6 20.5 22.7 57.9 98.5 Closed thermocoupl e (mV) - 0.906 -0.37 -0.118 1.258 2.44 20
-20 0 20 40 60 80 100 120 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 f(x) = 0.03 x − 0.91 R² = 0.99 Thermocouple Data for Close Device Temperature (C) Voltage (mV) Figure 14: Graph of thermocouple (close type) Voltage vs Temperature 2. Calibration of Thermistor Table 3: Calibration of Thermistor Data Ice Water Ice Water + Room Temp "Room Temp" Water Room Temp + Heated Heated Water Thermoco uple Module (C) -1.6 20.5 22.7 57.9 98.5 Thermoco uple Module (K) 271.65 293.75 295.95 331.15 371.75 1/T 0.003681 207 0.003404 255 0.003378 949 0.00301 978 0.00268 998 Thermiste r (k ohms) 7 3.65 2.74 0.68 0.23 Ln R 1.946 1.295 1.008 -0.3857 -1.470 21
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0 0 0 0 1 2 3 4 5 6 7 8 f(x) = 0 exp( 3576.86 x ) R² = 0.99 Resistance VS 1/T (Thermistor) Temperature Resistance Figure 15: Resistance vs 1/T Graph for Thermistor The graph below shows that the temperature and the resister have an inverse relationship, when the temperature increases the resistance decreases. 22
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260 280 300 320 340 360 380 0 1 2 3 4 5 6 7 8 f(x) = 93014.94 exp( − 0.04 x ) R² = 0.99 Temperature VS Resistance Temperature Resistance Figure 16: Thermistor Temperature vs Resistance 0 0 0 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 f(x) = 3576.86 x − 11.09 R² = 0.99 ln R vs Inverse of Temperature (Thermistor) 1/T (1/K) ln R Figure 17: Thermistor in® vs Inverse of Temperature From the graph above, we obtained the equation of the slope which equals to β : y = 3576.9 ( 1 T ) − 11.092 23
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Therefore, β = 3576.9 Sensitivity Calculations R 0 = 2740 Ω T 0 = 22.7 C + 273.25 K = 295.95 K T = 98.5 C + 273.25 K = 371.75 K β = 3576.9 S = R 0 ∗ e [ ( β ( 1 T − 1 T 0 ) ) ] ∗ ( − β T 2 ) ¿ 2740 ∗ e [ ( 3576.9 ( 1 371.75 − 1 295.95 ) ) ] ∗ ( − 3576.9 371.75 2 ) =− 6.032 Therefore, the sensitivity S= − 6.032 3. Calibration f Resistance Temperature Detector (RTD) and IR With the use of RTD we were able to get the data below: Table 4: Calibration f Resistance Temperature Detector (RTD) Data Ice Water Ice Water + Room Temp "Room Temp" Water Room Temp + Heated Heated Water Thermocou ple Module (C) -1.6 20.5 22.7 57.9 98.5 RTD (ohms) 100.5 105.8 108.3 122 136 24
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95 100 105 110 115 120 125 130 135 140 -20 0 20 40 60 80 100 120 f(x) = − 0 x² + 3.14 x − 296.19 R² = 0.99 RTD Resistance (Ω) Temperature (C) Figure 18: RTD Temperature vs Resistance The Graph above shows that the slope is a linear relationship, which means as the resistance increases the temperature increases. 4. Data acquisition of TC and determination of response time Table 5 and graph (Figure 19) below represents the Transient Analysis Cold to Hot from the enclosed type thermocouple. Table 5: LabView Software data (cold to hot) Time (sec) Temperature (C) 0.16 15.39477 0.2 24.52082 0.3 47.3224 0.4 62.13902 0.5 70.89153 25
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0.6 76.97129 0.7 81.14288 0.8 84.55118 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0 10 20 30 40 50 60 70 80 90 Cold to Hot (enclosed) Figure 19: Transient Analysis Cold to Hot Table 6 and graph (Figure 20) below represent the Transient Analysis Hot to Cold from the enclosed type of thermocouple. Table 6: LabView Software data (hot to cold) Time (sec) Temperature (C) 7.38 98.20386 7.4 96.32197 7.45 86.83902 7.5 75.44552 7.55 64.04716 7.6 54.55279 7.65 46.58255 7.7 39.73198 26
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7.75 34.40786 7.8 29.4648 7.85 25.66733 7.87 24.13864 7.3 7.4 7.5 7.6 7.7 7.8 7.9 0 20 40 60 80 100 120 Hot To Cold (enclosed) Time (s) Temperature (C) Figure 19: Transient Analysis Hot to Cold Table 6: Calculations of Experimental Phase Lag for High Pass Filter Time (s) Temperature (C) ln ¿¿ 0.16 15.39477 0 0.2 24.52082 -0.14152 0.3 47.3224 -0.61929 0.4 62.13902 -1.12677 0.5 70.89153 -1.62192 0.6 76.97129 -2.21087 0.7 81.14288 -3.01016 0.79 84.16985 -5.20047 27
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0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 -6 -5 -4 -3 -2 -1 0 f(x) = − 6.46 x + 1.37 R² = 0.93 Transient analysis Cold to hot enclosed Transient analysis Cold to hot enclosed Linear (Transient analysis Cold to hot enclosed) Time (s) ln((( − _ ))/(( _0− _ ) )) 𝑇 𝑇 ∝ 𝑇 𝑇 ∝ Figure 15: Transient Analysis Linear Cold to Hot The figure 15 above represents the graph of Transient Analysis Linear Cold to Hot and the relationship between time and ln ( ( T − T ∝ ) ( T 0 − T ∝ ) ) . These results were obtained from the LabView Software. Y =− 6.4608 x + 1.3728 m = tan θ =− 6.4608 θ = tan − 1 ( − 6.4608 ) = ¿ − 1.417 ¿ ResponceTime = 1 m = 1 − 6.4608 =− 0.1548 sec 28
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Discussion In this experiment, we’ve measured many types of water temperatures with many different types of methods. The beakers we measured were filled with ice cold water, hot boiling water, water in the room temperature, mixture of ice-cold water and water in room temperature, and mixture of hot water and water in room temperature. The first method we used is the use of thermocouple. With this device we were able to obtain data of the relationship of temperature and voltage and compared it to the linear equation obtained from Microsoft Excel. Next, we used the thermistor method to obtain the change of resistance and temperature. As we can see in the graph we have proven that the relationship between the thermistor resistance and temperature are inverse proportion. The third method we used in this experiment is the use of RTD, as usual we used this device to measure the different water temperatures. As the graph shows we obtained the linear relationship between resistance and temperature. 29
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Conclusion In conclusion, we were able to understand the various measurement tools used to measure the temperature of water, such as thermistor, thermocouple, resistance temperature detector (RTD). Also, we main reason the two types of values were close and not exact because the set frequency and predicted frequency were closely different. Also, there’s a possibility of a measurement error from the oscilloscope and other stuff that were used to collect data. In the end we understand that frequencies change and there is a low chance of obtaining the perfect frequency. 30
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Bibliography Holman, J. Experimental Methods for Engineers 8 th edition . Mc Graw Hill. Zhu, C. (2009). Me 343 Laboratory Introduction . The Vernier. (2023, June 16). LabQuest Mini - Vernier . Vernier Science Education. https://vernier.com/product/labquest-mini/ Industrial Quick Search. (n.d.). Thermocouple: What is it? How Does it Work? Types Of . IQS Directory. https://www.iqsdirectory.com/articles/thermocouple.html Support, P. (2019, October 18). Improving Phidgets Hardware Reliability - Phidgets Support . Phidgets Support. Retrieved June 17, 2023, from https://www.phidgets.com/docs/Improving_Phidgets_Hardware_Reliability#Device_Res ets_.28Due_to_Grounding_Issues.29 31
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Appendix Detailed Sample Calculation : S = dR dT = a R 0 = β + 2 γT R =− 0.0018 T 2 + 3.1382 T − 296.19 ¿ 296.19 ( − 0.0000060772 T 2 + 0.01060 T − 1 ) T = 25 ℃ β =− 0.0000060772 a = 0.0106 S = a + 2 βT Sensitivity S = 0.0106 + 2 ∗ ( − 0.0000060772 ) ∗ ( 25 + 273.15 ) = 0.006971 Nomenclature: Symbol Description I Current S Sensitivity T Temperature V Voltage t Time K Absolute temperature 32
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R Resistance ρ Resistivity a Resistance temperature coefficients Original Data: Beaker Ice Water Ice Water + Room Temp "Room Temp" Water Room Temp + Heated Heated Water IR Detector (C) -1 15 20 58 97 Thermocou ple Module (C) -1.6 20.5 22.7 57.9 98.5 RTD (ohms) 100.5 105.8 108.3 122 136 Thermister (k ohms) 7 3.65 2.74 0.68 0.23 Open thermocou ple (mV) -5.67 -4.8 -0.53 -0.48 -0.87 Closed thermocou ple (mV) -0.906 -0.37 -0.118 1.258 2.44 IR device (mV) 0.548 0.202 0.047 0.9 1.87 33
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ME 343 Laboratory Instructions Safety Hazards Instrumentation Laboratory Room 214 HAZARD: Rotating Equipment / Machine Tools Personal Protective Equipment : Safety Goggles; Standing Shields, Sturdy Shoes. Personal Care 1. Do not wear loose clothing, Neck Ties/Scarves; Jewelry (remove). 2. Tie back long hair. HAZARD: Heating – Burns Personal Protective Equipment : High temperature gloves; High temperature apron. HAZARD: Electrical - Burns / Shock Personal Care: Take Care while doing electrical connections, particularly with grounding; do not use frayed electrical cords. HAZARD: Water / Slip Hazard Personal Care: Clean any spills immediately. HAZARD: Noise Personal Protective Equipment: Ear Plugs 34
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Measurement of Temperature & Sensor Characteristics Objectives: 1. Temperature measurement by Thermocouple (TC) 2. 2. Additional methods of Temperature measurement i. Resistance Thermometer (RTD) ii. Thermister iii. Infrared Thermometer 3. Study of sensor characteristics i. Sensitivity of Thermister ii. Signal Drifting (Self Heating) of Thermister iii. Response Time of Thermocouple Major Equipments : Thermocouple (K type), Platinum Resistance Thermometer (RTD), Thermister, Infrared Thermometer, Digital Multimeter, Whestone Bridge, TC Module, Electric Heater Procedure : 1) Temperature Measurement with Thermocouple (TC) a. Connect a Thermocouple (type K) to the TC module and TC module to a digital voltmeter. Use this as the reference standard for temperature measurement. b. Put the TC into a beaker filled with ice cubes and small amount of water (avoid direct contact between thermocouple and beaker wall). Read output of voltmeter reading. Note that, TC module reading is in °C or °F. c. Remove the TC module and connect TC directly to the voltmeter and take measurements (reading is now in mV). d. Prepare a beaker of boiling water with electric heater. Record the TC readings with and without the TC module. e. Repeat steps 2 and 3 for Room temperature (about 24°C), 50°C and 75°C and 100°C by mixing ice and boiling water. 35
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2) Temperature Measurement with Platinum Resistance Thermometer (RTD) a. Connect a Platinum Resistance Thermometer to a digital voltmeter, ohms scale. b. Record the readings of voltmeter for water temperature at 0, 24, 50, 75, and 100°C. Use the TC reading (with module) as the standard reference. 3) Temperature Measurement with Thermister a. Connect a Thermister to a digital voltmeter, KΩ scale. b. Record the readings of voltmeter for water temperature at 0, 24, 50, 75, and 100°C. Use the TC reading (with module) as the standard reference. 4) Temperature Measurement with Infrared Thermometer a. Connect an Infrared Thermometer to a digital voltmeter, KΩ scale. b. Record the readings of voltmeter for water temperature at 0, 24, 50, 75, and 100°C. Use the TC reading (with module) as the standard reference. 5) Self-heating with Thermistor Measurement at Room Temperature a. Connect the Thermistor to a Wheatstone bridge and measure the fixed resistors Rfa and Rfb. b. Set the input voltage to 1 Volt on D.C. power supply and adjust the variable resistor to balance the bridge at room temperature (eo < 5 mV). Record Radj. c. Set the input voltage to 10 Volts on D. C. Power supply wait for self-heating of system, then adjust the variable resistor to balance the bridge and read Radj. 6) Transient Temperature Measurement and Response Time of Thermocouple with LABVIEW Data Acquisition System a. Switch the National Instrument interface panel to “Thermocouple” (not to BNC!) and “Temperature ref”. b. Connect the Thermocouple to National Instrument interface panel to “Thermocouple”. c. Open a VI file (c:\me343\transient-T.vi) d. Setup parameters: 36
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e. Prepare beaker of boiling water and icy water (ice with little water in beaker). f. Insert the TC into a beaker filled with boiling water (placed on a heater). g. Set the sampling frequency in “windows/show diagram”. The sampling frequency is set by selecting the value of sampling period in ms (say, 10 ms of sampling period yields a sampling frequency of 100 Hz or 100 sampling points a second). Save and close the diagram. h. Start the data acquisition process by clicking run button ( > )on LABVIEWData Acquisition System. Quickly relocate the TC from the boiling water into icy water. Stop the sampling as soon as the temperature is stabilized. i. Reset the time window by selecting the desired time range on the time window (i.e., reset the lower limit by replacing the most left value on the time scale while the high limit on the most right) so that the transient curve is best shown on the window. Record at least 10 points from the transient curve. j. Repeat steps 6 and 7 by quickly relocating the TC from the icy water into boiling water. k. Find thermal response time of thermocouple using lumped capacitance model. 37
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Bonus Question 1. Determination of β, direct least square method; Include discussion, logarithmic plot (linearization) 0 0 0 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 f(x) = 3576.86 x − 11.09 R² = 0.99 ln R vs Inverse of Temperature (Thermistor) 1/T ln R The figure above is the graph for the Thermistor ln(R) vs Inverse temperature. As we can see in the graph the equation is of this diagram is: y = 3576.9 ( 1 / T )− 11.092 . This shows that β = 3576.9 , and R² = 0.9908. 38
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2. Compare the response time of open type and encased type of Thermocouple. Open Type Enclose Type Tim e Temperatur e ln ( ( T − T ∝ ) ( T 0 − T ∝ ) ) Temperatur e ln ( ( T − T ∝ ) ( T 0 − T ∝ ) ) 0.22 29.8469 -0.23443 6.241723 0 0.23 32.49761 -0.2841 33.64378 -0.34354 0.24 35.17193 -0.33684 52.64396 -0.67794 0.25 37.44011 -0.38386 65.95518 -1.00395 0.26 39.73198 -0.43373 76.20841 -1.3562 0.27 41.61785 -0.47672 84.9325 -1.80136 0.28 43.90937 -0.53157 90.2466 -2.21925 0.29 45.81881 -0.5797 92.89134 -2.5179 0.3 47.3224 -0.61929 94.41612 -2.74185 0.31 49.2316 -0.67193 95.94081 -3.03087 0.32 50.75887 -0.71614 96.70312 -3.21425 0.33 52.64396 -0.77354 97.46541 -3.43898 0.34 53.78927 -0.81009 98.20386 -3.71884 0.35 55.31628 -0.86101 98.58499 -3.90117 0.36 56.46147 -0.90097 98.96611 -4.12432 0.37 57.96447 -0.95596 98.96611 -4.12432 0.38 59.87292 -1.03045 99.72834 -4.81748 0.39 61.01792 -1.07796 99.72834 -4.81748 39
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0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 -6 -5 -4 -3 -2 -1 0 f(x) = − 6.46 x + 1.37 R² = 0.93 Transient analysis Cold to hot enclosed Time ln((( − _ ))/(( _0− _ ) )) 𝑇 𝑇 ∝ 𝑇 𝑇 ∝ Figure for enclosed Thermocouple 0.2 0.22 0.24 0.26 0.28 0.3 0.32 0.34 0.36 0.38 0.4 -6 -5 -4 -3 -2 -1 0 f(x) = − 28.17 x + 5.93 R² = 0.98 Transit analysis Cold to Hot open Time ln((( − _ ))/(( _0− _ ) )) 𝑇 𝑇 ∝ 𝑇 𝑇 ∝ Figure for Open Thermocouple 40
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Calculation for Open Thermocouple y =− 28.167 T + 5.9326 m = tan ( θ ) =− 28.167 θ = tan − 1 ( − 28.167 ) =− 1.5353 Responcetime ( τ ) = 1 m = 1 − 28.1167 =− 0.03550 sec Calculation for Closed Thermocouple y =− 6.4608 x + 1.3728 m = tan ( θ ) =− 6.4608 θ = tan − 1 ( − 6.4608 ) =− 1.4172 Responcetime ( τ ) = 1 m = 1 − 6.4608 =− 0.1548 sec The calculations and graph show that the open thermocouple is more sensitive than close thermocouple and the open thermocouple’s response time is very quicker than the closed one. 41
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