I. Objective
To study the principles of operation and calibrate 2 resistance temperature sensors and a thermistor. To calibrate a mercury-in-glass thermometer. To determine the resolution of the resistance thermometers.and their temperature coefficients of resistance. To determine the uncertainty in the temperature standard used in the calibration.
II. Apparatus
1. Temperature controlled bath
2. Platinum resistance sensors
3. Thermistor
4. Nickel resistance sensor
5. Precision mercury-in-glass thermometer
6. Digital ohmmeter
III. Principles and Background
The term resistance temperature sensor usually denotes a metallic conductor whose resistance increases with temperature. The term thermistor denotes a semiconductor whose resistance usually decreases with increasing temperature. Devices to measure resistance such as ohmmeters and resistance bridges are used with resistance temperature sensors or thermistors to make resistance thermometers. The accuracy and resolution of such a thermometer depends upon the properties of the sensor and of the resistance measuring device.
For a metallic conductor, the relationship between electrical resistance and temperature can be adequately approximated by a quadratic equation,
R

R o
1

 a

T

T o
 
T

T o

2

(1) where R o
is the resistance of the sensor at a known reference temperature T o
, R is the from calibration. In this experiment, you may try a linear function. You may find that a linear approximation to eqn. (1) provides an accurate calibration.
In the case of thermistors, an exponential equation often applies:
R

R o e



1
T

1
T o


(2) where R is the resistance of the thermistor at the temperature T, and R resistance at the temperature T o
(Kelvin or Rankine) and ß is characteristic of the semiconducting material. o
is the
. The temperatures are expressed in degrees absolute

In this experiment, sensor 2 is a thermistor, and sensor 3 (platinum) and sensor 1
(nickel) are resistance temperature sensors to be calibrated. Sensor 4 is the platinum resistance temperature sensor which is serving as the standard.
In order to use the thermistors or resistance temperature sensors to measure temperature, the temperature-resistance relation for each sensor must be established by calibration. In this experiment three sensors will be calibrated using a controlled temperature bath and a platinum resistance thermometer (sensor 4) as the temperature standard. Platinum resistance thermometers are noted for their stability and are used to interpolate between fixed points in the International Practical
Temperature Scale in the range from -260ºC to +950ºC The platinum resistance temperature sensor used in this experiment was made by Rosemount Corporation for industrial use and has not been calibrated as carefully as the "Standard Sensor" which is used by the Bureau of Standards. The "Standard Sensor" was obtainable from
Rosemount at a higher price than we were willing to pay for Experiment 4. The calibration data for sensor 4 is in Table 1.
Table 1. Calibration data for MODEL 104 Platinum Resistance
Temperature Detector (Rosemount Engineering Co.)
Resistance of Sensor
(Ohms)
Temperature
(  F)
400.20
407.27
416.08
424.85
433.63
442.39
451.14
459.85
468.55
477.25
32
40
50
60
70
80
90
100
110
120
485.95
494.64
503.64
511.94
520.55
130
140
150
160
170
529.15
537.75
546.35
554.91
180
190
200
210
563.36 220
Equation (3) may be used to calculate the temperature-resistance relationship as well.
It is merely a least squares quadratic fit to the table. Equation (3) has been expressed in

C .
T = (6.4989 x 10
-5
) R
4
2
+ (0.57722) R4 - 241.41,

C (3)
The actual temperature may differ from the one in the table or the one given by equation (3) by as much as 0.2

C , since we were not willing to pay for a better

calibration. The estimate of the error was provided by the manufacturer after a study of several sensors and is treated like a random error since we do not know its sign or magnitude.
In order to determine the uncertainty in the bath temperature, it is necessary to combine the uncertainties due to several factors. The calibration uncertainty for sensor
4 must be combined with the uncertainty resulting from uncertainty in the resistance measurement (the ohmmeter specifications are given below) and uncertainty resulting from actual fluctuations in the bath temperature.
The sensitivity of a sensor is given by the slope of the calibration curve. In the case of the sensors to be calibrated in this experiment, the sensitivity, S, is given by:
S
 dR dT
, ohms/deg (4)
The resolution of a thermometer is defined as the smallest change in temperature which can be detected by the thermometer. It depends upon the sensitivity of the sensor and the smallest change in resistance which can be measured by the ohmmeter (i.e., the resolution of the ohmmeter). If the resolution of the ohmmeter is  R, then the resolution of the thermometer,  T is given by:

T


S
R
(5)
The temperature coefficient of resistance  is often used to describe sensors. It is merely the sensitivity expressed as a percent of the resistance of the sensor.
 
1 dR
x 100, % per

C
R dT
(6)
The ohmmeter used in this experiment (HP 3468A) permits measurements to be made with as many as 6 digits. The resolution of the ohmmeter equals the resistance represented by a change of one digit in the least significant place (i.e., the right most digit). The accuracy as given by HP is shown below (see lab 3, p. 3-3 for an example calculation):
Range Upto
30 
300 
3 k 
30 k 
300 k 
3 M 
30 M 
Accuracy Up to One Year After Calibration
(% of reading + number of counts)
.034 + 41
.017 + 5
.016 + 2
.016 + 2
.016 + 2
.016 + 2
.078 + 2
You will note that the resolution of the ohmmeter is better than the accuracy. That is, it is possible to detect small changes in resistance and still be uncertain about the actual value. It is also likely that the uncertainty in the temperature measurements will be larger than the resolution. You will be able to detect small changes in temperature

but will not know exactly what the temperatures are. This is not unusual when measuring temperatures since it is difficult to get absolute calibration standards with high accuracy. However, it is less difficult to produce sensors which are highly sensitive.
The temperature sensors used in this experiment are immersed in a thermostatically controlled bath. The thermostat is a thermometer which contains a wire in the thermometer stem. The position of the wire is determined by the nut riding on the threaded shaft and can be changed by turning the magnetically coupled adjusting cap.
An electrical circuit detects contact between the wire and the mercury. The device is called a contact thermometer. When the wire is not in contact with the mercury, the
IV. Procedure
1. Record the initial temperature of the bath with the mercury thermometer and 4 sensors. Then turn the power control knob to 100 and turn on the controller. This will turn on the pump and the heater if the thermostat setting is higher than the bath temperature. heater is turned on. This on-off regulation can not provide absolutely constant temperature but causes the temperature to oscillate about the point determined by the position of the wire. Thus the temperature cycles with the same period as the heater.
You will use a high resolution sensor to study these cycles. The temperature controller has a variable power heater and a pump to maintain vigorous mixing.
2. Increase the temperature in the bath by about 10

C by setting the contact thermometer at 10

C above room temperature and turning the power control to its maximum setting. When the temperature has reached the set point, the red light will go out. The light is on when the controller is supplying heat to the bath. Adjust the heating power so that the 'on cycle' and 'off cycle' are of similar duration. After the bath temperature has stabilized, take readings for all four sensors and the mercury-in-glass thermometer. Be sure to record multiple measurements of the fluctuating signals for each
temperature. You will need these measurements to obtain an estimate of precision.
3. Increase the temperature in steps of 10

C , taking readings described in step 2 at each step. Do not exceed 70

C .
V. Suggested Data Analysis
1. Use the data for sensor 4 to determine the temperature of the bath at each calibration point. Prepare a calibration table by tabulating the bath temperature and the resistance of sensors 1, 2 and 3 as well as the mercury-inglass thermometer.
2. One of the most important issues in the calibration of a device is the accuracy of the calibration. Determine the uncertainty in the temperature of the bath at one point in the middle of the range covered (i.e. data point # out of 5). Be sure to consider accuracy of the ohmmeter, accuracy of the ohmmeter, sensor
4 calibration, and bath temperature fluctuations.
3. Describe each source of uncertainty; compare their magnitudes; determine which source is most significant; discuss possible ways to reduce the magnitude of each source.

4. Plot the natural log of resistance of the thermistor (sensor 2) as a function of


1
T

T
1 o

 . Remember that T is expressed as an absolute temperature. A straight line should result if the sensor is described by equation (2). Be sure your graphs include error bars, a curve fit and its uncertainty from a regression analysis. Choose T o
equal to 300 K and find R graph. What is the uncertainty in  ? o
and β from the
5. Prepare a calibration graph of resistance versus temperature for sensors 1, 2 and 3. Include the results of a regression analysis including uncertainty of the metal RTDs. You are only expected to insert a trend line for the non-linear thermistor.
6. Find the sensitivity and temperature coefficient of resistance for all four sensors at a temperature near the midpoint of the range. Use the curve fit results from question (5) to find the sensitivity. Find the resolution of the resistance thermometers at the same temperature. Compare these values with the uncertainty in the bath temperature.