İzmir Institute of Technology
CHEMICAL ENGINEERING DEPARTMENT
2008-2009 Spring Semester
CHE 310
CHEMICAL ENGINEERING LABORATORY I
Temperature Measurements
Objectives:
The purpose of this experiment is to measure the temperature of different systems at
ambient and low temperatures using bulb thermometers, thermocouples, platinum
resistance temperature detector and thermistor, and to compare the accuracy and the
precision of each device.
THEORY
Although most of us are familiar with the mercury bulb thermometer, there are many other
methods of temperature measurement. Included in this demonstration are thermocouples,
thermistors and platinum RTD (PRTD). All of them infer temperature by sensing some
change in a physical characteristic and has different specific properties which determine
their use and practical application.
The resistance of semiconductor and conductor materials is influenced differently by
temperature. In semiconductors, resistance increases as temperature decreases. These
effects are explained by the temperature dependence of conductivity in the material;
mobility of the charge carries increases with decreasing temperature. In conductors, as
temperature decreases, mobility of the charge carries increases and the number of carriers
stays constant. Therefore, resistance decreases.
Most commonly used temperature measurement methods are:




Thermometer
Thermocouple
Resistance Temperature Detector (RTD)
Thermistor
Advantages and disadvantages of these methods are summarized in Table 1.
Factors affecting the selection of temperature sensors:
 desired temperature range
 tolerable limit to the error in the measurement
 conditions under which the measurement is to be performed
 possibility of the sensor to be affected by contact (contact or non-contact T sensor)
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Table 1. Comparison of widely used temperature sensing technologies
Sensor type
Parameter
Advantages
Disadvantages
Thermocouple
Voltage vs T
Low cost
Simple
No moving parts, less likely to be
broken
Reasonably short response time
Reasonable repeatability and
accuracy
Most robust temperature sensor
available
Wide operating T range depending
on the wires used (-200 to1800oC)
No external power supply required
Interchangeable (due to standard
connectors)
Suitable for remote temperature
measuring and sensing
Non-linear
Relatively low stability
Low sensitivity
Low voltage output
Reference junction compensation
required
Low accuracy (system errors of
less than 1°C can be difficult to
achieve)
RTD
Resistance vs T
NTC thermistor
Resistance vs T
Linearity of electrical output is
better than thermocouples
Higher signal-to-noise ratio
High stability
Wide operating T range
Interchangeable over wide T
range
Suitable for remote temperature
measuring and sensing
Large change in resistance vs T
Fast time response
Small size
Inexpensive
Interchangeable to high tolerance
High stability
Suitable for remote temperature
measuring and sensing
Self heating
Requires a current source
Response time may not be fast
enough for some applications
Small change in resistance vs T
Sensitive to shock and vibration
Expensive
Operating temperature limited to
approximately -60 to 300oC
Current source required
Non-linear
Interchangeable over relatively
narrow T ranges
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Thermometer
A thermometer is an instrument that measures the temperature using a substance having a
property that changes in a regular way with its temperature. The most direct 'regular' way
is a linear one:
T(x) = ax + b
T
: temperature of the substance and changes as the property x of the
substance changes
a and b : constants depend on the substance used (may be evaluated by
specifying two temperature points on the scale, such as 0 for
freezing point of water and 100°C for its boiling point )
Liquid-in-Glass Thermometers are based on the fact that most fluids
expand on heating. The fluid is contained in a sealed glass bulb, and its
expansion is measured using a scale etched in the stem of the
thermometer.
The most widely used fluid is mercury, covering a wide temperature range
from -38°C to 356°C, although the introduction of a gas into the
instrument can increase the range to 600°C or beyond. Other fluids
include ethyl alcohol, toluene and technical pentane, which can be used
down to -200 °C. The mercury-in-glass thermometer contains a bulb filled
with mercury that is allowed to expand into a capillary. Its rate of
expansion is calibrated on the glass scale.
Thermocouple
Thermocouple is a thermoelectric temperature sensor
which consists of two dissimilar metallic wires that
are connected at two different junctions, one for
temperature measurement and the other for reference.
The temperature difference between the two
junctions is detected by measuring the change in
voltage (electromotive force, EMF) across the
dissimilar metals at the temperature measurement
junction.
Thermoelectric Effect
Thermocouples manipulate the fact that the electromotive force (EMF) between two
dissimilar metals is a function of their temperature difference. However, three major
effects are involved in a thermocouple circuit: the Seebeck, Peltier, and Thomson effects.
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The Seebeck effect describes the
electromotive force (EMF) existing
between two dissimilar metallic materials.
The change in material EMF with respect to
a change in temperature is called the
Seebeck coefficient or thermoelectric
sensitivity. This coefficient is usually a
nonlinear function of temperature.
EMF that is reversible and associated with
changes in temperature is called the Peltier
effect. Finally, the Thomson effect relates
the reversible thermal gradient and EMF in
a homogeneous conductor.
Thermocouple Circuit
Suppose that the Seebeck coefficients of two dissimilar metallic materials, metal A and
metal B, and the lead wires are SA, SB, and Slead respectively. All three Seebeck coefficients
are functions of temperature. The voltage output Vout measured at the gage is,
ref

Vout 
tip
S lead (T )
gage
ref

 S B (T )
tip
dT
dT
dx   S A (T )
dx
dx
dx
ref
gage
dT
dT
dx   S lead (T )
dx 
dx
dx
ref
Ttip
Tref
Ttip
Tref
Ttip
Tref
 S A (T )dT   S B (T )dT 
Tref
Ttip
 S
A
(T )  S B (T )dT
: temperature at the reference point
: temperature at the probe tip
Note that mathematically the voltage induced
by the temperature and/or material mismatch of
the lead wires cancels, whereas in reality the
lead wires will introduce noise into the circuit.
If the Seebeck coefficient functions of the two
thermocouple wire materials are pre-calibrated
and the reference temperature Tref is known
(usually set by a 0°C ice bath), the temperature
at the probe tip becomes the only unknown and
can be directly related to the voltage readout.
5
If the Seebeck coefficients are nearly constant across the targeted temperature range, the
integral in the above equation can be simplified, allowing one to solve directly for the
temperature at the probe tip,
Vout  S A  S B Ttip  Tref   Ttip  Tref 
Vout
S A  SB
In practice, vendors will provide calibration functions for their products. These functions
are usually high order polynomials and are calibrated with respect to a certain reference
temperature, e.g., 0°C. Suppose that the coefficients of the calibration polynomials are a0,
a1, a2, ..., an. The temperature at the probe tip can then be related to the voltage output as,
Ttip  a0  a1Vout  a 2Vout  ...  anVout
2
n
Note that the above formula is effective only if the reference temperature TRef in the
experiment is kept the same as the reference temperature specified on the data sheet.
Furthermore, these coefficients are unit sensitive. Make sure to use the vendor-specified
temperature unit (i.e. Celcius, Fahrenheit or Kelvin) when plugging in numbers.
Thermoelectric Sensitivity
The Seebeck coefficients (thermoelectric sensitivities) of some common materials at 0°C
are listed in the following table.
Material
Aluminum
Antimony
Bismuth
Cadmium
Carbon
Constantan
Copper
Germanium
Seebeck
Coeff. *
3.5
47
-72
7.5
3.0
-35
6.5
300
Material
Gold
Iron
Lead
Mercury
Nichrome
Nickel
Platinum
Potassium
Seebeck
Coeff. *
6.5
19
4.0
0.6
25
-15
0
-9.0
Material
Rhodium
Selenium
Silicon
Silver
Sodium
Tantalum
Tellurium
Tungsten
Seebeck
Coeff.*
6.0
900
440
6.5
-2.0
4.5
500
7.5
6
Type of Thermocouples
The following table provides a summary of basic thermocouple properties.
Type
Materials
Temperature
Range (°C)
Sensitivity
@ 25°C
(µV/°C)
K
Chromel (+), Alumel (-)
-270~1350
40.6
T
Copper (+), Constantan (-)
-270~400
40.6
S
Platinum 10% Rhodium (+),
Platinum (-)
-50~1750
6
E
Chromel (+), Constantan (-)
-270~1000
60.9
J
Iron (+), Constantan (-)
R
B
-210~1200
Platinum 13% Rhodium (+),
Platinum (-)
Platinum 30% Rhodium (+),
Platinum 6% Rhodium (-)
51.7
-50~1750
6
-50~1750
6
Error*
LT: ±2.2~1.1°C
HT: ±0.375~0.75%
LT: ±1~2%
HT: ±1.5% or ±0.42°C
LT: ±2.8°C
HT: ±0.5%
LT: ±1.67°C
HT: ±0.5%
LT: ±2.2~1.1°C
HT: ±0.375~0.75%
LT: ±2.8°C
HT: ±0.5%
LT: ±2.8°C
HT: ±0.5%
App.**
I,O
I,O,R,V
I,O
I,O
I,O,R,V
I,O
I,O
*
: LT = Low temperature range, HT = High temperature range
** : I = Inert media, O = Oxidizing media, R = Reducing media, V = Vacuum
Constantan, Alumel, and Chromel are trade names of their respective owners.
Resistance Temperature Detector (RTD)
The Resistance Temperature Detector (RTD) is based on the positive temperature
coefficient of electrical resistance. The potential that is developed as a result of Ohm's law
is proportional to the temperature to be measured (E = IexcRRTD). Examples are RTD's are
shown schematically below.
Common metals used in RTDs include platinum, copper, nickel, BalcoTM (70% Ni-30%
Fe), and tungsten. Their temperature ranges are listed in the following table.
Material
Platinum (Pt)
T Range (oC)
Note
-260 ~ 1000 < 550 °C in most applications
Copper (Cu)
-200 ~ 260
Nickel (Ni)
Balco
(70% Ni-30% Fe)
Tungsten (W)
-200 ~ 430
-100 ~ 230
Linearity is not good
Linearity is not good; cheap to
fabricate; high resistance
-100 ~ 1200
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The resistance-temperature (R-T) relationship
plays a central role in resistance temperature
detectors (RTDs). The R-T relationship of some
common RTD materials are illustratrated in the
following schematic where the y-axis is the
normalized resistance with respect to resistance
at 0 °C, x-axis is the temperature.
For a given material, the resistance at any
temperature can be obtained by curve-fitting the
R-T curve. Suppose that a nth degree polynomial
least-square-curve-fit is used. The temperature
function will then be,
 R
T  b0  b1 
R
 ref


  b2  R

R

 ref
2


  ...  bn  R

R

 ref




Resistance-Temperature relationship
for some RTD materials
n
where b0 + b1 + … + bn = Tref
Some references suggest to express the resistance as a function of temperature (rather than
temperature as a function of resistance), i.e.,

R  Rref 1  a1T  a2 T 2  ...  an T n

where T = T - Tref
Although such a relationship is mathematically correct, its usefulness is limited. After all,
we are interested in determining temperature from a resistance measurement.
A Simplified Case
Some materials have an almost linear R-T relationship within a certain temperature range,
T1 < T < T2. Such a linear function would take the form,

R  R ref 1   (T  Tref )

Rearranging to bring temperature out gives,
T  Tref
R

 R  1
ref 


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Both the measured temperature and the reference temperature should be within the (T1,T2)
temperature range,
T1 < {T, Tref} < T2
Thermistor
Thermistor is a “thermally sensitive resistor” which is generally composed of
semiconductor materials of metallic oxides such as manganese, nickel, cobalt, copper, iron
and titanium.. They offer accuracy similar to RTDs within narrow temperature ranges near
ambient temperature.
Thermistor applications are based on the resistance-temperature characteristic of a
thermistor. The thermistor is a non-linear device, i.e. resistance versus temperature
relationship is not linear. With increasing temperature the nonlinearity decreases. An
individual thermistor curve can be closely approximated by the use of Steinhart-Hart
equation:
1
 A  B ln R  C (ln R) 3
T
where T
R
A, B, C
: temperature (oK)
: resistance of the thermistor
: curve-fitting constants
A, B and C are coefficients derived from measurements by selecting three data points (R,
T) on the data curve and solving the three simultaneous equations. They are important for
an instrumentation setup. Thermistors are calibrated at three different temperatures usually at 0, 25 and 70°C.
There are two basic types of thermistors:
 Negative temperature coefficient (NTC) thermistors
(much more commonly used)
 Positive temperature coefficient (PTC) thermistors
has a resistance that increases with increasing
temperature
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EQUIPMENT:
 Testo 945 pocket size measuring instrument accepting K and T Type
thermocouples, PRTD probe and NTC thermistor.
 bulb thermometers
 stirred tank with water at ambient temperature
 ice bath
 beaker of boiling water on a hot plate
 beaker of solution at low temperature
Temperature Sensor
Type
K Type
Thermocouple
T Type
Thermocouple
Platinum Resistance
Temperature
Detector (PRTD)
Negative
Temperature
Coefficient (NTC)
Thermistor
Temperature
Range (oC)
t99
(sec)
L
(mm)
prob
(mm)
Accuracy
(±1 digit)
-60 - 1000
5
500
1.5
±0.3°C or 0.5% of M.V.
-50 - 350
5
110
4
±0.3°C or 0.5% of M.V.
-50 - 400
12
110
3
±0.2°C or ±0.1% of M.V.
4
±0.2°C (-25 to +74.9°C)
±0.4°C (+75 to +99.9°C)
±0.5% of M.V.
(remainder of range)
-50 - 150
10
110
PROCEDURE
Temperature measurements will be performed using the bulb thermometers and the Testo
945 pocket size measuring instrument accepting K and T Type thermocouples, PRTD
probe and NTC thermistor. 4 different temperature systems will be measured; a water bath
at ambient temperature, boiling water, an ice bath and solution at low temperature.
Perform the temperature measurements for each system as follows:
1. Using thermometers
 Submerge each thermometer into the bath and record the temperatures
 Repeat the measurements three times using each thermometer
 Take the mean of the three readings and record these values for each thermometer.
2. Using K type thermocouple
 Attach the K type thermocouple probe to the 1st socket of the instrument and make
necessary changes in configuration
 Set the instrument to record the temperature for 15 min continuously and to take the
mean value
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 Insert the thermistor into the ice water
 Record the temperatures.
3. Using T type thermocouple
 Detach the K type thermocouple probe and attach T type
 Repeat the same procedure as for K type
4. Using PRTD
 Attach the PRTD probe to the 2nd socket of the instrument
 Set the instrument to record the temperature for 15 min and to take the mean
5. Using NTC
- Follow the same procedure as for PRTD
Repeat the measurements three times using each temperature-measuring device for each
system.
DATA ANALYSIS
Record the mean temperatures and the averages in the following table.
System
water bath @
ambient T
boiling water
Reading #
1st
1st
2nd
3rd
2nd
3rd
solution @ low
temperature
ice bath
1st
2nd
3rd
1st
2nd
3rd
1st thermometer
2nd thermometer
K type
thermocouple
T type
thermocouple
PRTD
NTC
1. Perform data analysis calculating the average, deviation for each reading, standard
deviation, variance, percent error for each temperature measurement device using the
following formulas:
When a set of observations x1, x2, x3…xn of an instrument is taken, the individual
readings will vary somewhat from each other, and we are usually concerned with the
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average of all the readings. If each reading is denoted by xi and there are n readings, the
average is given by
xm 
1 n
 xi
n i 1
The deviation di for each reading is defined by
d i  xi  x m
The standard deviation (root-mean-square deviation) is defined by
1 n

    ( xi  x m ) 2 
 n i 1

1
2
and the square of the standard deviation 2 is called the variance.
% Error = (2 / xm) * 100
2. Precision is degree of numerical agreement among measurements of the same quantity,
or the repeatability of the readings. Compare precision of each measuring device.
3. Accuracy is degree of conformity with the exact value. Compare the average
temperature values with the "exact temperatures" of the systems that will be given by
the instructor to determine the accuracy for each device.
4. Present your Reading Number versus Temperature data for each device in graphical
form.
DISCUSSION
1. Suggest some reasons for the deviations from the "exact values"
2. Suggest some reasons for low precision for the devices.
3. Why would you expect the PRTD to be more accurate than the NTC Thermistor?
4. Is the temperature in the constant temperature bath truly constant? Did you notice
temperature fluctuations, and if so, what was their magnitude? What is the effect of
these fluctuations on the accuracy of your measurements? How will the number of
measurements affect the accuracy of your measurements?
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