Measurement
and
Instrumentations
Temperature
Measurements
Lecturer, Masoud Kamoleka
1
Principles of temperature measurement
• Temperature measurement is very important in all
spheres of life and especially so in the process
industries. However, it poses particular problems, since
temperature measurement cannot be related to a
fundamental standard of temperature in the same way
that the measurement of other quantities can be related
to the primary standards of mass, length and time. If
two bodies of lengths l1 and l2 are connected together
end to end, the result is a body of length l1 + l2. A similar
relationship exists between separate masses and
separate times. However, if two bodies at the same
temperature are connected together, the joined body
has the same temperature as each of the original
bodies.
2
Principles of temperature measurement
• In the absence of such a relationship, it is necessary to establish
fixed, reproducible reference points for temperature in the form
of freezing and boiling points of substances where the transition
between solid, liquid and gaseous states is sharply defined.
The International Practical Temperature Scale (IPTS) uses this
philosophy and defines six primary fixed points for reference
temperatures in terms of:
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the triple point of equilibrium hydrogen _259.34°C
the boiling point of oxygen _182.962°C
the boiling point of water 100.0°C
the freezing point of zinc 419.58°C
the freezing point of silver 961.93°C
the freezing point of gold 1064.43°C
(all at standard atmospheric pressure)
3
Principles of temperature measurement
Instruments to measure temperature can be divided
into separate classes according to the physical principle
on which they operate. The main principles used are:
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Thermal expansion
The thermoelectric effect
Resistance change
Sensitivity of semiconductor device
Radiative heat emission
Thermography
Resonant frequency change
Sensitivity of fibre optic devices
Acoustic thermometry
Colour change
Change of state of material.
4
Thermal Expansion
• Expansion thermometers
Most solids and liquids expands when they
undergo an increase in temperature. The
direct observation of the increase of size, or of
the signal from a primary transducer detecting
it, is used to indicate temperature in many
thermometers.
5
Thermal Expansion
A: Expansion of Solids
• The change (δθ) of temperature is given by
δι= ια δθ
where,
α is the coefficient of linear expansion, usually taken
as constant over a particular temperature range
The bonding together of two strip of metal having difference
expansion rate to form bimetal strip , as shown in Fig 1, causes
bending of the strip when subjected to temperature change.
Fig 1: Deflection of a bimetal strip
6
Expansion of Solids
• Referring to fig 1, let the initial straight length of the bimetal strip be ιo at
temperature 0 °C, and αA and αB be linear expansion coefficients of
materials A and B respectively, where αA < αB,
• If the strip is assumed to bend in a circular arc when subjected to a
temperature θ, then
r  d expanded length of strip B

r
expanded length of strip A
l o (1   B )

l o (1   A )
r
d (1   A )
 ( B   A )
• If invar is used for strip A, then αA is virtually zero, and the equation
becomes
r  d  B
7
Exercise
A bimetal- strip has one end fixed and the
other free, the length of the cantilever being
40mm. the thickness of each metal is 1mm,
and the element is initially straight at 20 °C.
Calculate the movement of the free end in a
perpendicular direction from the initial line
when the temperature is 180 °C, if one metal
is invar and the other is a nickel-chrome-iron
alloy with a linear expansion coefficient (α) of
12.5×10-6/ °C
8
Expansion of liquids
Perfect gas thermometer
• The ideal- gas equation, PV=mRT, show that, for a given mass of
gas, the temperature is proportional to the pressure if the volume is
constant, and proportional to the volume if the pressure is
constant.
• It is much simpler to contain a gas in a constant volume and
measure the pressure than to measure the volume at constant
pressure; hence constant-volume gas thermometers are common,
whilst constant- pressure ones are rare.
• The simple laboratory type is illustrated in Fig 2
Fig 2: vapour- pressure thermometer
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Expansion of liquids
• The industrial type illustrated in Fig 3, is filled usually with nitrogen,
or for lower temperature hydrogen, the overall range covered being
about -120 °C to 300 °C.
• At the higher temperature, diffusion of the filler gas through metal
wall is excessive, the loss of gas leading to loss of calibration.
Fig 3: gas thermometer
10
Thermoelectric effect sensors (thermocouples)
Fig 4: gas thermometer
When two wires composed of dissimilar metals are joined at both ends and one of the
ends is heated, a continuous current flows in the “thermoelectric” circuit. Thomas
Seebeck made this discovery in 1821. This thermoelectric circuit is shown in Figure 4(a). If
this circuit is broken at the center, as shown in Figure 4(b), the new open circuit voltage
(known as “the Seebeck voltage”) is a function of the junction temperature and the
compositions of the two metals.
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Thermoelectric effect sensors
(thermocouples)
• Thermoelectric effect sensors rely on the
physical principle that, when any two different
metals are connected together, an e.m.f.,
which is a function of the temperature, is
generated at the junction between the metals.
The general form of this relationship is:
e = a1T+ a2T2 + a3T3 +…….+anTn
Where,
……(1)
e = the e.m.f generated and
T = the absolute temperature.
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Thermoelectric effect sensors (thermocouples)
• This is clearly non-linear, which is inconvenient for
measurement applications. Fortunately, for certain
pairs of materials, the terms involving squared and
higher powers of T (a2T2, a3T3 etc.) are approximately
zero and the e.m.f.–temperature relationship is
approximately linear according to:
e ≈a1T
…….(2)
Wires of such pairs of materials are connected together at one
end, and in this form are known as thermocouples.
Thermocouples are a very important class of device as they
provide the most commonly used method of measuring
temperatures in industry.
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Thermoelectric effect sensors
(thermocouples)
Thermocouples are manufactured from various
combinations of
• the base metals copper and iron,
• the base-metal alloys of alumel (Ni/Mn/Al/Si), chromel
(Ni/Cr), constantan (Cu/Ni), nicrosil (Ni/Cr/Si) and nisil
(Ni/Si/Mn),
• the noble metals platinum and tungsten, and
• The noble-metal alloys of platinum/rhodium and
tungsten/rhenium.
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Thermoelectric effect sensors
(thermocouples)
• Only certain combinations of these are used as thermocouples and
each standard combination is known by an internationally
recognized type letter, for instance type K is chromel–alumel. The
e.m.f.–temperature characteristics for some of these standard
thermocouples are shown in Figure 5: these show reasonable
linearity over at least part of their temperature-measuring ranges.
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Fig. 5. E.m.f. temperature characteristics for some standard thermocouple materials.
Thermoelectric effect sensors
(thermocouples)
16
Thermoelectric effect sensors
(thermocouples)
• A typical thermocouple, made from one chromel wire and
one constantan wire, is shown in Figure 6(a). For analysis
purposes, it is useful to represent the thermocouple by its
equivalent electrical circuit, shown in Figure 6(b). The e.m.f.
generated at the point where the different wires are
connected together is represented by a voltage source, E1,
and the point is known as the hot junction.
The temperature of the hot
junction is customarily shown as Th
on the diagram. The e.m.f.
generated at the hot junction is
measured at the open ends of the
thermocouple, which is known as
the reference junction.
Fig. 6(a) Thermocouple; (b) equivalent circuit.
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Thermoelectric effect sensors
(thermocouples)
• In order to make a thermocouple conform to
some precisely defined e.m.f.–temperature
characteristic, it is necessary that all metals
used are refined to a high degree of pureness
and all alloys are manufactured to an exact
specification.
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Thermoelectric effect sensors
(thermocouples)
• It is clearly impractical to connect a voltage-measuring instrument at the
open end of the thermocouple to measure its output in such close
proximity to the environment whose temperature is being measured, and
therefore extension leads up to several metres long are normally
connected between the thermocouple and the measuring instrument.
• This modifies the equivalent circuit to that shown in Figure 7(a). There are
now three junctions in the system and consequently three voltage
sources, E1, E2 and E3, with the point of measurement of the e.m.f. (still
called the reference junction) being moved to the open ends of the
extension leads.
Fig. 7 (a) Equivalent circuit for thermocouple with extension leads; (b) equivalent circuit for thermocouple
and extension leads connected to a meter.
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Thermoelectric effect sensors
(thermocouples)
• The measuring system is completed by connecting the
extension leads to the voltage measuring instrument. As
the connection leads will normally be of different
materials to those of the thermocouple extension leads,
this introduces two further e.m.f.-generating junctions E4
and E5 into the system as shown in Figure 7(b). The net
output e.m.f. measured (Em) is then given by:
Em = E1 + E2 + E3 + E4 +E5
……….3
and this can be re-expressed in terms of E1 as:
E1= Em ̶ E2 ̶ E3 ̶ E4 ̶ E5
……….4
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Thermoelectric effect sensors
(thermocouples)
• In order to apply equation (1) to calculate the
measured temperature at the hot junction, E1 has to
be calculated from equation (4). To do this, it is
necessary to calculate the values of E2, E3, E4 and E5.
It is usual to choose materials for the extension lead
wires such that the magnitudes of E2 and E3 are
approximately zero, irrespective of the junction
temperature. This avoids the difficulty that would
otherwise arise in measuring the temperature of
the junction between the thermocouple wires and
the extension leads, and also in determining the
e.m.f./temperature
relationship
for
the
thermocouple–extension lead combination.
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Zero Junction
• A zero junction e.m.f. is most easily achieved by choosing
the extension leads to be of the same basic materials as
the thermocouple,
• but where their cost per unit length is greatly reduced by
manufacturing them to a lower specification.
• However, such a solution is still prohibitively expensive in
the case of noble metal thermocouples, and it is necessary
in this case to search for base-metal extension leads that
have a similar thermoelectric behaviour to the noble-metal
thermocouple.
• In this form, the extension leads are usually known as
compensating leads.
• A typical example of this is the use of nickel/copper–copper
extension leads connected to a platinum/rhodium–platinum
thermocouple.
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Zero Junction
• Copper compensating leads are also sometimes
used with some types of base metal
thermocouples and, in such cases, the law of
intermediate metals can be applied to
compensate for the e.m.f. at the junction
between the thermocouple and compensating
leads.
• To analyse the effect of connecting the extension
leads to the voltage-measuring instrument, a
thermoelectric law known as the law of
intermediate metals can be used.
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Zero Junction
• To analyse the effect of connecting the extension leads to
the voltage-measuring instrument, a thermoelectric law
known as the law of intermediate metals can be used.
• This states that “The e.m.f. generated at the junction
between two metals or alloys A and C is equal to the sum
of the e.m.f. generated at the junction between metals or
alloys A and B and the e.m.f. generated at the junction
between metals or alloys B and C, where all junctions are
at the same temperature”. This can be expressed more
simply as:
eAC =eAB + eBC……………… (5)
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Zero Junction
Suppose we have an iron–constantan thermocouple connected by
copper leads to a meter.
We can express E4 and E5 in Figure 7 as:
E4 = eiron_copper; E5 = ecopper_constantan
The sum of E4 and E5 can be expressed as:
E4 = eiron_copper + ecopper_constantan
Applying equation (5):
eiron_copper + ecopper_constantan = eiron_constantan
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Fig 8. Effective e.m.f. sources in a thermocouple measurement system.
Zero Junction
• Thus, the effect of connecting the thermocouple extension wires to
the copper leads to the meter is cancelled out, and the actual e.m.f.
at the reference junction is equivalent to that arising from an iron–
constantan connection at the reference junction temperature,
which can be calculated according to equation (1). Hence, the
equivalent circuit in Figure 7(b) becomes simplified to that shown in
Figure 8. The e.m.f. Em measured by the voltage-measuring
instrument is the sum of only two e.m.f.s, consisting of the e.m.f.
generated at the hot junction temperature E1 and the e.m.f.
generated at the reference junction temperature Eref. The e.m.f.
generated at the hot junction can then be calculated as:
• Eref can be calculated from equation (1) if the temperature of
the reference junction is known.
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Zero Junction
• In practice, this is often achieved by immersing the reference
junction in an ice bath to maintain it at a reference temperature of
0°C. (Fig 9)
Figure 9. Thermocouple kept at 0°C in an ice bath.
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Thermocouple table
• Although the preceding discussion has suggested that the
unknown temperature T can be evaluated from the calculated
value of the e.m.f. E1 at the hot junction using equation (1), this is
very difficult to do in practice because equation (1) is a high
order polynomial expression.
• An approximate translation between the value of E1 and
temperature can be achieved by expressing equation (1) in
graphical form as in Figure 5
• However, this is not usually of sufficient accuracy, and it is normal
practice to use tables of e.m.f. and temperature values known as
thermocouple tables.
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Thermocouple table
• These include compensation for the effect of
the e.m.f. generated at the reference junction
(Eref), which is assumed to be at 0°C. Thus, the
tables are only valid when the reference
junction is exactly at this temperature.
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Thermocouple table
• Example 1
If the e.m.f. output measured from a chromel–
constantan thermocouple is 13.419mV with the
reference junction at 0°C, the appropriate column
in the tables shows that this corresponds to a hot
junction temperature of 200°C.
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Thermocouple table
• Example 2
If the measured output e.m.f. for a chromel–
constantan thermocouple (reference junction at
0°C) was 10.65 mV, it is necessary to carry out
linear interpolation between the temperature of
160°C corresponding to an e.m.f. of 10.501mV
shown in the tables and the temperature of
170°C corresponding to an e.m.f. of 11.222 mV.
This interpolation procedure gives an indicated
hot junction temperature of 162°C.
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Resistance temperature detectors
(RTDs)
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RTDs
Figure 1. Resistance temperature detector.
• Resistance temperature detectors
(RTDs)
are
temperature
transducers made of conductive
wire elements. The most common
types of wires used in RTDs are
platinum, nickel, copper, and
nickel-iron. A protective sheath
material (protecting tube) covers
these wires, which are coiled
around an insulator that serves as a
support. Figure 1 shows the
construction of an RTD. In an RTD,
the resistance of the conductive
wires increases linearly with an
increase in the temperature being
measured; for this reason, RTDs are
said to have a positive temperature
coefficient.
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RTDs
• The resistance of most
metals increases in a
reasonably linear way with
temperature (Figure 2) and
can be represented by the
equation:
Figure 2: Resistance variation with
temperature for metals
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RTDs
Resistance temperature detectors (RTDs) are simple resistive elements in the form
of coils of metal wire, e.g. platinum, nickel or copper alloys.
Platinum detectors have
• high linearity,
• good repeatability,
• high long term stability,
• can give an accuracy of ±0.5% or
better,
• a range of about -200 °C to +850 °C,
• Can be used in a wide range of
environments without
deterioration, but are more
expensive than the other metals.
They are, however, very widely
used.
Nickel and copper alloys are
• Cheaper but have less
stability, are more prone to
interaction with the
environment and cannot be
used over such large
temperature ranges
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• RTDs are generally used in a
bridge circuit configuration.
Figure 3 illustrates an RTD in
a bridge circuit. A bridge
circuit provides an output
proportional to changes in
resistance. Since the RTD is
the variable resistor in the
bridge (i.e., it reacts to
temperature changes), the
bridge output will be
proportional
to
the
temperature measured by
the RTD.
Figure 3. RTD in a bridge circuit.
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RTDs
Figure 3. RTD in a bridge circuit.
• As shown in Figure 3, an RTD
element may be located away
from its bridge circuit. In this
configuration, the user must be
aware of the lead wire resistance
created by the wire connecting
the RTD with the bridge circuit.
The lead wire resistance causes
the total resistance in the RTD
arm of the bridge to increase,
since the lead wire resistance
adds to the RTD resistance. If the
RTD circuit does not receive
proper lead wire compensation, it
will provide an erroneous
measurement.
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RTDs
Figure 4. RTD bridge configuration with lead wire compensation.
• Figure 4 presents a typical wire
compensation method used to
balance lead wire resistance.
The lead resistances of wires L1
and L2 are identical because
they are made of the same
material. These two resistances,
RL1 and RL2, are added to R2 and
RRTD, respectively. This adds the
wire resistance to two adjacent
sides of the bridge, thereby
compensating for the resistance
of the lead wire in the RTD
measurement. The equations in
Figure 4 represent the bridge
before and after compensation.
Note that RL3 has no influence
on the bridge circuit since it is
connected to the detector.
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RTDs
Figure 4. RTD bridge configuration with lead wire
compensation.
R
R1
 3
R2 RRTD
Without lead wire consideration
R3
R1

R2 RRTD  RL1  RL 2
Taking lead wire into
consideration (no compensation)
R3
R1

R2  RL1 RRTD  RL 2
Taking lead wire into
consideration (with compensation)
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THERMISTORS
Figure 5. Different types of thermistors.
• Like RTDs, thermistors (see Figure 5) are
semiconductor temperature sensor that
exhibit changes in internal resistance
proportional to changes in temperature.
Thermistors are made from mixtures of metal
oxides, such as oxides of cobalt, chromium,
nickel, manganese, iron, and titanium. These
semiconductor
materials
exhibit
a
temperature-versus-resistance
behaviour
that is opposite of the behaviour of RTD
conducting materials. As the temperature
increases, the resistance of a thermistor
decreases; therefore, a thermistor is said to
have a negative temperature coefficient.
Although most thermistors have negative
coefficients, some do have positive
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temperature coefficients.