Experiment 4
Calibration of Temperature Sensors
I.
Objective:
The purposes of this experiment are to: (1) acquaint you with common thermometry instruments,
(2) impart a fundamental understanding of the physical principles that underpin these devices, and
(3) point out the respective advantages and disadvantages that these instruments offer.
II.
Apparatus
3 ½” Floppy Diskette (Supplied by the student.)
Personal Computer Running LabView
Keithley 2000 6 ½ Digit Multimeter Equipped with 2000-SCAN MUX Card
Julabo F12-MD PID Temperature-Controlled Bath
Type-J 0.250” Dia. Sheathed Thermocouple Omega GJ QSS-14G-12
Type-J 0.0625” Dia. Sheathed Thermocouple Omega GJ QSS-116G-12
Type-T 0.250” Dia. Sheathed Thermocouple Omega GT QSS-14G-12
Type-T 0.0625” Dia. Sheathed Thermocouple Omega GT QSS-116G-12
Industrial Thermistor Omega ON-970-44006 (10 k @ 25 C)
Industrial Resistance Temperaure Detector (RTD) Rosemount 563792 1, S/N 0693603
Precision Mercury Thermometer (NIST Certified) Omega GT-3554Y (-1-100 C +/- 0.1 C)
Standard Alcohol Laboratory Thermometer Fisher 14-997
III.
Introduction:
Thermometry is an essential element in many industrial processes. For example, when extruding
polymers such as polyethylene, the extruder is partitioned into several thermal zones. The
temperature of each zone must be maintained within strict limits. If for instance, the temperature
in any zone is too great, then the polymer will burn and carbon will be deposited on the interior
walls of the extruder. This carbon is nearly impossible to remove and it has an unfortunate
tendency to break-off when the extruder is in operation. These chunks of carbon contaminate the
end product. The product is subsequently sent to a landfill because it can be neither sold nor
recycled. Clearly, control relies upon accurate measurement of the operating temperatures.
Thermometers:
These devices are the oldest thermometry instruments and their use is well known. Two
thermometers are used in this experiment. One should be familiar with the standard alcohol
thermometer. The precision thermometer uses mercury and it has been calibrated at NIST.
Thermocouples:
These devices consist of two dissimilar metals that are joined at the ends. When these junctions
are held at different temperatures, a thermoelectric potential difference exists. This is called the
Seebeck effect and one may measure the thermoelectric potential ( or electromotive force, emf) to
infer temperature junction temperatures. The potential, temperature range, and sensitivities of
thermocouples depend upon the combinations of wire used. The Type-T thermocouples employ
copper and constantan and the Type-J thermocouples employ iron and constantan.
Thermoelectric potentials are typically small (mV). A calibration relation e.g., formula or table,
relates temperature to thermoelectric potential. The NIST (formerly NBS) thermocouple tables
comprise standard calibrations for the most popular thermocouple types. The accuracy of these
tables is approximately +/- 2 degrees C. Please refer to the introductory section of Experiment 3
for more complete information on thermocouples.
Resistance Temperature Detectors (RTD):
These devices use the property that the electrical resistance of materials varies with temperature.
RTDs typically consist of a platinum wire enclosed within a sheath. The Callendar-Van Duesen
calibration equation,
T (C  )   (0.01  T (C  )  1)  (0.01  T (C  )
,
R()  R0 ()  R0 ()   
(1)
  (0.01  T (C  )  1)  (0.01  T (C  ) 3 )



relates wire resistance to temperature. The symbols R0 , , , and  represent calibration
constants. The factory-determined values of these constants are stamped on the metal tag
attached to the RTD used in this laboratory. Record these constants and the serial number of the
RTD in your lab notebook. Note that the constant  is used only when the measurement
temperature is below 0 C, i.e.,   0 when T  0 C  . The manufacturer reports the accuracy of
Eqn. (1) to be  0.06 C over the range from 0 to 100 C when their calibration coefficients are
used. The calibration constants of the RTD are NIST (National Institute for Standards and
Technology) traceable. This implies that the RTD was calibrated against internationally accepted
temperature standards.
Thermistors:
These devices also use the property that the electrical resistance of materials varies with
temperature. In contrast to RTDs, thermistors are made of semiconductor materials. Unlike
metals, the temperature-resistance dependence of semiconductor materials is strongly non-linear.
Consequently among thermometry instruments, thermistors generally have the greatest
sensitivity, but their useful range is comparatively small. The calibration equation are typically of
the form
1
 A  Bln R   C ln R 3 .
T (K )
(2)
Julabo F-12MD Constant Temperature Bath:
The following diagrams and instructions are exerpted from the Julabo manual.
Operating controls and functional elements
9
10
11
12
7
5
6
!
1a
8
2
3
4
13a
14
16a
15a
19
24a 24b
1b
13b
23 22
25
21
25
16b 15b 17 18
Rear view
1a/1b
Mains power switch, illuminated,
for circulator / cooling machine
2
Start / stop key
3
Working temperature T1
4
Working temperature T2
5
High temperature warning limit
6
Low temperature warning limit
7
Safety temperature
8
Adjustable excess temperature protection
(safety temperature)
9
MULTI-DISPLAY (LED) temperature indication
10
Cursors left/right
11
Edit keys (increase/decrease setting)
12
Enter key (store)
Error! Objects cannot be created from editing field codes. Indicator light - Alarm
Indicator light - Cooling
Error! Objects cannot be created from editing field codes. Indicator light - Heating
13a
Connector: Control cable for cooling machine
13b
Connector: Cooling machine control
5
14
1
9
6
RS232C interface
15a
Mains fuses for circulator
15b
Mains fuses for cooling machine
16a
Mains power cable for circulator
16b
Mains power cable with plug
17
Built-in mains outlet for connection of circulator
18
Selector dial for cooling machine
Position "1" for operation with MD circulator.
19
Control cable for cooling machine
21
Removable venting grid
22
Drain tap
23
Drain port
24a
Pump connector for feed
24b
Pump connector for return
Only for water cooled models:
25
Cooling water OUTLET / INLET
Filling / draining
Filling
Take care that no liquid enters the interior of the circulator.
 Recommended maximum filling level with water as bath liquid: 25 mm
below the tank rim
 Recommended maximum filling level with bath oils: 40 mm below the
tank rim
ATTENTION: the volume of bath oils will increase due to
thermal expansion when the bath temperature rises.
Exercise CAUTION when emptying hot bath liquids!
Start:
 Press the start/stop key.
- The MULTI-DISPLAY (LED) indicates the actual bath temperature.
(example: 21.0 °C)
- An illuminated indicator light in the "T1" or "T2" key indicates the
activated working temperature.
Stop:
 Press the start/stop key.
The MULTI-DISPLAY (LED) indicates the message "OFF".
Setting the temperatures
Setting the working temperature "T1":
 Press the setpoint key
.
The indicator light blinks and the value previously set appears on the
MULTI-DISPLAY (LED).
 Use the cursor keys
to move left or right on the display until
the numeral you wish to change is blinking.
 Use the increase/decrease arrows
to change the selected
numeral (-, 0, 1, 2, 3, ... 9).
 Press enter
to store the selected value (example: -15.0 °C).
The working temperature is maintained constant after a short heat-up time
(e. g. -15.0 °C).
Setting the working temperature "T2":
 Press the setpoint key

Same procedure

as with "T1"

(example: 25.0 °C).
.
Selecting the working temperature:
 Press the setpoint key
 Press the setpoint key
and then enter
and then enter
.
.
Technical specifications
MD
Display resolution
°C
0.1
ATC - Absolute Temp. Calibration
°C
±3
Heater capacity
at 115V
at 230 V
Pressure pump:
pressure/flow rate
Watts
Watts
head max./Lpm
Electrical connectors:
Alarm output
Computer interface
1000
2000
11.5 ft/15
24-0 V DC / max. 25 mA
RS232C
Mains power connection
V/Hz
115/60
V/Hz
208-230/60
All measurements have been carried out at:
rated voltage and frequency
ambient temperature: 20 °C
Technical changes without prior notification reserved.
Working temperature range
°C
Temperature stability
°C
±0.01
Cooling capacity
(bath liquid: ethanol)
°C
Watts450 320 140 30
Refrigerant
F34
F12
-34 ... 200
-25 ... 200
±0.01
+20 0 -20 -30
200 120 25
+20
0 -20
R134a
R134a
24x30/15
15x13/15
Bath opening/bath depth:
WxD/H
Bath volume: from...to
liters
Dimensions:
WxDxH
Shipping weigth
Mains power connection V/Hz
Cm.
14 ... 20
In.
Cm.
3 ... 4,5
15x23x25
38x58x61
6x9x10
20x36x55
lbs/kg
106/45
51/23
115/60
115/60
Keithley 2000 DMM:
The use of the Keithley 2000 is described in the following section. One should note that the connections and
measurement procedures are described to facilitate the uncertainty analysis, but physically, these connections are
automatically made by the SCAN-2000 multiplexer card.
Voltage Measurements:
To measure voltage with the Keithley 2000, high and low leads are connected to the inputs depicted in Figure 1.
Sense
Input
(+) Red Lead
Hi
(-) Black Lead
Lo
Figure 1: DC voltage measurement instrument connections.
Once the leads have been properly connected, the “DCV” function is selected---one should watch for the DCV
LEDS to appear when the Keithley is in scan mode during data acquisition. The Keithley 2000 is a 6 ½ Digit
Multimeter. The DC voltage accuracy is listed in Table 1.
Table 1. Keithley 2000 DC Voltage Accuracy
Range
100.0000 mV
1.000000 V
10.00000 V
100.0000 V
1000.000 V
Resolution
0.1 V
1.0 V
10 V
100 V
1 mV
Accuracy (ppm RDG + ppm RANGE)
50 + 35
30 + 7
30 + 5
45 + 6
45 + 6
Keithley reports their multimeter accuracies with (ppm of RDG + ppm of RANGE), where 1 ppm=10 -6. For
example, suppose 5.00000 V is measured on the 10.00000 V range. Then the accuracy estimate is (30106
5.00000 V+510-610.00000 V)= 200 V.
Resistance Measurements:
The Keithley 2000 has two modes for measuring resistance. The two-wire mode is illustrated in Figure 2.
V1
i
V2
Figure 2. Two-wire resistance measurement circuit.
One should note that in this mode, the multimeter passes a current through the restive load and it simultaneously
measures the voltage across the terminals. This method is employed to measure the thermistor resistance.
The two-wire mode is simple, but it has the undesirable consequence that the resistance of the lead wires is included
in the measurement. This could introduce substantial error while measuring small resistances.
The four-wire mode compensates for lead wire resistance. The circuit is depicted in Figure 3.
Input Hi
i
Hi
Sense
Lo
Input Lo
Figure 3. Four-wire resistance measurement circuit.
The four-wire technique uses separate wires to apply a current and to measure the voltage drop. Consequently only
the voltage drop across the resistive load is measured, and the effects of the lead resistance are eliminated. The fourwire method is used to measure the RTD resistance. The connections are illustrated in Figure 4.
Sense
Input
Red
Red
Hi
White
White
Lo
Figure 4. Four-wire resistance measurement instrument connections.
The accuracy of the resistance measurements are estimated from Table 2.
Table 2. Keithley 2000 resistance measurement accuracy.
Range
100.0000 
1.000000 k
10.00000 k
100.0000 k
1.000000 M
10.00000 M
100.0000 M
Resolution
100 
1 m
10 m
100 m
1
10 
100 
Accuracy (ppm RDG + ppm RANGE)
100 + 40
100 + 10
100 + 10
100 + 10
100 + 10
400 + 10
1500 + 30
The measurement accurcies listed in Table 2 apply to both two- and four-wire modes.
Procedure:
1.
Inspect all electrical connections. Verify that the Keithley 2000 will use the rear inputs i.e., the “Inputs” button
is depressed.
2.
Verify that the liquid level in the circulator bath is within acceptable limits.
3.
Prepare the ice bath. Fill the thermos bottle with ice and DI water so that there are no air gaps. Adding water
serves two purposes. a) Fills all the air pockets in the ice filled thermos bottle and b) Ice water mixture is at 0 C
(which is what we want), whereas just ice could be at a lower temperature than 0 C.
4.
Record instrument data e.g., thermometer resolution, RTD calibration constants, and serial numbers.
5.
Energize equipment i.e., turn on the F-12 Circulator bath, MD controller, Keithley 2000, computer, and
monitor.
6.
Activate the Julabo MD controller and adjust the setpoint temperature to 10 C. One should note that it takes
approximately 35 minutes for the water bath to cool from room temperature to 10 C. The approximate bath
temperature is indicated by the Julabo MD LED display.
7.
Start up the PC and the Lab4B data acquisition software should start up on its own. If it doesn’t or if the PC is
already booted up, click on the Lab4B icon on the desktop. when prompted choose “Start New Calibration” if
you are starting to calibrate for the first time. If the program had crashed midway and you just started it back on,
choose “Continue Previous Calibration”.
8.
When the bath reaches setpoint temperature, acquire data:
a.
b.
c.
d.
9.
Select the trial to acquire (1-10). One should note that 10 measurements are suggested.
Read the Alcohol and Mercury thermometers and enter the measurements in the appropriate boxes for these
instruments. These boxes are located below the Data Table. One can either enter the value in these boxes or
set the adjacent slider at the appropriate position. The former is a better option
Press the “Acquire” button to obtain the output from the other instruments.
Repeat steps a-c for subsequent trials.
Write the data to a file:
a.
b.
Press the “Write Data to File” button.
Use the pull-down menu to select the directory to which the file will be written. Please choose the
“C:\Lab4B_student” directory. This is the default directory that the software prompts you to save in.
c.
d.
e.
Name the output file and click “Ok.” One should note that this file name must be unique and that the
default extension is “.txt” to ensure that Windows will recognize that it is an ASCII file.
Use Windows Explorer to view the data file in notepad.
Once you saved the data, you can click on the clear button to clear the data from the screen and proceed to
calibrate at other temperatures.
10. Adjust the setpoint temperature and repeat steps 8 and 9 for bath temperatures of approximately 15, 20, 25, 30,
and 40 C.
11. Copy the data files to the 3 ½” floppy diskette.
12. Press the “End DAQ” button to stop the VI and close all application windows.
13. Shut down the computer (Using the “Start” menu).
14. Turn off all equipment.
15. See the TA on duty to check-out.
16. Perform data reduction and uncertainty analysis.
17. Write laboratory report.
Data Analysis:
1.
Consolidate the multiple samples to single measurements and estimate total uncertainties:
a. Compute mean measurements of each device at every setpoint temperature.
b. Estimate the precision uncertainties of the mean measurements (assume 95% confidence level).
c. Estimate the bias uncertainties of the mean measurements.
d. Estimate the total uncertainty of each mean measurement.
Document the procedure used to complete steps a-d and tabulate the results of each step. After completing step d,
tabulate setpoint temperatures, mean meaurements and their appropriate uncertainties. A table for each instrument
should be prepared (eight tables). Of note, one must adhere to significant figure reporting conventions to receive
credit for this step. Examine the tabulated results of steps a-d. For each instrument, determine whether bias or
precision limits the uncertainty of the measurement. Which measurements are the most precise? Which
measurements are the most accurate? How could the uncertainties of these measurements be reduced? What factors
contribute to the measurement uncertainty? Which can be controlled and which cannot? Could bath temperature
fluctuates contribute to uncertainty? Does the data support the assumption that the bath temperature is constant?
2.
Use the RTD data to determine the bath temperatures. Please note that the Callendar-Van Duesen equation and
the manufacturer’s calibration coefficients are employed. In addition, estimate the uncertainty in the RTD bath
temperature measurements. One should note that there are essentially two factors that contribute to the overall
uncertainty in this measurement. What are these factors? Which factor dominates? What would one need to do
to improve i.e., increase accuracy, of this measurement?
3.
One should recall that a calibration standard is by assumption, error-free. In actuality, they have uncertainty
and calibrating an instrument is essentially a procedure for substituting the uncertainty of the standard for the
uncertainty of the test instrument. Obviously, the uncertainty of standard must be smaller than the test
instrument for this to be a worthwhile endeavor. Thus the instrument with the smallest uncertainty is most
suitable to be the calibration standard. Determine which instrument yields the smallest temperature uncertainty.
Hints: The calibration coefficients of the thermistor are unknown, hence it cannot be a standard. It is better to
use a sensor with NIST traceable calibration as the calibration standard against which the other sensors are
calibrated. If the thermocouple reference tables and the thermocouple voltages were used to estimate the bath
temperature, what would the temperature uncertainties be? Further examination of the tables prepared in step
1d and the results of step 2 should whittle the choices for calibration standard down to two instruments. What
are these instruments? Which device is your choice for the calibration standard?
4.
Determine calibration equations for each instrument:
a. The relationship between the thermistor resistance and temperature is non-linear. The expression
R  A exp( BT ) , seems to fit the thermistor data well. R is the thermistor resistance and T is the bath
temperature (determined by the calibration standard). Determine the coefficients A and B using linear
regression. Plot both the thermistor data and the fitted line. Also, plot error bars and estimate the
uncertainty in the calibration equation.
b. Determine calibration equations for the thermometers---assuming of course, that neither is the calibration
standard. Use linear regression analysis and estimate the uncertainty in the calibration equation. Do these
instruments have offsets? If so, how do they compare to the instrument resolution?
c. Determine calibration equations for the thermocouples.
5.
Compute the sensitivity of each instrument.
References:
The Temperature Handbook Omega Engineering Inc., Stamford, CT 06907-0047
Beckwith, Marangoni, and Lienhard, Mechanical Measurements, Addison-Wesley.