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Lecture Notes
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TEMPERATURE MEASUREMENTS
I Dynamic Response and Dynamic Error
Instruments seldom respond instantaneously to changes in the measured
variables rather they show some delay in response The response
generally starts quickly and then becomes gradual in reaching a steady-
state value The time lapse when a system is exposed to a change until
the system starts to response is the lag time (or dead time) There are
several factors that influence the speed of response of a temperature
sensor such as
bull The mass of the shield of the temperature sensor
bull The insulating air space between the sensor and the protecting well
CHE 215 page of 21 H Muhamad 1
bull The velocity of the moving medium being measured
bull The type of medium being measured
When the temperature sensor (or any other sensorinstrument) is exposed
to a step change in the environment of which it is sensing the
temperature the temperature readout of the sensor is lower than the
actual temperature This difference is known as the dynamic error of the
sensor as shown in Figure1 and 2 below (for first-order response
instrument)
00
200
400
600
800
1000
1200
0 02 04 06 08 1 12 14 16 18 2Time (sec)
Tem
pera
ture
(C)
T-dynamic
Step change (ideal T response)
actual T response
dynamic errror
dynamic error
Figure 1 Temperature response to a step change
CHE 215 page of 21 H Muhamad 2
0
02
04
06
08
1
12
0 02 04 06 08 1 12 14 16 18 2
Time (sec)
Nor
mal
ized
dyn
amic
err
or (X
tXo)
Dynamic error
time constant = 025 s
XtXo = 0368
Figure 2 Dynamic errors
As an example shown in Figures 1 and 2 a temperature sensor is in an
environment at temperature T1 of 20oC The temperature of the
environment is assumed to have a surge in temperature to T2 of 100oC
(ideal step change) Therefore the initial (maximum) dynamic error Xo =
(T2-T1) = (100- 20) = 80oC The dynamic error of the temperature
reading is defined as
Xt = T2 -Td
Where Td is the actual temperature response (or temperature reading) of
the temperature sensor at a given time t after it was exposed to the step
change in temperature
CHE 215 page of 21 H Muhamad 3
As shown in Figure 2 the dynamic error of the temperature sensor shows
an exponential decay trend Therefore the rate of change of the dynamic
error can be written as
XkdtdX
minus= (1)
Integration of Equation (1) for time t = 0 to some time t gives
tkXX
o
t minus=⎟⎟⎠
⎞⎜⎜⎝
⎛ln (2)
kt
o
t eXX minus=⎟⎟
⎠
⎞⎜⎜⎝
⎛ (3)
When t is equal to the time constant tc of the sensor which is defined as
tc=1k then
36801 ==⎟⎟⎠
⎞⎜⎜⎝
⎛ minuseXX
o
t (4)
Therefore as indicated by Equation (4) when the elapsed time is equal
to the time constant the response of the sensor has covered 632 of the
step change in the temperature as shown below At t = tc
Td = T2 ndashXtc = T2 ndash 0368 Xo
Td = T2 ndash 0368(T2-T1)
Td ndashT1 = T2 ndash 0368T2 + 0368T1 ndash T1
(Td ndashT1) = 0632 (T2 ndash T1)
CHE 215 page of 21 H Muhamad 4
(Td ndashT1) is 632 of the overall step change (T2 ndash T1)
A first-order-response instrument shows a quick response initially the
response then slows down considerably to the point of achieving a
steady-state measurement The bare-wire thermocouple usually exhibits
a first-order response to a step change in temperature of the environment
it is in From the energy balance for the sensor and the surrounding the
first-order temperature response can be described by the following
differential equation
FTTtdTd
=+sdotτ (5)
where τ is the time constant of the temperature sensor T is the dynamic
temperature of the sensor TF is the step change of temperature and t is
time ( ) ( )( )τexp100 tTTTT F minusminussdotminus+=
However for a shielded temperature sensor with a low thermal
conductivity shield the temperature response could exhibit a second-
order temperature response as described by
( ) FSWSW TTdtdT
tdTd
=+++sdotsdot ττττ 2
2 (6)
CHE 215 page of 21 H Muhamad 5
where τW and τS are the time constant of the sensor itself and the shield
of the sensor respectively The ratio of (τW + τS)(2radic(τW τS)) is known
as the damping ratio For a large damping ratio (greater than 10) the
profile is similar to that of the first order system) On the other hand for
smaller damping ratio the profile is oscillating
( ) ( ) ( )⎟⎟⎠
⎞⎜⎜⎝
⎛minus
minusminusminus+minus+=
sw
wwssF
ttTTTTττ
ττττ expexp100
II Temperature Measurements
1 Thermometer
Common liquid used
bull Alcohol for temperature range from 50 ndash 200oC
bull Xylene for temperature range from -40 to 400oC
bull Hg for temperature range from -37 to 350oC (Hg freezes at -378oC)
Cautions
bull Do not immerse the whole stem of the thermometer in the
environment where the temperature is measured Only place the bulb
of the thermometer in the environment so to avoid error due to
different thermal expansion coefficients of liquid and glass
bull Allow the liquid level in the thermometer stabilized before taking the
temperature reading
CHE 215 page of 21 H Muhamad 6
bull Precision of liquid filled thermometer is frac12 of the smallest division on
the scale Highly accurate Hg thermometer from NIST (National
Institute of Standards and Testing) could measure to plusmn 005oC
2 Resistance temperature detector (RTD)
RTD is basically an electrical wire typically Pt Ag Ni Cu etc which
is used to sense the temperature change based on the principle of the
temperature dependency of the wire resistance as shown below
( )[ ]11 1 TTRR minus+= α (7)
Where R and R1 is the resistances of the wire at T and T1 respectively
and the linear temperature coefficient of the wire resistance which is
defined as below
( )( )121
12TTR
RRminus
minus=α (8)
CHE 215 page of 21 H Muhamad 7
Where R2 is the wire resistance at T2
However the relationship between the wire resistance and temperature
is usually non-linear The relationship can then be expressed as
[ ]21 bTaTRR o ++= (9)
Where Ro is the wire resistance at the reference temperature of zero oC
An RTD sensor can be integrated into a Wheatstone bridge circuit to
convert the RTD resistance change with temperature to a voltage output
The voltage output can be calibrated to give readings of temperature
a) No lead wire
1 At the calibrated temperature
Ro Rx Rx = R0
Vs Va = Ro(Ro+Ro)middotVs = Vs2
Ro Ro Vb = Ro(Ro+Ro)middotVs = Vs2
Vab = Va ndash Vb = 0
CHE 215 page of 21 H Muhamad 8
2 At some other temperature
Rx = Ro +ΔR
Va = Ro(Ro+Ro)middotVs = Vs2
Vb = Ro(Ro+Rx)middotVs = Ro(Ro + Ro + ΔR)middotVs = Ro( 2Ro + ΔR)middotVs
Vab= Vs2 - Ro( 2Ro + ΔR)middotVs = Vs[12 ndash Ro(2Ro + ΔR)]
Vab= Vs[(2Ro + ΔR-2Ro)(2(2Ro+ ΔR))]= Vs[(ΔRRo)(2(2+ ΔRRo))]
o
oSR2R1
RR4
VVabΔ+Δ
sdot=
Since ΔR ltlt Ro ΔR2Ro ltlt 1 Vab can be simplified as
o
SR
R4
VVab Δsdot= (10)
b) With lead wire
(in ldquoExperimental Methods for Engineersrdquo J Holman)
CHE 215 page of 21 H Muhamad 9
RL 1 At the calibrated temperature
Ro Rx (RL + Rx) = Ro
Vs Va = Ro(Ro+Ro)middotVs = Vs2
Ro Ro Vb = Ro(Ro+Ro)middotVs = Vs2
Vab = Va ndash Vb = 0
b) At some other temperature
(RL + Rx) = Ro +ΔRx+ ΔRL for the RTD wire and the lead wire
Va = Ro(Ro+Ro)middotVs = Vs2
Vb = Ro(Ro + Ro + ΔRx+ ΔRL)middotVs
Vab= Vs2 - Ro(2 Ro + ΔRx+ ΔRL)middotVs
Vab= Vs[(2Ro + ΔRx+ ΔRL -2Ro)(2(2Ro+ ΔRx+ ΔRL))]
Vab = (Vs4) [((ΔRx+ ΔRL )Ro) (1+ ΔRx 2Ro + ΔRL 2Ro)]
Since ΔRx and ΔRL ltlt Ro ΔRx2Ro ltlt 1 and ΔRL2Ro ltlt 1 the
equation for Vab can be simplified as
( )o
LSR
RRx4
VVab Δ+Δsdot= (11)
CHE 215 page of 21 H Muhamad 10
ΔRL is not known not calibrated and uncontrollable since it is exposed
to the outside environment that is subject to sporadic changes This is a
source of error in the temperature measurement by RTD
c) Lead wire compensation
(in ldquoExperimental Methods for Engineersrdquo J Holman)
RL 1 At the calibrated temperature
Ro Rx (RL + Rx) = Ro (RL + RD) = Ro
Vs Va = Ro(Ro+Ro)middotVs = Vs2
Ro RL Vb = Ro(Ro+Ro)middotVs = Vs2
RD Vab = Va ndash Vb = 0
CHE 215 page of 21 H Muhamad 11
b) At some other temperature
(RL + Rx) = Ro +ΔRx+ ΔRL for the RTD wire and the lead wire
(RL + RD) = Ro + ΔRL for the dummy wire
Va = Ro(Ro+Ro)middotVs = Vs2
Vb = (Ro+ΔRL) [(Ro+ΔRL) + (Ro + ΔRx+ ΔRL)]middotVs
Vab= Vs2 - (Ro+ΔRL)(2 Ro + ΔRx+ 2ΔRL)middotVs
Vab= Vs[(2Ro + ΔRx+ 2ΔRL -2Ro- 2ΔRL)(2(2Ro+ ΔRx+ 2ΔRL))]
Vab = (Vs4) [ΔRx (Ro + ΔRx 2 + ΔRL)]
Vab = (Vs4) [ΔRxRo (1 + ΔRx 2Ro + ΔRLRo)]
Since ΔRx and ΔRL ltlt Ro ΔRx2Ro ltlt 1 and ΔRLRo ltlt 1 the
equation for Vab can be simplified as
o
SRRx
4VVab Δ
sdot= (12)
Equation (12) has the same form as that of Equation (10) where the
uncertain ΔRL is eliminated
CHE 215 page of 21 H Muhamad 12
3 Thermistors
Thermistors are semiconductor sensors whose resistances decrease with
temperature such as FeO NiO MnO hellip The relationship of the
thermistor resistance and temperature can be written as below
⎥⎦
⎤⎢⎣
⎡⎟⎟⎠
⎞⎜⎜⎝
⎛minusβ
= oT1
T1
o eRR (13)
where Ro is the resistance of the thermistor at the ref temperature To
CHE 215 page of 21 H Muhamad 13
Generally thermistors are more sensitive than RTD They can have a
precision of plusmn 001oC as compared with plusmn 01oC for RTD In addition
the error due to lead wire is insignificant since the resistance of the
thermistor is very high compared to that of the lead wire However the
suitable temperature range for thermistors is narrower from -100 to
400oC while RTD can cover from -100 to 1000 oC
4 Thermocouple
A thermocouple consists of two dissimilar metal wires twisted together
to form a junction that can act as a temperature sensor For example
copper wire and constantan wire (55 copper plus 45 nickel)
bull Seebeck effect
The use of a thermocouple as a temperature sensor is based on the
principle of the Seebeck effect The Seebeck effect states that an emf is
generated in the thermocouple when the junction is heated or cooled
Junction copper A
Constantan B
CHE 215 page of 21 H Muhamad 14
VAB is finite when the junction is at a temperature different from that at
the terminals A and B
bull Law of intermediate metals
Junction copper A
iron
Constantan B
When another metal (iron) is added to the thermocouple circuit as shown
in the above sketch two more junctions are formed at points A and B
As long as the junctions at A and B are kept at the same temperature the
emf generated by the main junction isnrsquot altered ie the temperature
reading doesnrsquot change
bull Law of intermediate temperatures
hot junction copper cold junction
E
constantan
CHE 215 page of 21 H Muhamad 15
For the same thermocouple ie the same two dissimilar metal junctions
the emf generated at different temperatures are additive
E3 = E1 + E2
Where E1 is the emf for the cold junction at 0oC and the hot junction at
50 oC E2 is the emf for the cold junction at 50oC and hot junction at 100
oC E3 is the emf for the cold junction at 0oC and hot junction at 100 oC
Precautions for use of TC
bull Extension wire should have similar properties as those of the TC
otherwise the two junctions of the extension wires and the TC wires
should be kept at the same temperature
bull Extension wire should be thick (having a low resistance) so to
minimize the error associated with the wire heating since the wire
resistance R = ρLS where ρ is the resistivity of the wire L is the
length and S is the cross-sectional area of the wire
5 Correction for temperature measurement under high-velocity
For temperature measurements of a flow at high speed usually gas flow
the effect of the stagnation point at the tip of the temperature sensor on
CHE 215 page of 21 H Muhamad 16
the reading could be significant At the stagnation point the stagnation
temperature Ts is
cp
S gCu
TT2
2α+= infin (14)
Where Tinfin is the temperature of the bulk gas uinfin is the velocity of gas the
flow Cp is the specific heat of the gas
The temperature registered by the sensor (the measured temperature) is
usually different than the stagnation temperature due to the effect of the
shield intruding in the flow path The measured temperature is called the
recovery temperature It is strongly dependent on the configuration of
the sensor and the shield The relative difference between the measured
temperature by the sensor Tr and the stagnation temperature TS is
known as the recovery factor r
infinminusinfinminus
=TTTTr
s
r (15)
7 Temperature measurements by radiation
The temperature of an object can be determined from the total thermal
radiation emitted from the object For an ideal body the total energy
emitted is proportional to the fourth power of the temperature
CHE 215 page of 21 H Muhamad 17
However most practical objects are non-ideal bodies and a correction
must be made to obtain the true temperature of the target This
correction is done by the emissivity of the non-ideal body as below
(16) 4TE σε=
Where E is the energy emitted by the object at the temperature T (in K
or oR) ɛ is the emissivity of the object (ɛ le 10) and σ is the Stefan-
Boltzmann constant
σ = 174x10-9 BTU(hft2oR4) or 5669x10-8 W(m2K4)
When an object is an ideal body the emissivity ɛ is equal to 10 and
Equation (16) is then known as the Stefan-Boltzmann equation
CHE 215 page of 21 H Muhamad 18
71 Optical Pyrometer
The optical pyrometer is simply a photometer that matches the energy
emitted from a reference source with the incoming one from the target
source As an example in the laboratory of this course the target source
is an incandescent lamp whose tungsten filament temperature can be
varied by adjusting the current through it (by adjusting a knob on the
optical pyrometer) When the brightness of the reference filament in the
optical pyrometer matches the brightness of the target filament being
measured the image of the reference filament blends into the colour of
the background of the viewing field in the optical pyrometer At this
point the intensity of the energy emitted from the target is equal to that
emitted from the reference and hence the temperature of the target (light
bulb) can be read from the display on a digital readout
2 Total Radiation Pyrometer
The total radiation pyrometer is the most commonly used pyrometer for
continuous non-contacting measurement of temperature Radiation (both
infrared and visible) passes through a lens and is then concentrated on a
heat-sensing element which produces an electric signal This sensing
element or detector may be a thermopile a thin thermistor flake or a
CHE 215 page of 21 H Muhamad 19
resistance thermometer Thermopiles are the most commonly used
Ambient temperature compensation may be required since the body of
the pyrometer is heated by the target radiation and the thermopile is
sensitive to the body heat
The current (or voltage) produced by the sensing detector is sent to a
potentiometer or a millivoltmeter where the current can be read The
total radiation pyrometer can be used to measure low temperature
However temperatures measured are also subject to errors
bull if the source is not an ideal body Error = (1 - ɛ14)
bull if the optical system gets dirty and adsorbs too much radiation
bull If part of the radiant energy is absorbed before it reaches the
instruments such as absorption by smoke and dust Gases such as
carbon dioxide sulphur dioxide and water vapour absorb infrared
radiation
The emissivity of a material (usually written ε or e) is the relative ability
of its surface to emit energy by radiation It is the ratio of energy
radiated by a particular material to energy radiated by a black body at
CHE 215 page of 21 H Muhamad 20
CHE 215 page of 21 H Muhamad 21
the same temperature A true black body would have an ε = 1 while any
real object would have ε lt 1 Emissivity is a dimensionless quantity
In general the duller and blacker a material is the closer its emissivity is
to 1 The more reflective a material is the lower its emissivity Highly
polished silver has an emissivity of about 002[1]
bull The velocity of the moving medium being measured
bull The type of medium being measured
When the temperature sensor (or any other sensorinstrument) is exposed
to a step change in the environment of which it is sensing the
temperature the temperature readout of the sensor is lower than the
actual temperature This difference is known as the dynamic error of the
sensor as shown in Figure1 and 2 below (for first-order response
instrument)
00
200
400
600
800
1000
1200
0 02 04 06 08 1 12 14 16 18 2Time (sec)
Tem
pera
ture
(C)
T-dynamic
Step change (ideal T response)
actual T response
dynamic errror
dynamic error
Figure 1 Temperature response to a step change
CHE 215 page of 21 H Muhamad 2
0
02
04
06
08
1
12
0 02 04 06 08 1 12 14 16 18 2
Time (sec)
Nor
mal
ized
dyn
amic
err
or (X
tXo)
Dynamic error
time constant = 025 s
XtXo = 0368
Figure 2 Dynamic errors
As an example shown in Figures 1 and 2 a temperature sensor is in an
environment at temperature T1 of 20oC The temperature of the
environment is assumed to have a surge in temperature to T2 of 100oC
(ideal step change) Therefore the initial (maximum) dynamic error Xo =
(T2-T1) = (100- 20) = 80oC The dynamic error of the temperature
reading is defined as
Xt = T2 -Td
Where Td is the actual temperature response (or temperature reading) of
the temperature sensor at a given time t after it was exposed to the step
change in temperature
CHE 215 page of 21 H Muhamad 3
As shown in Figure 2 the dynamic error of the temperature sensor shows
an exponential decay trend Therefore the rate of change of the dynamic
error can be written as
XkdtdX
minus= (1)
Integration of Equation (1) for time t = 0 to some time t gives
tkXX
o
t minus=⎟⎟⎠
⎞⎜⎜⎝
⎛ln (2)
kt
o
t eXX minus=⎟⎟
⎠
⎞⎜⎜⎝
⎛ (3)
When t is equal to the time constant tc of the sensor which is defined as
tc=1k then
36801 ==⎟⎟⎠
⎞⎜⎜⎝
⎛ minuseXX
o
t (4)
Therefore as indicated by Equation (4) when the elapsed time is equal
to the time constant the response of the sensor has covered 632 of the
step change in the temperature as shown below At t = tc
Td = T2 ndashXtc = T2 ndash 0368 Xo
Td = T2 ndash 0368(T2-T1)
Td ndashT1 = T2 ndash 0368T2 + 0368T1 ndash T1
(Td ndashT1) = 0632 (T2 ndash T1)
CHE 215 page of 21 H Muhamad 4
(Td ndashT1) is 632 of the overall step change (T2 ndash T1)
A first-order-response instrument shows a quick response initially the
response then slows down considerably to the point of achieving a
steady-state measurement The bare-wire thermocouple usually exhibits
a first-order response to a step change in temperature of the environment
it is in From the energy balance for the sensor and the surrounding the
first-order temperature response can be described by the following
differential equation
FTTtdTd
=+sdotτ (5)
where τ is the time constant of the temperature sensor T is the dynamic
temperature of the sensor TF is the step change of temperature and t is
time ( ) ( )( )τexp100 tTTTT F minusminussdotminus+=
However for a shielded temperature sensor with a low thermal
conductivity shield the temperature response could exhibit a second-
order temperature response as described by
( ) FSWSW TTdtdT
tdTd
=+++sdotsdot ττττ 2
2 (6)
CHE 215 page of 21 H Muhamad 5
where τW and τS are the time constant of the sensor itself and the shield
of the sensor respectively The ratio of (τW + τS)(2radic(τW τS)) is known
as the damping ratio For a large damping ratio (greater than 10) the
profile is similar to that of the first order system) On the other hand for
smaller damping ratio the profile is oscillating
( ) ( ) ( )⎟⎟⎠
⎞⎜⎜⎝
⎛minus
minusminusminus+minus+=
sw
wwssF
ttTTTTττ
ττττ expexp100
II Temperature Measurements
1 Thermometer
Common liquid used
bull Alcohol for temperature range from 50 ndash 200oC
bull Xylene for temperature range from -40 to 400oC
bull Hg for temperature range from -37 to 350oC (Hg freezes at -378oC)
Cautions
bull Do not immerse the whole stem of the thermometer in the
environment where the temperature is measured Only place the bulb
of the thermometer in the environment so to avoid error due to
different thermal expansion coefficients of liquid and glass
bull Allow the liquid level in the thermometer stabilized before taking the
temperature reading
CHE 215 page of 21 H Muhamad 6
bull Precision of liquid filled thermometer is frac12 of the smallest division on
the scale Highly accurate Hg thermometer from NIST (National
Institute of Standards and Testing) could measure to plusmn 005oC
2 Resistance temperature detector (RTD)
RTD is basically an electrical wire typically Pt Ag Ni Cu etc which
is used to sense the temperature change based on the principle of the
temperature dependency of the wire resistance as shown below
( )[ ]11 1 TTRR minus+= α (7)
Where R and R1 is the resistances of the wire at T and T1 respectively
and the linear temperature coefficient of the wire resistance which is
defined as below
( )( )121
12TTR
RRminus
minus=α (8)
CHE 215 page of 21 H Muhamad 7
Where R2 is the wire resistance at T2
However the relationship between the wire resistance and temperature
is usually non-linear The relationship can then be expressed as
[ ]21 bTaTRR o ++= (9)
Where Ro is the wire resistance at the reference temperature of zero oC
An RTD sensor can be integrated into a Wheatstone bridge circuit to
convert the RTD resistance change with temperature to a voltage output
The voltage output can be calibrated to give readings of temperature
a) No lead wire
1 At the calibrated temperature
Ro Rx Rx = R0
Vs Va = Ro(Ro+Ro)middotVs = Vs2
Ro Ro Vb = Ro(Ro+Ro)middotVs = Vs2
Vab = Va ndash Vb = 0
CHE 215 page of 21 H Muhamad 8
2 At some other temperature
Rx = Ro +ΔR
Va = Ro(Ro+Ro)middotVs = Vs2
Vb = Ro(Ro+Rx)middotVs = Ro(Ro + Ro + ΔR)middotVs = Ro( 2Ro + ΔR)middotVs
Vab= Vs2 - Ro( 2Ro + ΔR)middotVs = Vs[12 ndash Ro(2Ro + ΔR)]
Vab= Vs[(2Ro + ΔR-2Ro)(2(2Ro+ ΔR))]= Vs[(ΔRRo)(2(2+ ΔRRo))]
o
oSR2R1
RR4
VVabΔ+Δ
sdot=
Since ΔR ltlt Ro ΔR2Ro ltlt 1 Vab can be simplified as
o
SR
R4
VVab Δsdot= (10)
b) With lead wire
(in ldquoExperimental Methods for Engineersrdquo J Holman)
CHE 215 page of 21 H Muhamad 9
RL 1 At the calibrated temperature
Ro Rx (RL + Rx) = Ro
Vs Va = Ro(Ro+Ro)middotVs = Vs2
Ro Ro Vb = Ro(Ro+Ro)middotVs = Vs2
Vab = Va ndash Vb = 0
b) At some other temperature
(RL + Rx) = Ro +ΔRx+ ΔRL for the RTD wire and the lead wire
Va = Ro(Ro+Ro)middotVs = Vs2
Vb = Ro(Ro + Ro + ΔRx+ ΔRL)middotVs
Vab= Vs2 - Ro(2 Ro + ΔRx+ ΔRL)middotVs
Vab= Vs[(2Ro + ΔRx+ ΔRL -2Ro)(2(2Ro+ ΔRx+ ΔRL))]
Vab = (Vs4) [((ΔRx+ ΔRL )Ro) (1+ ΔRx 2Ro + ΔRL 2Ro)]
Since ΔRx and ΔRL ltlt Ro ΔRx2Ro ltlt 1 and ΔRL2Ro ltlt 1 the
equation for Vab can be simplified as
( )o
LSR
RRx4
VVab Δ+Δsdot= (11)
CHE 215 page of 21 H Muhamad 10
ΔRL is not known not calibrated and uncontrollable since it is exposed
to the outside environment that is subject to sporadic changes This is a
source of error in the temperature measurement by RTD
c) Lead wire compensation
(in ldquoExperimental Methods for Engineersrdquo J Holman)
RL 1 At the calibrated temperature
Ro Rx (RL + Rx) = Ro (RL + RD) = Ro
Vs Va = Ro(Ro+Ro)middotVs = Vs2
Ro RL Vb = Ro(Ro+Ro)middotVs = Vs2
RD Vab = Va ndash Vb = 0
CHE 215 page of 21 H Muhamad 11
b) At some other temperature
(RL + Rx) = Ro +ΔRx+ ΔRL for the RTD wire and the lead wire
(RL + RD) = Ro + ΔRL for the dummy wire
Va = Ro(Ro+Ro)middotVs = Vs2
Vb = (Ro+ΔRL) [(Ro+ΔRL) + (Ro + ΔRx+ ΔRL)]middotVs
Vab= Vs2 - (Ro+ΔRL)(2 Ro + ΔRx+ 2ΔRL)middotVs
Vab= Vs[(2Ro + ΔRx+ 2ΔRL -2Ro- 2ΔRL)(2(2Ro+ ΔRx+ 2ΔRL))]
Vab = (Vs4) [ΔRx (Ro + ΔRx 2 + ΔRL)]
Vab = (Vs4) [ΔRxRo (1 + ΔRx 2Ro + ΔRLRo)]
Since ΔRx and ΔRL ltlt Ro ΔRx2Ro ltlt 1 and ΔRLRo ltlt 1 the
equation for Vab can be simplified as
o
SRRx
4VVab Δ
sdot= (12)
Equation (12) has the same form as that of Equation (10) where the
uncertain ΔRL is eliminated
CHE 215 page of 21 H Muhamad 12
3 Thermistors
Thermistors are semiconductor sensors whose resistances decrease with
temperature such as FeO NiO MnO hellip The relationship of the
thermistor resistance and temperature can be written as below
⎥⎦
⎤⎢⎣
⎡⎟⎟⎠
⎞⎜⎜⎝
⎛minusβ
= oT1
T1
o eRR (13)
where Ro is the resistance of the thermistor at the ref temperature To
CHE 215 page of 21 H Muhamad 13
Generally thermistors are more sensitive than RTD They can have a
precision of plusmn 001oC as compared with plusmn 01oC for RTD In addition
the error due to lead wire is insignificant since the resistance of the
thermistor is very high compared to that of the lead wire However the
suitable temperature range for thermistors is narrower from -100 to
400oC while RTD can cover from -100 to 1000 oC
4 Thermocouple
A thermocouple consists of two dissimilar metal wires twisted together
to form a junction that can act as a temperature sensor For example
copper wire and constantan wire (55 copper plus 45 nickel)
bull Seebeck effect
The use of a thermocouple as a temperature sensor is based on the
principle of the Seebeck effect The Seebeck effect states that an emf is
generated in the thermocouple when the junction is heated or cooled
Junction copper A
Constantan B
CHE 215 page of 21 H Muhamad 14
VAB is finite when the junction is at a temperature different from that at
the terminals A and B
bull Law of intermediate metals
Junction copper A
iron
Constantan B
When another metal (iron) is added to the thermocouple circuit as shown
in the above sketch two more junctions are formed at points A and B
As long as the junctions at A and B are kept at the same temperature the
emf generated by the main junction isnrsquot altered ie the temperature
reading doesnrsquot change
bull Law of intermediate temperatures
hot junction copper cold junction
E
constantan
CHE 215 page of 21 H Muhamad 15
For the same thermocouple ie the same two dissimilar metal junctions
the emf generated at different temperatures are additive
E3 = E1 + E2
Where E1 is the emf for the cold junction at 0oC and the hot junction at
50 oC E2 is the emf for the cold junction at 50oC and hot junction at 100
oC E3 is the emf for the cold junction at 0oC and hot junction at 100 oC
Precautions for use of TC
bull Extension wire should have similar properties as those of the TC
otherwise the two junctions of the extension wires and the TC wires
should be kept at the same temperature
bull Extension wire should be thick (having a low resistance) so to
minimize the error associated with the wire heating since the wire
resistance R = ρLS where ρ is the resistivity of the wire L is the
length and S is the cross-sectional area of the wire
5 Correction for temperature measurement under high-velocity
For temperature measurements of a flow at high speed usually gas flow
the effect of the stagnation point at the tip of the temperature sensor on
CHE 215 page of 21 H Muhamad 16
the reading could be significant At the stagnation point the stagnation
temperature Ts is
cp
S gCu
TT2
2α+= infin (14)
Where Tinfin is the temperature of the bulk gas uinfin is the velocity of gas the
flow Cp is the specific heat of the gas
The temperature registered by the sensor (the measured temperature) is
usually different than the stagnation temperature due to the effect of the
shield intruding in the flow path The measured temperature is called the
recovery temperature It is strongly dependent on the configuration of
the sensor and the shield The relative difference between the measured
temperature by the sensor Tr and the stagnation temperature TS is
known as the recovery factor r
infinminusinfinminus
=TTTTr
s
r (15)
7 Temperature measurements by radiation
The temperature of an object can be determined from the total thermal
radiation emitted from the object For an ideal body the total energy
emitted is proportional to the fourth power of the temperature
CHE 215 page of 21 H Muhamad 17
However most practical objects are non-ideal bodies and a correction
must be made to obtain the true temperature of the target This
correction is done by the emissivity of the non-ideal body as below
(16) 4TE σε=
Where E is the energy emitted by the object at the temperature T (in K
or oR) ɛ is the emissivity of the object (ɛ le 10) and σ is the Stefan-
Boltzmann constant
σ = 174x10-9 BTU(hft2oR4) or 5669x10-8 W(m2K4)
When an object is an ideal body the emissivity ɛ is equal to 10 and
Equation (16) is then known as the Stefan-Boltzmann equation
CHE 215 page of 21 H Muhamad 18
71 Optical Pyrometer
The optical pyrometer is simply a photometer that matches the energy
emitted from a reference source with the incoming one from the target
source As an example in the laboratory of this course the target source
is an incandescent lamp whose tungsten filament temperature can be
varied by adjusting the current through it (by adjusting a knob on the
optical pyrometer) When the brightness of the reference filament in the
optical pyrometer matches the brightness of the target filament being
measured the image of the reference filament blends into the colour of
the background of the viewing field in the optical pyrometer At this
point the intensity of the energy emitted from the target is equal to that
emitted from the reference and hence the temperature of the target (light
bulb) can be read from the display on a digital readout
2 Total Radiation Pyrometer
The total radiation pyrometer is the most commonly used pyrometer for
continuous non-contacting measurement of temperature Radiation (both
infrared and visible) passes through a lens and is then concentrated on a
heat-sensing element which produces an electric signal This sensing
element or detector may be a thermopile a thin thermistor flake or a
CHE 215 page of 21 H Muhamad 19
resistance thermometer Thermopiles are the most commonly used
Ambient temperature compensation may be required since the body of
the pyrometer is heated by the target radiation and the thermopile is
sensitive to the body heat
The current (or voltage) produced by the sensing detector is sent to a
potentiometer or a millivoltmeter where the current can be read The
total radiation pyrometer can be used to measure low temperature
However temperatures measured are also subject to errors
bull if the source is not an ideal body Error = (1 - ɛ14)
bull if the optical system gets dirty and adsorbs too much radiation
bull If part of the radiant energy is absorbed before it reaches the
instruments such as absorption by smoke and dust Gases such as
carbon dioxide sulphur dioxide and water vapour absorb infrared
radiation
The emissivity of a material (usually written ε or e) is the relative ability
of its surface to emit energy by radiation It is the ratio of energy
radiated by a particular material to energy radiated by a black body at
CHE 215 page of 21 H Muhamad 20
CHE 215 page of 21 H Muhamad 21
the same temperature A true black body would have an ε = 1 while any
real object would have ε lt 1 Emissivity is a dimensionless quantity
In general the duller and blacker a material is the closer its emissivity is
to 1 The more reflective a material is the lower its emissivity Highly
polished silver has an emissivity of about 002[1]
0
02
04
06
08
1
12
0 02 04 06 08 1 12 14 16 18 2
Time (sec)
Nor
mal
ized
dyn
amic
err
or (X
tXo)
Dynamic error
time constant = 025 s
XtXo = 0368
Figure 2 Dynamic errors
As an example shown in Figures 1 and 2 a temperature sensor is in an
environment at temperature T1 of 20oC The temperature of the
environment is assumed to have a surge in temperature to T2 of 100oC
(ideal step change) Therefore the initial (maximum) dynamic error Xo =
(T2-T1) = (100- 20) = 80oC The dynamic error of the temperature
reading is defined as
Xt = T2 -Td
Where Td is the actual temperature response (or temperature reading) of
the temperature sensor at a given time t after it was exposed to the step
change in temperature
CHE 215 page of 21 H Muhamad 3
As shown in Figure 2 the dynamic error of the temperature sensor shows
an exponential decay trend Therefore the rate of change of the dynamic
error can be written as
XkdtdX
minus= (1)
Integration of Equation (1) for time t = 0 to some time t gives
tkXX
o
t minus=⎟⎟⎠
⎞⎜⎜⎝
⎛ln (2)
kt
o
t eXX minus=⎟⎟
⎠
⎞⎜⎜⎝
⎛ (3)
When t is equal to the time constant tc of the sensor which is defined as
tc=1k then
36801 ==⎟⎟⎠
⎞⎜⎜⎝
⎛ minuseXX
o
t (4)
Therefore as indicated by Equation (4) when the elapsed time is equal
to the time constant the response of the sensor has covered 632 of the
step change in the temperature as shown below At t = tc
Td = T2 ndashXtc = T2 ndash 0368 Xo
Td = T2 ndash 0368(T2-T1)
Td ndashT1 = T2 ndash 0368T2 + 0368T1 ndash T1
(Td ndashT1) = 0632 (T2 ndash T1)
CHE 215 page of 21 H Muhamad 4
(Td ndashT1) is 632 of the overall step change (T2 ndash T1)
A first-order-response instrument shows a quick response initially the
response then slows down considerably to the point of achieving a
steady-state measurement The bare-wire thermocouple usually exhibits
a first-order response to a step change in temperature of the environment
it is in From the energy balance for the sensor and the surrounding the
first-order temperature response can be described by the following
differential equation
FTTtdTd
=+sdotτ (5)
where τ is the time constant of the temperature sensor T is the dynamic
temperature of the sensor TF is the step change of temperature and t is
time ( ) ( )( )τexp100 tTTTT F minusminussdotminus+=
However for a shielded temperature sensor with a low thermal
conductivity shield the temperature response could exhibit a second-
order temperature response as described by
( ) FSWSW TTdtdT
tdTd
=+++sdotsdot ττττ 2
2 (6)
CHE 215 page of 21 H Muhamad 5
where τW and τS are the time constant of the sensor itself and the shield
of the sensor respectively The ratio of (τW + τS)(2radic(τW τS)) is known
as the damping ratio For a large damping ratio (greater than 10) the
profile is similar to that of the first order system) On the other hand for
smaller damping ratio the profile is oscillating
( ) ( ) ( )⎟⎟⎠
⎞⎜⎜⎝
⎛minus
minusminusminus+minus+=
sw
wwssF
ttTTTTττ
ττττ expexp100
II Temperature Measurements
1 Thermometer
Common liquid used
bull Alcohol for temperature range from 50 ndash 200oC
bull Xylene for temperature range from -40 to 400oC
bull Hg for temperature range from -37 to 350oC (Hg freezes at -378oC)
Cautions
bull Do not immerse the whole stem of the thermometer in the
environment where the temperature is measured Only place the bulb
of the thermometer in the environment so to avoid error due to
different thermal expansion coefficients of liquid and glass
bull Allow the liquid level in the thermometer stabilized before taking the
temperature reading
CHE 215 page of 21 H Muhamad 6
bull Precision of liquid filled thermometer is frac12 of the smallest division on
the scale Highly accurate Hg thermometer from NIST (National
Institute of Standards and Testing) could measure to plusmn 005oC
2 Resistance temperature detector (RTD)
RTD is basically an electrical wire typically Pt Ag Ni Cu etc which
is used to sense the temperature change based on the principle of the
temperature dependency of the wire resistance as shown below
( )[ ]11 1 TTRR minus+= α (7)
Where R and R1 is the resistances of the wire at T and T1 respectively
and the linear temperature coefficient of the wire resistance which is
defined as below
( )( )121
12TTR
RRminus
minus=α (8)
CHE 215 page of 21 H Muhamad 7
Where R2 is the wire resistance at T2
However the relationship between the wire resistance and temperature
is usually non-linear The relationship can then be expressed as
[ ]21 bTaTRR o ++= (9)
Where Ro is the wire resistance at the reference temperature of zero oC
An RTD sensor can be integrated into a Wheatstone bridge circuit to
convert the RTD resistance change with temperature to a voltage output
The voltage output can be calibrated to give readings of temperature
a) No lead wire
1 At the calibrated temperature
Ro Rx Rx = R0
Vs Va = Ro(Ro+Ro)middotVs = Vs2
Ro Ro Vb = Ro(Ro+Ro)middotVs = Vs2
Vab = Va ndash Vb = 0
CHE 215 page of 21 H Muhamad 8
2 At some other temperature
Rx = Ro +ΔR
Va = Ro(Ro+Ro)middotVs = Vs2
Vb = Ro(Ro+Rx)middotVs = Ro(Ro + Ro + ΔR)middotVs = Ro( 2Ro + ΔR)middotVs
Vab= Vs2 - Ro( 2Ro + ΔR)middotVs = Vs[12 ndash Ro(2Ro + ΔR)]
Vab= Vs[(2Ro + ΔR-2Ro)(2(2Ro+ ΔR))]= Vs[(ΔRRo)(2(2+ ΔRRo))]
o
oSR2R1
RR4
VVabΔ+Δ
sdot=
Since ΔR ltlt Ro ΔR2Ro ltlt 1 Vab can be simplified as
o
SR
R4
VVab Δsdot= (10)
b) With lead wire
(in ldquoExperimental Methods for Engineersrdquo J Holman)
CHE 215 page of 21 H Muhamad 9
RL 1 At the calibrated temperature
Ro Rx (RL + Rx) = Ro
Vs Va = Ro(Ro+Ro)middotVs = Vs2
Ro Ro Vb = Ro(Ro+Ro)middotVs = Vs2
Vab = Va ndash Vb = 0
b) At some other temperature
(RL + Rx) = Ro +ΔRx+ ΔRL for the RTD wire and the lead wire
Va = Ro(Ro+Ro)middotVs = Vs2
Vb = Ro(Ro + Ro + ΔRx+ ΔRL)middotVs
Vab= Vs2 - Ro(2 Ro + ΔRx+ ΔRL)middotVs
Vab= Vs[(2Ro + ΔRx+ ΔRL -2Ro)(2(2Ro+ ΔRx+ ΔRL))]
Vab = (Vs4) [((ΔRx+ ΔRL )Ro) (1+ ΔRx 2Ro + ΔRL 2Ro)]
Since ΔRx and ΔRL ltlt Ro ΔRx2Ro ltlt 1 and ΔRL2Ro ltlt 1 the
equation for Vab can be simplified as
( )o
LSR
RRx4
VVab Δ+Δsdot= (11)
CHE 215 page of 21 H Muhamad 10
ΔRL is not known not calibrated and uncontrollable since it is exposed
to the outside environment that is subject to sporadic changes This is a
source of error in the temperature measurement by RTD
c) Lead wire compensation
(in ldquoExperimental Methods for Engineersrdquo J Holman)
RL 1 At the calibrated temperature
Ro Rx (RL + Rx) = Ro (RL + RD) = Ro
Vs Va = Ro(Ro+Ro)middotVs = Vs2
Ro RL Vb = Ro(Ro+Ro)middotVs = Vs2
RD Vab = Va ndash Vb = 0
CHE 215 page of 21 H Muhamad 11
b) At some other temperature
(RL + Rx) = Ro +ΔRx+ ΔRL for the RTD wire and the lead wire
(RL + RD) = Ro + ΔRL for the dummy wire
Va = Ro(Ro+Ro)middotVs = Vs2
Vb = (Ro+ΔRL) [(Ro+ΔRL) + (Ro + ΔRx+ ΔRL)]middotVs
Vab= Vs2 - (Ro+ΔRL)(2 Ro + ΔRx+ 2ΔRL)middotVs
Vab= Vs[(2Ro + ΔRx+ 2ΔRL -2Ro- 2ΔRL)(2(2Ro+ ΔRx+ 2ΔRL))]
Vab = (Vs4) [ΔRx (Ro + ΔRx 2 + ΔRL)]
Vab = (Vs4) [ΔRxRo (1 + ΔRx 2Ro + ΔRLRo)]
Since ΔRx and ΔRL ltlt Ro ΔRx2Ro ltlt 1 and ΔRLRo ltlt 1 the
equation for Vab can be simplified as
o
SRRx
4VVab Δ
sdot= (12)
Equation (12) has the same form as that of Equation (10) where the
uncertain ΔRL is eliminated
CHE 215 page of 21 H Muhamad 12
3 Thermistors
Thermistors are semiconductor sensors whose resistances decrease with
temperature such as FeO NiO MnO hellip The relationship of the
thermistor resistance and temperature can be written as below
⎥⎦
⎤⎢⎣
⎡⎟⎟⎠
⎞⎜⎜⎝
⎛minusβ
= oT1
T1
o eRR (13)
where Ro is the resistance of the thermistor at the ref temperature To
CHE 215 page of 21 H Muhamad 13
Generally thermistors are more sensitive than RTD They can have a
precision of plusmn 001oC as compared with plusmn 01oC for RTD In addition
the error due to lead wire is insignificant since the resistance of the
thermistor is very high compared to that of the lead wire However the
suitable temperature range for thermistors is narrower from -100 to
400oC while RTD can cover from -100 to 1000 oC
4 Thermocouple
A thermocouple consists of two dissimilar metal wires twisted together
to form a junction that can act as a temperature sensor For example
copper wire and constantan wire (55 copper plus 45 nickel)
bull Seebeck effect
The use of a thermocouple as a temperature sensor is based on the
principle of the Seebeck effect The Seebeck effect states that an emf is
generated in the thermocouple when the junction is heated or cooled
Junction copper A
Constantan B
CHE 215 page of 21 H Muhamad 14
VAB is finite when the junction is at a temperature different from that at
the terminals A and B
bull Law of intermediate metals
Junction copper A
iron
Constantan B
When another metal (iron) is added to the thermocouple circuit as shown
in the above sketch two more junctions are formed at points A and B
As long as the junctions at A and B are kept at the same temperature the
emf generated by the main junction isnrsquot altered ie the temperature
reading doesnrsquot change
bull Law of intermediate temperatures
hot junction copper cold junction
E
constantan
CHE 215 page of 21 H Muhamad 15
For the same thermocouple ie the same two dissimilar metal junctions
the emf generated at different temperatures are additive
E3 = E1 + E2
Where E1 is the emf for the cold junction at 0oC and the hot junction at
50 oC E2 is the emf for the cold junction at 50oC and hot junction at 100
oC E3 is the emf for the cold junction at 0oC and hot junction at 100 oC
Precautions for use of TC
bull Extension wire should have similar properties as those of the TC
otherwise the two junctions of the extension wires and the TC wires
should be kept at the same temperature
bull Extension wire should be thick (having a low resistance) so to
minimize the error associated with the wire heating since the wire
resistance R = ρLS where ρ is the resistivity of the wire L is the
length and S is the cross-sectional area of the wire
5 Correction for temperature measurement under high-velocity
For temperature measurements of a flow at high speed usually gas flow
the effect of the stagnation point at the tip of the temperature sensor on
CHE 215 page of 21 H Muhamad 16
the reading could be significant At the stagnation point the stagnation
temperature Ts is
cp
S gCu
TT2
2α+= infin (14)
Where Tinfin is the temperature of the bulk gas uinfin is the velocity of gas the
flow Cp is the specific heat of the gas
The temperature registered by the sensor (the measured temperature) is
usually different than the stagnation temperature due to the effect of the
shield intruding in the flow path The measured temperature is called the
recovery temperature It is strongly dependent on the configuration of
the sensor and the shield The relative difference between the measured
temperature by the sensor Tr and the stagnation temperature TS is
known as the recovery factor r
infinminusinfinminus
=TTTTr
s
r (15)
7 Temperature measurements by radiation
The temperature of an object can be determined from the total thermal
radiation emitted from the object For an ideal body the total energy
emitted is proportional to the fourth power of the temperature
CHE 215 page of 21 H Muhamad 17
However most practical objects are non-ideal bodies and a correction
must be made to obtain the true temperature of the target This
correction is done by the emissivity of the non-ideal body as below
(16) 4TE σε=
Where E is the energy emitted by the object at the temperature T (in K
or oR) ɛ is the emissivity of the object (ɛ le 10) and σ is the Stefan-
Boltzmann constant
σ = 174x10-9 BTU(hft2oR4) or 5669x10-8 W(m2K4)
When an object is an ideal body the emissivity ɛ is equal to 10 and
Equation (16) is then known as the Stefan-Boltzmann equation
CHE 215 page of 21 H Muhamad 18
71 Optical Pyrometer
The optical pyrometer is simply a photometer that matches the energy
emitted from a reference source with the incoming one from the target
source As an example in the laboratory of this course the target source
is an incandescent lamp whose tungsten filament temperature can be
varied by adjusting the current through it (by adjusting a knob on the
optical pyrometer) When the brightness of the reference filament in the
optical pyrometer matches the brightness of the target filament being
measured the image of the reference filament blends into the colour of
the background of the viewing field in the optical pyrometer At this
point the intensity of the energy emitted from the target is equal to that
emitted from the reference and hence the temperature of the target (light
bulb) can be read from the display on a digital readout
2 Total Radiation Pyrometer
The total radiation pyrometer is the most commonly used pyrometer for
continuous non-contacting measurement of temperature Radiation (both
infrared and visible) passes through a lens and is then concentrated on a
heat-sensing element which produces an electric signal This sensing
element or detector may be a thermopile a thin thermistor flake or a
CHE 215 page of 21 H Muhamad 19
resistance thermometer Thermopiles are the most commonly used
Ambient temperature compensation may be required since the body of
the pyrometer is heated by the target radiation and the thermopile is
sensitive to the body heat
The current (or voltage) produced by the sensing detector is sent to a
potentiometer or a millivoltmeter where the current can be read The
total radiation pyrometer can be used to measure low temperature
However temperatures measured are also subject to errors
bull if the source is not an ideal body Error = (1 - ɛ14)
bull if the optical system gets dirty and adsorbs too much radiation
bull If part of the radiant energy is absorbed before it reaches the
instruments such as absorption by smoke and dust Gases such as
carbon dioxide sulphur dioxide and water vapour absorb infrared
radiation
The emissivity of a material (usually written ε or e) is the relative ability
of its surface to emit energy by radiation It is the ratio of energy
radiated by a particular material to energy radiated by a black body at
CHE 215 page of 21 H Muhamad 20
CHE 215 page of 21 H Muhamad 21
the same temperature A true black body would have an ε = 1 while any
real object would have ε lt 1 Emissivity is a dimensionless quantity
In general the duller and blacker a material is the closer its emissivity is
to 1 The more reflective a material is the lower its emissivity Highly
polished silver has an emissivity of about 002[1]
As shown in Figure 2 the dynamic error of the temperature sensor shows
an exponential decay trend Therefore the rate of change of the dynamic
error can be written as
XkdtdX
minus= (1)
Integration of Equation (1) for time t = 0 to some time t gives
tkXX
o
t minus=⎟⎟⎠
⎞⎜⎜⎝
⎛ln (2)
kt
o
t eXX minus=⎟⎟
⎠
⎞⎜⎜⎝
⎛ (3)
When t is equal to the time constant tc of the sensor which is defined as
tc=1k then
36801 ==⎟⎟⎠
⎞⎜⎜⎝
⎛ minuseXX
o
t (4)
Therefore as indicated by Equation (4) when the elapsed time is equal
to the time constant the response of the sensor has covered 632 of the
step change in the temperature as shown below At t = tc
Td = T2 ndashXtc = T2 ndash 0368 Xo
Td = T2 ndash 0368(T2-T1)
Td ndashT1 = T2 ndash 0368T2 + 0368T1 ndash T1
(Td ndashT1) = 0632 (T2 ndash T1)
CHE 215 page of 21 H Muhamad 4
(Td ndashT1) is 632 of the overall step change (T2 ndash T1)
A first-order-response instrument shows a quick response initially the
response then slows down considerably to the point of achieving a
steady-state measurement The bare-wire thermocouple usually exhibits
a first-order response to a step change in temperature of the environment
it is in From the energy balance for the sensor and the surrounding the
first-order temperature response can be described by the following
differential equation
FTTtdTd
=+sdotτ (5)
where τ is the time constant of the temperature sensor T is the dynamic
temperature of the sensor TF is the step change of temperature and t is
time ( ) ( )( )τexp100 tTTTT F minusminussdotminus+=
However for a shielded temperature sensor with a low thermal
conductivity shield the temperature response could exhibit a second-
order temperature response as described by
( ) FSWSW TTdtdT
tdTd
=+++sdotsdot ττττ 2
2 (6)
CHE 215 page of 21 H Muhamad 5
where τW and τS are the time constant of the sensor itself and the shield
of the sensor respectively The ratio of (τW + τS)(2radic(τW τS)) is known
as the damping ratio For a large damping ratio (greater than 10) the
profile is similar to that of the first order system) On the other hand for
smaller damping ratio the profile is oscillating
( ) ( ) ( )⎟⎟⎠
⎞⎜⎜⎝
⎛minus
minusminusminus+minus+=
sw
wwssF
ttTTTTττ
ττττ expexp100
II Temperature Measurements
1 Thermometer
Common liquid used
bull Alcohol for temperature range from 50 ndash 200oC
bull Xylene for temperature range from -40 to 400oC
bull Hg for temperature range from -37 to 350oC (Hg freezes at -378oC)
Cautions
bull Do not immerse the whole stem of the thermometer in the
environment where the temperature is measured Only place the bulb
of the thermometer in the environment so to avoid error due to
different thermal expansion coefficients of liquid and glass
bull Allow the liquid level in the thermometer stabilized before taking the
temperature reading
CHE 215 page of 21 H Muhamad 6
bull Precision of liquid filled thermometer is frac12 of the smallest division on
the scale Highly accurate Hg thermometer from NIST (National
Institute of Standards and Testing) could measure to plusmn 005oC
2 Resistance temperature detector (RTD)
RTD is basically an electrical wire typically Pt Ag Ni Cu etc which
is used to sense the temperature change based on the principle of the
temperature dependency of the wire resistance as shown below
( )[ ]11 1 TTRR minus+= α (7)
Where R and R1 is the resistances of the wire at T and T1 respectively
and the linear temperature coefficient of the wire resistance which is
defined as below
( )( )121
12TTR
RRminus
minus=α (8)
CHE 215 page of 21 H Muhamad 7
Where R2 is the wire resistance at T2
However the relationship between the wire resistance and temperature
is usually non-linear The relationship can then be expressed as
[ ]21 bTaTRR o ++= (9)
Where Ro is the wire resistance at the reference temperature of zero oC
An RTD sensor can be integrated into a Wheatstone bridge circuit to
convert the RTD resistance change with temperature to a voltage output
The voltage output can be calibrated to give readings of temperature
a) No lead wire
1 At the calibrated temperature
Ro Rx Rx = R0
Vs Va = Ro(Ro+Ro)middotVs = Vs2
Ro Ro Vb = Ro(Ro+Ro)middotVs = Vs2
Vab = Va ndash Vb = 0
CHE 215 page of 21 H Muhamad 8
2 At some other temperature
Rx = Ro +ΔR
Va = Ro(Ro+Ro)middotVs = Vs2
Vb = Ro(Ro+Rx)middotVs = Ro(Ro + Ro + ΔR)middotVs = Ro( 2Ro + ΔR)middotVs
Vab= Vs2 - Ro( 2Ro + ΔR)middotVs = Vs[12 ndash Ro(2Ro + ΔR)]
Vab= Vs[(2Ro + ΔR-2Ro)(2(2Ro+ ΔR))]= Vs[(ΔRRo)(2(2+ ΔRRo))]
o
oSR2R1
RR4
VVabΔ+Δ
sdot=
Since ΔR ltlt Ro ΔR2Ro ltlt 1 Vab can be simplified as
o
SR
R4
VVab Δsdot= (10)
b) With lead wire
(in ldquoExperimental Methods for Engineersrdquo J Holman)
CHE 215 page of 21 H Muhamad 9
RL 1 At the calibrated temperature
Ro Rx (RL + Rx) = Ro
Vs Va = Ro(Ro+Ro)middotVs = Vs2
Ro Ro Vb = Ro(Ro+Ro)middotVs = Vs2
Vab = Va ndash Vb = 0
b) At some other temperature
(RL + Rx) = Ro +ΔRx+ ΔRL for the RTD wire and the lead wire
Va = Ro(Ro+Ro)middotVs = Vs2
Vb = Ro(Ro + Ro + ΔRx+ ΔRL)middotVs
Vab= Vs2 - Ro(2 Ro + ΔRx+ ΔRL)middotVs
Vab= Vs[(2Ro + ΔRx+ ΔRL -2Ro)(2(2Ro+ ΔRx+ ΔRL))]
Vab = (Vs4) [((ΔRx+ ΔRL )Ro) (1+ ΔRx 2Ro + ΔRL 2Ro)]
Since ΔRx and ΔRL ltlt Ro ΔRx2Ro ltlt 1 and ΔRL2Ro ltlt 1 the
equation for Vab can be simplified as
( )o
LSR
RRx4
VVab Δ+Δsdot= (11)
CHE 215 page of 21 H Muhamad 10
ΔRL is not known not calibrated and uncontrollable since it is exposed
to the outside environment that is subject to sporadic changes This is a
source of error in the temperature measurement by RTD
c) Lead wire compensation
(in ldquoExperimental Methods for Engineersrdquo J Holman)
RL 1 At the calibrated temperature
Ro Rx (RL + Rx) = Ro (RL + RD) = Ro
Vs Va = Ro(Ro+Ro)middotVs = Vs2
Ro RL Vb = Ro(Ro+Ro)middotVs = Vs2
RD Vab = Va ndash Vb = 0
CHE 215 page of 21 H Muhamad 11
b) At some other temperature
(RL + Rx) = Ro +ΔRx+ ΔRL for the RTD wire and the lead wire
(RL + RD) = Ro + ΔRL for the dummy wire
Va = Ro(Ro+Ro)middotVs = Vs2
Vb = (Ro+ΔRL) [(Ro+ΔRL) + (Ro + ΔRx+ ΔRL)]middotVs
Vab= Vs2 - (Ro+ΔRL)(2 Ro + ΔRx+ 2ΔRL)middotVs
Vab= Vs[(2Ro + ΔRx+ 2ΔRL -2Ro- 2ΔRL)(2(2Ro+ ΔRx+ 2ΔRL))]
Vab = (Vs4) [ΔRx (Ro + ΔRx 2 + ΔRL)]
Vab = (Vs4) [ΔRxRo (1 + ΔRx 2Ro + ΔRLRo)]
Since ΔRx and ΔRL ltlt Ro ΔRx2Ro ltlt 1 and ΔRLRo ltlt 1 the
equation for Vab can be simplified as
o
SRRx
4VVab Δ
sdot= (12)
Equation (12) has the same form as that of Equation (10) where the
uncertain ΔRL is eliminated
CHE 215 page of 21 H Muhamad 12
3 Thermistors
Thermistors are semiconductor sensors whose resistances decrease with
temperature such as FeO NiO MnO hellip The relationship of the
thermistor resistance and temperature can be written as below
⎥⎦
⎤⎢⎣
⎡⎟⎟⎠
⎞⎜⎜⎝
⎛minusβ
= oT1
T1
o eRR (13)
where Ro is the resistance of the thermistor at the ref temperature To
CHE 215 page of 21 H Muhamad 13
Generally thermistors are more sensitive than RTD They can have a
precision of plusmn 001oC as compared with plusmn 01oC for RTD In addition
the error due to lead wire is insignificant since the resistance of the
thermistor is very high compared to that of the lead wire However the
suitable temperature range for thermistors is narrower from -100 to
400oC while RTD can cover from -100 to 1000 oC
4 Thermocouple
A thermocouple consists of two dissimilar metal wires twisted together
to form a junction that can act as a temperature sensor For example
copper wire and constantan wire (55 copper plus 45 nickel)
bull Seebeck effect
The use of a thermocouple as a temperature sensor is based on the
principle of the Seebeck effect The Seebeck effect states that an emf is
generated in the thermocouple when the junction is heated or cooled
Junction copper A
Constantan B
CHE 215 page of 21 H Muhamad 14
VAB is finite when the junction is at a temperature different from that at
the terminals A and B
bull Law of intermediate metals
Junction copper A
iron
Constantan B
When another metal (iron) is added to the thermocouple circuit as shown
in the above sketch two more junctions are formed at points A and B
As long as the junctions at A and B are kept at the same temperature the
emf generated by the main junction isnrsquot altered ie the temperature
reading doesnrsquot change
bull Law of intermediate temperatures
hot junction copper cold junction
E
constantan
CHE 215 page of 21 H Muhamad 15
For the same thermocouple ie the same two dissimilar metal junctions
the emf generated at different temperatures are additive
E3 = E1 + E2
Where E1 is the emf for the cold junction at 0oC and the hot junction at
50 oC E2 is the emf for the cold junction at 50oC and hot junction at 100
oC E3 is the emf for the cold junction at 0oC and hot junction at 100 oC
Precautions for use of TC
bull Extension wire should have similar properties as those of the TC
otherwise the two junctions of the extension wires and the TC wires
should be kept at the same temperature
bull Extension wire should be thick (having a low resistance) so to
minimize the error associated with the wire heating since the wire
resistance R = ρLS where ρ is the resistivity of the wire L is the
length and S is the cross-sectional area of the wire
5 Correction for temperature measurement under high-velocity
For temperature measurements of a flow at high speed usually gas flow
the effect of the stagnation point at the tip of the temperature sensor on
CHE 215 page of 21 H Muhamad 16
the reading could be significant At the stagnation point the stagnation
temperature Ts is
cp
S gCu
TT2
2α+= infin (14)
Where Tinfin is the temperature of the bulk gas uinfin is the velocity of gas the
flow Cp is the specific heat of the gas
The temperature registered by the sensor (the measured temperature) is
usually different than the stagnation temperature due to the effect of the
shield intruding in the flow path The measured temperature is called the
recovery temperature It is strongly dependent on the configuration of
the sensor and the shield The relative difference between the measured
temperature by the sensor Tr and the stagnation temperature TS is
known as the recovery factor r
infinminusinfinminus
=TTTTr
s
r (15)
7 Temperature measurements by radiation
The temperature of an object can be determined from the total thermal
radiation emitted from the object For an ideal body the total energy
emitted is proportional to the fourth power of the temperature
CHE 215 page of 21 H Muhamad 17
However most practical objects are non-ideal bodies and a correction
must be made to obtain the true temperature of the target This
correction is done by the emissivity of the non-ideal body as below
(16) 4TE σε=
Where E is the energy emitted by the object at the temperature T (in K
or oR) ɛ is the emissivity of the object (ɛ le 10) and σ is the Stefan-
Boltzmann constant
σ = 174x10-9 BTU(hft2oR4) or 5669x10-8 W(m2K4)
When an object is an ideal body the emissivity ɛ is equal to 10 and
Equation (16) is then known as the Stefan-Boltzmann equation
CHE 215 page of 21 H Muhamad 18
71 Optical Pyrometer
The optical pyrometer is simply a photometer that matches the energy
emitted from a reference source with the incoming one from the target
source As an example in the laboratory of this course the target source
is an incandescent lamp whose tungsten filament temperature can be
varied by adjusting the current through it (by adjusting a knob on the
optical pyrometer) When the brightness of the reference filament in the
optical pyrometer matches the brightness of the target filament being
measured the image of the reference filament blends into the colour of
the background of the viewing field in the optical pyrometer At this
point the intensity of the energy emitted from the target is equal to that
emitted from the reference and hence the temperature of the target (light
bulb) can be read from the display on a digital readout
2 Total Radiation Pyrometer
The total radiation pyrometer is the most commonly used pyrometer for
continuous non-contacting measurement of temperature Radiation (both
infrared and visible) passes through a lens and is then concentrated on a
heat-sensing element which produces an electric signal This sensing
element or detector may be a thermopile a thin thermistor flake or a
CHE 215 page of 21 H Muhamad 19
resistance thermometer Thermopiles are the most commonly used
Ambient temperature compensation may be required since the body of
the pyrometer is heated by the target radiation and the thermopile is
sensitive to the body heat
The current (or voltage) produced by the sensing detector is sent to a
potentiometer or a millivoltmeter where the current can be read The
total radiation pyrometer can be used to measure low temperature
However temperatures measured are also subject to errors
bull if the source is not an ideal body Error = (1 - ɛ14)
bull if the optical system gets dirty and adsorbs too much radiation
bull If part of the radiant energy is absorbed before it reaches the
instruments such as absorption by smoke and dust Gases such as
carbon dioxide sulphur dioxide and water vapour absorb infrared
radiation
The emissivity of a material (usually written ε or e) is the relative ability
of its surface to emit energy by radiation It is the ratio of energy
radiated by a particular material to energy radiated by a black body at
CHE 215 page of 21 H Muhamad 20
CHE 215 page of 21 H Muhamad 21
the same temperature A true black body would have an ε = 1 while any
real object would have ε lt 1 Emissivity is a dimensionless quantity
In general the duller and blacker a material is the closer its emissivity is
to 1 The more reflective a material is the lower its emissivity Highly
polished silver has an emissivity of about 002[1]
(Td ndashT1) is 632 of the overall step change (T2 ndash T1)
A first-order-response instrument shows a quick response initially the
response then slows down considerably to the point of achieving a
steady-state measurement The bare-wire thermocouple usually exhibits
a first-order response to a step change in temperature of the environment
it is in From the energy balance for the sensor and the surrounding the
first-order temperature response can be described by the following
differential equation
FTTtdTd
=+sdotτ (5)
where τ is the time constant of the temperature sensor T is the dynamic
temperature of the sensor TF is the step change of temperature and t is
time ( ) ( )( )τexp100 tTTTT F minusminussdotminus+=
However for a shielded temperature sensor with a low thermal
conductivity shield the temperature response could exhibit a second-
order temperature response as described by
( ) FSWSW TTdtdT
tdTd
=+++sdotsdot ττττ 2
2 (6)
CHE 215 page of 21 H Muhamad 5
where τW and τS are the time constant of the sensor itself and the shield
of the sensor respectively The ratio of (τW + τS)(2radic(τW τS)) is known
as the damping ratio For a large damping ratio (greater than 10) the
profile is similar to that of the first order system) On the other hand for
smaller damping ratio the profile is oscillating
( ) ( ) ( )⎟⎟⎠
⎞⎜⎜⎝
⎛minus
minusminusminus+minus+=
sw
wwssF
ttTTTTττ
ττττ expexp100
II Temperature Measurements
1 Thermometer
Common liquid used
bull Alcohol for temperature range from 50 ndash 200oC
bull Xylene for temperature range from -40 to 400oC
bull Hg for temperature range from -37 to 350oC (Hg freezes at -378oC)
Cautions
bull Do not immerse the whole stem of the thermometer in the
environment where the temperature is measured Only place the bulb
of the thermometer in the environment so to avoid error due to
different thermal expansion coefficients of liquid and glass
bull Allow the liquid level in the thermometer stabilized before taking the
temperature reading
CHE 215 page of 21 H Muhamad 6
bull Precision of liquid filled thermometer is frac12 of the smallest division on
the scale Highly accurate Hg thermometer from NIST (National
Institute of Standards and Testing) could measure to plusmn 005oC
2 Resistance temperature detector (RTD)
RTD is basically an electrical wire typically Pt Ag Ni Cu etc which
is used to sense the temperature change based on the principle of the
temperature dependency of the wire resistance as shown below
( )[ ]11 1 TTRR minus+= α (7)
Where R and R1 is the resistances of the wire at T and T1 respectively
and the linear temperature coefficient of the wire resistance which is
defined as below
( )( )121
12TTR
RRminus
minus=α (8)
CHE 215 page of 21 H Muhamad 7
Where R2 is the wire resistance at T2
However the relationship between the wire resistance and temperature
is usually non-linear The relationship can then be expressed as
[ ]21 bTaTRR o ++= (9)
Where Ro is the wire resistance at the reference temperature of zero oC
An RTD sensor can be integrated into a Wheatstone bridge circuit to
convert the RTD resistance change with temperature to a voltage output
The voltage output can be calibrated to give readings of temperature
a) No lead wire
1 At the calibrated temperature
Ro Rx Rx = R0
Vs Va = Ro(Ro+Ro)middotVs = Vs2
Ro Ro Vb = Ro(Ro+Ro)middotVs = Vs2
Vab = Va ndash Vb = 0
CHE 215 page of 21 H Muhamad 8
2 At some other temperature
Rx = Ro +ΔR
Va = Ro(Ro+Ro)middotVs = Vs2
Vb = Ro(Ro+Rx)middotVs = Ro(Ro + Ro + ΔR)middotVs = Ro( 2Ro + ΔR)middotVs
Vab= Vs2 - Ro( 2Ro + ΔR)middotVs = Vs[12 ndash Ro(2Ro + ΔR)]
Vab= Vs[(2Ro + ΔR-2Ro)(2(2Ro+ ΔR))]= Vs[(ΔRRo)(2(2+ ΔRRo))]
o
oSR2R1
RR4
VVabΔ+Δ
sdot=
Since ΔR ltlt Ro ΔR2Ro ltlt 1 Vab can be simplified as
o
SR
R4
VVab Δsdot= (10)
b) With lead wire
(in ldquoExperimental Methods for Engineersrdquo J Holman)
CHE 215 page of 21 H Muhamad 9
RL 1 At the calibrated temperature
Ro Rx (RL + Rx) = Ro
Vs Va = Ro(Ro+Ro)middotVs = Vs2
Ro Ro Vb = Ro(Ro+Ro)middotVs = Vs2
Vab = Va ndash Vb = 0
b) At some other temperature
(RL + Rx) = Ro +ΔRx+ ΔRL for the RTD wire and the lead wire
Va = Ro(Ro+Ro)middotVs = Vs2
Vb = Ro(Ro + Ro + ΔRx+ ΔRL)middotVs
Vab= Vs2 - Ro(2 Ro + ΔRx+ ΔRL)middotVs
Vab= Vs[(2Ro + ΔRx+ ΔRL -2Ro)(2(2Ro+ ΔRx+ ΔRL))]
Vab = (Vs4) [((ΔRx+ ΔRL )Ro) (1+ ΔRx 2Ro + ΔRL 2Ro)]
Since ΔRx and ΔRL ltlt Ro ΔRx2Ro ltlt 1 and ΔRL2Ro ltlt 1 the
equation for Vab can be simplified as
( )o
LSR
RRx4
VVab Δ+Δsdot= (11)
CHE 215 page of 21 H Muhamad 10
ΔRL is not known not calibrated and uncontrollable since it is exposed
to the outside environment that is subject to sporadic changes This is a
source of error in the temperature measurement by RTD
c) Lead wire compensation
(in ldquoExperimental Methods for Engineersrdquo J Holman)
RL 1 At the calibrated temperature
Ro Rx (RL + Rx) = Ro (RL + RD) = Ro
Vs Va = Ro(Ro+Ro)middotVs = Vs2
Ro RL Vb = Ro(Ro+Ro)middotVs = Vs2
RD Vab = Va ndash Vb = 0
CHE 215 page of 21 H Muhamad 11
b) At some other temperature
(RL + Rx) = Ro +ΔRx+ ΔRL for the RTD wire and the lead wire
(RL + RD) = Ro + ΔRL for the dummy wire
Va = Ro(Ro+Ro)middotVs = Vs2
Vb = (Ro+ΔRL) [(Ro+ΔRL) + (Ro + ΔRx+ ΔRL)]middotVs
Vab= Vs2 - (Ro+ΔRL)(2 Ro + ΔRx+ 2ΔRL)middotVs
Vab= Vs[(2Ro + ΔRx+ 2ΔRL -2Ro- 2ΔRL)(2(2Ro+ ΔRx+ 2ΔRL))]
Vab = (Vs4) [ΔRx (Ro + ΔRx 2 + ΔRL)]
Vab = (Vs4) [ΔRxRo (1 + ΔRx 2Ro + ΔRLRo)]
Since ΔRx and ΔRL ltlt Ro ΔRx2Ro ltlt 1 and ΔRLRo ltlt 1 the
equation for Vab can be simplified as
o
SRRx
4VVab Δ
sdot= (12)
Equation (12) has the same form as that of Equation (10) where the
uncertain ΔRL is eliminated
CHE 215 page of 21 H Muhamad 12
3 Thermistors
Thermistors are semiconductor sensors whose resistances decrease with
temperature such as FeO NiO MnO hellip The relationship of the
thermistor resistance and temperature can be written as below
⎥⎦
⎤⎢⎣
⎡⎟⎟⎠
⎞⎜⎜⎝
⎛minusβ
= oT1
T1
o eRR (13)
where Ro is the resistance of the thermistor at the ref temperature To
CHE 215 page of 21 H Muhamad 13
Generally thermistors are more sensitive than RTD They can have a
precision of plusmn 001oC as compared with plusmn 01oC for RTD In addition
the error due to lead wire is insignificant since the resistance of the
thermistor is very high compared to that of the lead wire However the
suitable temperature range for thermistors is narrower from -100 to
400oC while RTD can cover from -100 to 1000 oC
4 Thermocouple
A thermocouple consists of two dissimilar metal wires twisted together
to form a junction that can act as a temperature sensor For example
copper wire and constantan wire (55 copper plus 45 nickel)
bull Seebeck effect
The use of a thermocouple as a temperature sensor is based on the
principle of the Seebeck effect The Seebeck effect states that an emf is
generated in the thermocouple when the junction is heated or cooled
Junction copper A
Constantan B
CHE 215 page of 21 H Muhamad 14
VAB is finite when the junction is at a temperature different from that at
the terminals A and B
bull Law of intermediate metals
Junction copper A
iron
Constantan B
When another metal (iron) is added to the thermocouple circuit as shown
in the above sketch two more junctions are formed at points A and B
As long as the junctions at A and B are kept at the same temperature the
emf generated by the main junction isnrsquot altered ie the temperature
reading doesnrsquot change
bull Law of intermediate temperatures
hot junction copper cold junction
E
constantan
CHE 215 page of 21 H Muhamad 15
For the same thermocouple ie the same two dissimilar metal junctions
the emf generated at different temperatures are additive
E3 = E1 + E2
Where E1 is the emf for the cold junction at 0oC and the hot junction at
50 oC E2 is the emf for the cold junction at 50oC and hot junction at 100
oC E3 is the emf for the cold junction at 0oC and hot junction at 100 oC
Precautions for use of TC
bull Extension wire should have similar properties as those of the TC
otherwise the two junctions of the extension wires and the TC wires
should be kept at the same temperature
bull Extension wire should be thick (having a low resistance) so to
minimize the error associated with the wire heating since the wire
resistance R = ρLS where ρ is the resistivity of the wire L is the
length and S is the cross-sectional area of the wire
5 Correction for temperature measurement under high-velocity
For temperature measurements of a flow at high speed usually gas flow
the effect of the stagnation point at the tip of the temperature sensor on
CHE 215 page of 21 H Muhamad 16
the reading could be significant At the stagnation point the stagnation
temperature Ts is
cp
S gCu
TT2
2α+= infin (14)
Where Tinfin is the temperature of the bulk gas uinfin is the velocity of gas the
flow Cp is the specific heat of the gas
The temperature registered by the sensor (the measured temperature) is
usually different than the stagnation temperature due to the effect of the
shield intruding in the flow path The measured temperature is called the
recovery temperature It is strongly dependent on the configuration of
the sensor and the shield The relative difference between the measured
temperature by the sensor Tr and the stagnation temperature TS is
known as the recovery factor r
infinminusinfinminus
=TTTTr
s
r (15)
7 Temperature measurements by radiation
The temperature of an object can be determined from the total thermal
radiation emitted from the object For an ideal body the total energy
emitted is proportional to the fourth power of the temperature
CHE 215 page of 21 H Muhamad 17
However most practical objects are non-ideal bodies and a correction
must be made to obtain the true temperature of the target This
correction is done by the emissivity of the non-ideal body as below
(16) 4TE σε=
Where E is the energy emitted by the object at the temperature T (in K
or oR) ɛ is the emissivity of the object (ɛ le 10) and σ is the Stefan-
Boltzmann constant
σ = 174x10-9 BTU(hft2oR4) or 5669x10-8 W(m2K4)
When an object is an ideal body the emissivity ɛ is equal to 10 and
Equation (16) is then known as the Stefan-Boltzmann equation
CHE 215 page of 21 H Muhamad 18
71 Optical Pyrometer
The optical pyrometer is simply a photometer that matches the energy
emitted from a reference source with the incoming one from the target
source As an example in the laboratory of this course the target source
is an incandescent lamp whose tungsten filament temperature can be
varied by adjusting the current through it (by adjusting a knob on the
optical pyrometer) When the brightness of the reference filament in the
optical pyrometer matches the brightness of the target filament being
measured the image of the reference filament blends into the colour of
the background of the viewing field in the optical pyrometer At this
point the intensity of the energy emitted from the target is equal to that
emitted from the reference and hence the temperature of the target (light
bulb) can be read from the display on a digital readout
2 Total Radiation Pyrometer
The total radiation pyrometer is the most commonly used pyrometer for
continuous non-contacting measurement of temperature Radiation (both
infrared and visible) passes through a lens and is then concentrated on a
heat-sensing element which produces an electric signal This sensing
element or detector may be a thermopile a thin thermistor flake or a
CHE 215 page of 21 H Muhamad 19
resistance thermometer Thermopiles are the most commonly used
Ambient temperature compensation may be required since the body of
the pyrometer is heated by the target radiation and the thermopile is
sensitive to the body heat
The current (or voltage) produced by the sensing detector is sent to a
potentiometer or a millivoltmeter where the current can be read The
total radiation pyrometer can be used to measure low temperature
However temperatures measured are also subject to errors
bull if the source is not an ideal body Error = (1 - ɛ14)
bull if the optical system gets dirty and adsorbs too much radiation
bull If part of the radiant energy is absorbed before it reaches the
instruments such as absorption by smoke and dust Gases such as
carbon dioxide sulphur dioxide and water vapour absorb infrared
radiation
The emissivity of a material (usually written ε or e) is the relative ability
of its surface to emit energy by radiation It is the ratio of energy
radiated by a particular material to energy radiated by a black body at
CHE 215 page of 21 H Muhamad 20
CHE 215 page of 21 H Muhamad 21
the same temperature A true black body would have an ε = 1 while any
real object would have ε lt 1 Emissivity is a dimensionless quantity
In general the duller and blacker a material is the closer its emissivity is
to 1 The more reflective a material is the lower its emissivity Highly
polished silver has an emissivity of about 002[1]
where τW and τS are the time constant of the sensor itself and the shield
of the sensor respectively The ratio of (τW + τS)(2radic(τW τS)) is known
as the damping ratio For a large damping ratio (greater than 10) the
profile is similar to that of the first order system) On the other hand for
smaller damping ratio the profile is oscillating
( ) ( ) ( )⎟⎟⎠
⎞⎜⎜⎝
⎛minus
minusminusminus+minus+=
sw
wwssF
ttTTTTττ
ττττ expexp100
II Temperature Measurements
1 Thermometer
Common liquid used
bull Alcohol for temperature range from 50 ndash 200oC
bull Xylene for temperature range from -40 to 400oC
bull Hg for temperature range from -37 to 350oC (Hg freezes at -378oC)
Cautions
bull Do not immerse the whole stem of the thermometer in the
environment where the temperature is measured Only place the bulb
of the thermometer in the environment so to avoid error due to
different thermal expansion coefficients of liquid and glass
bull Allow the liquid level in the thermometer stabilized before taking the
temperature reading
CHE 215 page of 21 H Muhamad 6
bull Precision of liquid filled thermometer is frac12 of the smallest division on
the scale Highly accurate Hg thermometer from NIST (National
Institute of Standards and Testing) could measure to plusmn 005oC
2 Resistance temperature detector (RTD)
RTD is basically an electrical wire typically Pt Ag Ni Cu etc which
is used to sense the temperature change based on the principle of the
temperature dependency of the wire resistance as shown below
( )[ ]11 1 TTRR minus+= α (7)
Where R and R1 is the resistances of the wire at T and T1 respectively
and the linear temperature coefficient of the wire resistance which is
defined as below
( )( )121
12TTR
RRminus
minus=α (8)
CHE 215 page of 21 H Muhamad 7
Where R2 is the wire resistance at T2
However the relationship between the wire resistance and temperature
is usually non-linear The relationship can then be expressed as
[ ]21 bTaTRR o ++= (9)
Where Ro is the wire resistance at the reference temperature of zero oC
An RTD sensor can be integrated into a Wheatstone bridge circuit to
convert the RTD resistance change with temperature to a voltage output
The voltage output can be calibrated to give readings of temperature
a) No lead wire
1 At the calibrated temperature
Ro Rx Rx = R0
Vs Va = Ro(Ro+Ro)middotVs = Vs2
Ro Ro Vb = Ro(Ro+Ro)middotVs = Vs2
Vab = Va ndash Vb = 0
CHE 215 page of 21 H Muhamad 8
2 At some other temperature
Rx = Ro +ΔR
Va = Ro(Ro+Ro)middotVs = Vs2
Vb = Ro(Ro+Rx)middotVs = Ro(Ro + Ro + ΔR)middotVs = Ro( 2Ro + ΔR)middotVs
Vab= Vs2 - Ro( 2Ro + ΔR)middotVs = Vs[12 ndash Ro(2Ro + ΔR)]
Vab= Vs[(2Ro + ΔR-2Ro)(2(2Ro+ ΔR))]= Vs[(ΔRRo)(2(2+ ΔRRo))]
o
oSR2R1
RR4
VVabΔ+Δ
sdot=
Since ΔR ltlt Ro ΔR2Ro ltlt 1 Vab can be simplified as
o
SR
R4
VVab Δsdot= (10)
b) With lead wire
(in ldquoExperimental Methods for Engineersrdquo J Holman)
CHE 215 page of 21 H Muhamad 9
RL 1 At the calibrated temperature
Ro Rx (RL + Rx) = Ro
Vs Va = Ro(Ro+Ro)middotVs = Vs2
Ro Ro Vb = Ro(Ro+Ro)middotVs = Vs2
Vab = Va ndash Vb = 0
b) At some other temperature
(RL + Rx) = Ro +ΔRx+ ΔRL for the RTD wire and the lead wire
Va = Ro(Ro+Ro)middotVs = Vs2
Vb = Ro(Ro + Ro + ΔRx+ ΔRL)middotVs
Vab= Vs2 - Ro(2 Ro + ΔRx+ ΔRL)middotVs
Vab= Vs[(2Ro + ΔRx+ ΔRL -2Ro)(2(2Ro+ ΔRx+ ΔRL))]
Vab = (Vs4) [((ΔRx+ ΔRL )Ro) (1+ ΔRx 2Ro + ΔRL 2Ro)]
Since ΔRx and ΔRL ltlt Ro ΔRx2Ro ltlt 1 and ΔRL2Ro ltlt 1 the
equation for Vab can be simplified as
( )o
LSR
RRx4
VVab Δ+Δsdot= (11)
CHE 215 page of 21 H Muhamad 10
ΔRL is not known not calibrated and uncontrollable since it is exposed
to the outside environment that is subject to sporadic changes This is a
source of error in the temperature measurement by RTD
c) Lead wire compensation
(in ldquoExperimental Methods for Engineersrdquo J Holman)
RL 1 At the calibrated temperature
Ro Rx (RL + Rx) = Ro (RL + RD) = Ro
Vs Va = Ro(Ro+Ro)middotVs = Vs2
Ro RL Vb = Ro(Ro+Ro)middotVs = Vs2
RD Vab = Va ndash Vb = 0
CHE 215 page of 21 H Muhamad 11
b) At some other temperature
(RL + Rx) = Ro +ΔRx+ ΔRL for the RTD wire and the lead wire
(RL + RD) = Ro + ΔRL for the dummy wire
Va = Ro(Ro+Ro)middotVs = Vs2
Vb = (Ro+ΔRL) [(Ro+ΔRL) + (Ro + ΔRx+ ΔRL)]middotVs
Vab= Vs2 - (Ro+ΔRL)(2 Ro + ΔRx+ 2ΔRL)middotVs
Vab= Vs[(2Ro + ΔRx+ 2ΔRL -2Ro- 2ΔRL)(2(2Ro+ ΔRx+ 2ΔRL))]
Vab = (Vs4) [ΔRx (Ro + ΔRx 2 + ΔRL)]
Vab = (Vs4) [ΔRxRo (1 + ΔRx 2Ro + ΔRLRo)]
Since ΔRx and ΔRL ltlt Ro ΔRx2Ro ltlt 1 and ΔRLRo ltlt 1 the
equation for Vab can be simplified as
o
SRRx
4VVab Δ
sdot= (12)
Equation (12) has the same form as that of Equation (10) where the
uncertain ΔRL is eliminated
CHE 215 page of 21 H Muhamad 12
3 Thermistors
Thermistors are semiconductor sensors whose resistances decrease with
temperature such as FeO NiO MnO hellip The relationship of the
thermistor resistance and temperature can be written as below
⎥⎦
⎤⎢⎣
⎡⎟⎟⎠
⎞⎜⎜⎝
⎛minusβ
= oT1
T1
o eRR (13)
where Ro is the resistance of the thermistor at the ref temperature To
CHE 215 page of 21 H Muhamad 13
Generally thermistors are more sensitive than RTD They can have a
precision of plusmn 001oC as compared with plusmn 01oC for RTD In addition
the error due to lead wire is insignificant since the resistance of the
thermistor is very high compared to that of the lead wire However the
suitable temperature range for thermistors is narrower from -100 to
400oC while RTD can cover from -100 to 1000 oC
4 Thermocouple
A thermocouple consists of two dissimilar metal wires twisted together
to form a junction that can act as a temperature sensor For example
copper wire and constantan wire (55 copper plus 45 nickel)
bull Seebeck effect
The use of a thermocouple as a temperature sensor is based on the
principle of the Seebeck effect The Seebeck effect states that an emf is
generated in the thermocouple when the junction is heated or cooled
Junction copper A
Constantan B
CHE 215 page of 21 H Muhamad 14
VAB is finite when the junction is at a temperature different from that at
the terminals A and B
bull Law of intermediate metals
Junction copper A
iron
Constantan B
When another metal (iron) is added to the thermocouple circuit as shown
in the above sketch two more junctions are formed at points A and B
As long as the junctions at A and B are kept at the same temperature the
emf generated by the main junction isnrsquot altered ie the temperature
reading doesnrsquot change
bull Law of intermediate temperatures
hot junction copper cold junction
E
constantan
CHE 215 page of 21 H Muhamad 15
For the same thermocouple ie the same two dissimilar metal junctions
the emf generated at different temperatures are additive
E3 = E1 + E2
Where E1 is the emf for the cold junction at 0oC and the hot junction at
50 oC E2 is the emf for the cold junction at 50oC and hot junction at 100
oC E3 is the emf for the cold junction at 0oC and hot junction at 100 oC
Precautions for use of TC
bull Extension wire should have similar properties as those of the TC
otherwise the two junctions of the extension wires and the TC wires
should be kept at the same temperature
bull Extension wire should be thick (having a low resistance) so to
minimize the error associated with the wire heating since the wire
resistance R = ρLS where ρ is the resistivity of the wire L is the
length and S is the cross-sectional area of the wire
5 Correction for temperature measurement under high-velocity
For temperature measurements of a flow at high speed usually gas flow
the effect of the stagnation point at the tip of the temperature sensor on
CHE 215 page of 21 H Muhamad 16
the reading could be significant At the stagnation point the stagnation
temperature Ts is
cp
S gCu
TT2
2α+= infin (14)
Where Tinfin is the temperature of the bulk gas uinfin is the velocity of gas the
flow Cp is the specific heat of the gas
The temperature registered by the sensor (the measured temperature) is
usually different than the stagnation temperature due to the effect of the
shield intruding in the flow path The measured temperature is called the
recovery temperature It is strongly dependent on the configuration of
the sensor and the shield The relative difference between the measured
temperature by the sensor Tr and the stagnation temperature TS is
known as the recovery factor r
infinminusinfinminus
=TTTTr
s
r (15)
7 Temperature measurements by radiation
The temperature of an object can be determined from the total thermal
radiation emitted from the object For an ideal body the total energy
emitted is proportional to the fourth power of the temperature
CHE 215 page of 21 H Muhamad 17
However most practical objects are non-ideal bodies and a correction
must be made to obtain the true temperature of the target This
correction is done by the emissivity of the non-ideal body as below
(16) 4TE σε=
Where E is the energy emitted by the object at the temperature T (in K
or oR) ɛ is the emissivity of the object (ɛ le 10) and σ is the Stefan-
Boltzmann constant
σ = 174x10-9 BTU(hft2oR4) or 5669x10-8 W(m2K4)
When an object is an ideal body the emissivity ɛ is equal to 10 and
Equation (16) is then known as the Stefan-Boltzmann equation
CHE 215 page of 21 H Muhamad 18
71 Optical Pyrometer
The optical pyrometer is simply a photometer that matches the energy
emitted from a reference source with the incoming one from the target
source As an example in the laboratory of this course the target source
is an incandescent lamp whose tungsten filament temperature can be
varied by adjusting the current through it (by adjusting a knob on the
optical pyrometer) When the brightness of the reference filament in the
optical pyrometer matches the brightness of the target filament being
measured the image of the reference filament blends into the colour of
the background of the viewing field in the optical pyrometer At this
point the intensity of the energy emitted from the target is equal to that
emitted from the reference and hence the temperature of the target (light
bulb) can be read from the display on a digital readout
2 Total Radiation Pyrometer
The total radiation pyrometer is the most commonly used pyrometer for
continuous non-contacting measurement of temperature Radiation (both
infrared and visible) passes through a lens and is then concentrated on a
heat-sensing element which produces an electric signal This sensing
element or detector may be a thermopile a thin thermistor flake or a
CHE 215 page of 21 H Muhamad 19
resistance thermometer Thermopiles are the most commonly used
Ambient temperature compensation may be required since the body of
the pyrometer is heated by the target radiation and the thermopile is
sensitive to the body heat
The current (or voltage) produced by the sensing detector is sent to a
potentiometer or a millivoltmeter where the current can be read The
total radiation pyrometer can be used to measure low temperature
However temperatures measured are also subject to errors
bull if the source is not an ideal body Error = (1 - ɛ14)
bull if the optical system gets dirty and adsorbs too much radiation
bull If part of the radiant energy is absorbed before it reaches the
instruments such as absorption by smoke and dust Gases such as
carbon dioxide sulphur dioxide and water vapour absorb infrared
radiation
The emissivity of a material (usually written ε or e) is the relative ability
of its surface to emit energy by radiation It is the ratio of energy
radiated by a particular material to energy radiated by a black body at
CHE 215 page of 21 H Muhamad 20
CHE 215 page of 21 H Muhamad 21
the same temperature A true black body would have an ε = 1 while any
real object would have ε lt 1 Emissivity is a dimensionless quantity
In general the duller and blacker a material is the closer its emissivity is
to 1 The more reflective a material is the lower its emissivity Highly
polished silver has an emissivity of about 002[1]
bull Precision of liquid filled thermometer is frac12 of the smallest division on
the scale Highly accurate Hg thermometer from NIST (National
Institute of Standards and Testing) could measure to plusmn 005oC
2 Resistance temperature detector (RTD)
RTD is basically an electrical wire typically Pt Ag Ni Cu etc which
is used to sense the temperature change based on the principle of the
temperature dependency of the wire resistance as shown below
( )[ ]11 1 TTRR minus+= α (7)
Where R and R1 is the resistances of the wire at T and T1 respectively
and the linear temperature coefficient of the wire resistance which is
defined as below
( )( )121
12TTR
RRminus
minus=α (8)
CHE 215 page of 21 H Muhamad 7
Where R2 is the wire resistance at T2
However the relationship between the wire resistance and temperature
is usually non-linear The relationship can then be expressed as
[ ]21 bTaTRR o ++= (9)
Where Ro is the wire resistance at the reference temperature of zero oC
An RTD sensor can be integrated into a Wheatstone bridge circuit to
convert the RTD resistance change with temperature to a voltage output
The voltage output can be calibrated to give readings of temperature
a) No lead wire
1 At the calibrated temperature
Ro Rx Rx = R0
Vs Va = Ro(Ro+Ro)middotVs = Vs2
Ro Ro Vb = Ro(Ro+Ro)middotVs = Vs2
Vab = Va ndash Vb = 0
CHE 215 page of 21 H Muhamad 8
2 At some other temperature
Rx = Ro +ΔR
Va = Ro(Ro+Ro)middotVs = Vs2
Vb = Ro(Ro+Rx)middotVs = Ro(Ro + Ro + ΔR)middotVs = Ro( 2Ro + ΔR)middotVs
Vab= Vs2 - Ro( 2Ro + ΔR)middotVs = Vs[12 ndash Ro(2Ro + ΔR)]
Vab= Vs[(2Ro + ΔR-2Ro)(2(2Ro+ ΔR))]= Vs[(ΔRRo)(2(2+ ΔRRo))]
o
oSR2R1
RR4
VVabΔ+Δ
sdot=
Since ΔR ltlt Ro ΔR2Ro ltlt 1 Vab can be simplified as
o
SR
R4
VVab Δsdot= (10)
b) With lead wire
(in ldquoExperimental Methods for Engineersrdquo J Holman)
CHE 215 page of 21 H Muhamad 9
RL 1 At the calibrated temperature
Ro Rx (RL + Rx) = Ro
Vs Va = Ro(Ro+Ro)middotVs = Vs2
Ro Ro Vb = Ro(Ro+Ro)middotVs = Vs2
Vab = Va ndash Vb = 0
b) At some other temperature
(RL + Rx) = Ro +ΔRx+ ΔRL for the RTD wire and the lead wire
Va = Ro(Ro+Ro)middotVs = Vs2
Vb = Ro(Ro + Ro + ΔRx+ ΔRL)middotVs
Vab= Vs2 - Ro(2 Ro + ΔRx+ ΔRL)middotVs
Vab= Vs[(2Ro + ΔRx+ ΔRL -2Ro)(2(2Ro+ ΔRx+ ΔRL))]
Vab = (Vs4) [((ΔRx+ ΔRL )Ro) (1+ ΔRx 2Ro + ΔRL 2Ro)]
Since ΔRx and ΔRL ltlt Ro ΔRx2Ro ltlt 1 and ΔRL2Ro ltlt 1 the
equation for Vab can be simplified as
( )o
LSR
RRx4
VVab Δ+Δsdot= (11)
CHE 215 page of 21 H Muhamad 10
ΔRL is not known not calibrated and uncontrollable since it is exposed
to the outside environment that is subject to sporadic changes This is a
source of error in the temperature measurement by RTD
c) Lead wire compensation
(in ldquoExperimental Methods for Engineersrdquo J Holman)
RL 1 At the calibrated temperature
Ro Rx (RL + Rx) = Ro (RL + RD) = Ro
Vs Va = Ro(Ro+Ro)middotVs = Vs2
Ro RL Vb = Ro(Ro+Ro)middotVs = Vs2
RD Vab = Va ndash Vb = 0
CHE 215 page of 21 H Muhamad 11
b) At some other temperature
(RL + Rx) = Ro +ΔRx+ ΔRL for the RTD wire and the lead wire
(RL + RD) = Ro + ΔRL for the dummy wire
Va = Ro(Ro+Ro)middotVs = Vs2
Vb = (Ro+ΔRL) [(Ro+ΔRL) + (Ro + ΔRx+ ΔRL)]middotVs
Vab= Vs2 - (Ro+ΔRL)(2 Ro + ΔRx+ 2ΔRL)middotVs
Vab= Vs[(2Ro + ΔRx+ 2ΔRL -2Ro- 2ΔRL)(2(2Ro+ ΔRx+ 2ΔRL))]
Vab = (Vs4) [ΔRx (Ro + ΔRx 2 + ΔRL)]
Vab = (Vs4) [ΔRxRo (1 + ΔRx 2Ro + ΔRLRo)]
Since ΔRx and ΔRL ltlt Ro ΔRx2Ro ltlt 1 and ΔRLRo ltlt 1 the
equation for Vab can be simplified as
o
SRRx
4VVab Δ
sdot= (12)
Equation (12) has the same form as that of Equation (10) where the
uncertain ΔRL is eliminated
CHE 215 page of 21 H Muhamad 12
3 Thermistors
Thermistors are semiconductor sensors whose resistances decrease with
temperature such as FeO NiO MnO hellip The relationship of the
thermistor resistance and temperature can be written as below
⎥⎦
⎤⎢⎣
⎡⎟⎟⎠
⎞⎜⎜⎝
⎛minusβ
= oT1
T1
o eRR (13)
where Ro is the resistance of the thermistor at the ref temperature To
CHE 215 page of 21 H Muhamad 13
Generally thermistors are more sensitive than RTD They can have a
precision of plusmn 001oC as compared with plusmn 01oC for RTD In addition
the error due to lead wire is insignificant since the resistance of the
thermistor is very high compared to that of the lead wire However the
suitable temperature range for thermistors is narrower from -100 to
400oC while RTD can cover from -100 to 1000 oC
4 Thermocouple
A thermocouple consists of two dissimilar metal wires twisted together
to form a junction that can act as a temperature sensor For example
copper wire and constantan wire (55 copper plus 45 nickel)
bull Seebeck effect
The use of a thermocouple as a temperature sensor is based on the
principle of the Seebeck effect The Seebeck effect states that an emf is
generated in the thermocouple when the junction is heated or cooled
Junction copper A
Constantan B
CHE 215 page of 21 H Muhamad 14
VAB is finite when the junction is at a temperature different from that at
the terminals A and B
bull Law of intermediate metals
Junction copper A
iron
Constantan B
When another metal (iron) is added to the thermocouple circuit as shown
in the above sketch two more junctions are formed at points A and B
As long as the junctions at A and B are kept at the same temperature the
emf generated by the main junction isnrsquot altered ie the temperature
reading doesnrsquot change
bull Law of intermediate temperatures
hot junction copper cold junction
E
constantan
CHE 215 page of 21 H Muhamad 15
For the same thermocouple ie the same two dissimilar metal junctions
the emf generated at different temperatures are additive
E3 = E1 + E2
Where E1 is the emf for the cold junction at 0oC and the hot junction at
50 oC E2 is the emf for the cold junction at 50oC and hot junction at 100
oC E3 is the emf for the cold junction at 0oC and hot junction at 100 oC
Precautions for use of TC
bull Extension wire should have similar properties as those of the TC
otherwise the two junctions of the extension wires and the TC wires
should be kept at the same temperature
bull Extension wire should be thick (having a low resistance) so to
minimize the error associated with the wire heating since the wire
resistance R = ρLS where ρ is the resistivity of the wire L is the
length and S is the cross-sectional area of the wire
5 Correction for temperature measurement under high-velocity
For temperature measurements of a flow at high speed usually gas flow
the effect of the stagnation point at the tip of the temperature sensor on
CHE 215 page of 21 H Muhamad 16
the reading could be significant At the stagnation point the stagnation
temperature Ts is
cp
S gCu
TT2
2α+= infin (14)
Where Tinfin is the temperature of the bulk gas uinfin is the velocity of gas the
flow Cp is the specific heat of the gas
The temperature registered by the sensor (the measured temperature) is
usually different than the stagnation temperature due to the effect of the
shield intruding in the flow path The measured temperature is called the
recovery temperature It is strongly dependent on the configuration of
the sensor and the shield The relative difference between the measured
temperature by the sensor Tr and the stagnation temperature TS is
known as the recovery factor r
infinminusinfinminus
=TTTTr
s
r (15)
7 Temperature measurements by radiation
The temperature of an object can be determined from the total thermal
radiation emitted from the object For an ideal body the total energy
emitted is proportional to the fourth power of the temperature
CHE 215 page of 21 H Muhamad 17
However most practical objects are non-ideal bodies and a correction
must be made to obtain the true temperature of the target This
correction is done by the emissivity of the non-ideal body as below
(16) 4TE σε=
Where E is the energy emitted by the object at the temperature T (in K
or oR) ɛ is the emissivity of the object (ɛ le 10) and σ is the Stefan-
Boltzmann constant
σ = 174x10-9 BTU(hft2oR4) or 5669x10-8 W(m2K4)
When an object is an ideal body the emissivity ɛ is equal to 10 and
Equation (16) is then known as the Stefan-Boltzmann equation
CHE 215 page of 21 H Muhamad 18
71 Optical Pyrometer
The optical pyrometer is simply a photometer that matches the energy
emitted from a reference source with the incoming one from the target
source As an example in the laboratory of this course the target source
is an incandescent lamp whose tungsten filament temperature can be
varied by adjusting the current through it (by adjusting a knob on the
optical pyrometer) When the brightness of the reference filament in the
optical pyrometer matches the brightness of the target filament being
measured the image of the reference filament blends into the colour of
the background of the viewing field in the optical pyrometer At this
point the intensity of the energy emitted from the target is equal to that
emitted from the reference and hence the temperature of the target (light
bulb) can be read from the display on a digital readout
2 Total Radiation Pyrometer
The total radiation pyrometer is the most commonly used pyrometer for
continuous non-contacting measurement of temperature Radiation (both
infrared and visible) passes through a lens and is then concentrated on a
heat-sensing element which produces an electric signal This sensing
element or detector may be a thermopile a thin thermistor flake or a
CHE 215 page of 21 H Muhamad 19
resistance thermometer Thermopiles are the most commonly used
Ambient temperature compensation may be required since the body of
the pyrometer is heated by the target radiation and the thermopile is
sensitive to the body heat
The current (or voltage) produced by the sensing detector is sent to a
potentiometer or a millivoltmeter where the current can be read The
total radiation pyrometer can be used to measure low temperature
However temperatures measured are also subject to errors
bull if the source is not an ideal body Error = (1 - ɛ14)
bull if the optical system gets dirty and adsorbs too much radiation
bull If part of the radiant energy is absorbed before it reaches the
instruments such as absorption by smoke and dust Gases such as
carbon dioxide sulphur dioxide and water vapour absorb infrared
radiation
The emissivity of a material (usually written ε or e) is the relative ability
of its surface to emit energy by radiation It is the ratio of energy
radiated by a particular material to energy radiated by a black body at
CHE 215 page of 21 H Muhamad 20
CHE 215 page of 21 H Muhamad 21
the same temperature A true black body would have an ε = 1 while any
real object would have ε lt 1 Emissivity is a dimensionless quantity
In general the duller and blacker a material is the closer its emissivity is
to 1 The more reflective a material is the lower its emissivity Highly
polished silver has an emissivity of about 002[1]
Where R2 is the wire resistance at T2
However the relationship between the wire resistance and temperature
is usually non-linear The relationship can then be expressed as
[ ]21 bTaTRR o ++= (9)
Where Ro is the wire resistance at the reference temperature of zero oC
An RTD sensor can be integrated into a Wheatstone bridge circuit to
convert the RTD resistance change with temperature to a voltage output
The voltage output can be calibrated to give readings of temperature
a) No lead wire
1 At the calibrated temperature
Ro Rx Rx = R0
Vs Va = Ro(Ro+Ro)middotVs = Vs2
Ro Ro Vb = Ro(Ro+Ro)middotVs = Vs2
Vab = Va ndash Vb = 0
CHE 215 page of 21 H Muhamad 8
2 At some other temperature
Rx = Ro +ΔR
Va = Ro(Ro+Ro)middotVs = Vs2
Vb = Ro(Ro+Rx)middotVs = Ro(Ro + Ro + ΔR)middotVs = Ro( 2Ro + ΔR)middotVs
Vab= Vs2 - Ro( 2Ro + ΔR)middotVs = Vs[12 ndash Ro(2Ro + ΔR)]
Vab= Vs[(2Ro + ΔR-2Ro)(2(2Ro+ ΔR))]= Vs[(ΔRRo)(2(2+ ΔRRo))]
o
oSR2R1
RR4
VVabΔ+Δ
sdot=
Since ΔR ltlt Ro ΔR2Ro ltlt 1 Vab can be simplified as
o
SR
R4
VVab Δsdot= (10)
b) With lead wire
(in ldquoExperimental Methods for Engineersrdquo J Holman)
CHE 215 page of 21 H Muhamad 9
RL 1 At the calibrated temperature
Ro Rx (RL + Rx) = Ro
Vs Va = Ro(Ro+Ro)middotVs = Vs2
Ro Ro Vb = Ro(Ro+Ro)middotVs = Vs2
Vab = Va ndash Vb = 0
b) At some other temperature
(RL + Rx) = Ro +ΔRx+ ΔRL for the RTD wire and the lead wire
Va = Ro(Ro+Ro)middotVs = Vs2
Vb = Ro(Ro + Ro + ΔRx+ ΔRL)middotVs
Vab= Vs2 - Ro(2 Ro + ΔRx+ ΔRL)middotVs
Vab= Vs[(2Ro + ΔRx+ ΔRL -2Ro)(2(2Ro+ ΔRx+ ΔRL))]
Vab = (Vs4) [((ΔRx+ ΔRL )Ro) (1+ ΔRx 2Ro + ΔRL 2Ro)]
Since ΔRx and ΔRL ltlt Ro ΔRx2Ro ltlt 1 and ΔRL2Ro ltlt 1 the
equation for Vab can be simplified as
( )o
LSR
RRx4
VVab Δ+Δsdot= (11)
CHE 215 page of 21 H Muhamad 10
ΔRL is not known not calibrated and uncontrollable since it is exposed
to the outside environment that is subject to sporadic changes This is a
source of error in the temperature measurement by RTD
c) Lead wire compensation
(in ldquoExperimental Methods for Engineersrdquo J Holman)
RL 1 At the calibrated temperature
Ro Rx (RL + Rx) = Ro (RL + RD) = Ro
Vs Va = Ro(Ro+Ro)middotVs = Vs2
Ro RL Vb = Ro(Ro+Ro)middotVs = Vs2
RD Vab = Va ndash Vb = 0
CHE 215 page of 21 H Muhamad 11
b) At some other temperature
(RL + Rx) = Ro +ΔRx+ ΔRL for the RTD wire and the lead wire
(RL + RD) = Ro + ΔRL for the dummy wire
Va = Ro(Ro+Ro)middotVs = Vs2
Vb = (Ro+ΔRL) [(Ro+ΔRL) + (Ro + ΔRx+ ΔRL)]middotVs
Vab= Vs2 - (Ro+ΔRL)(2 Ro + ΔRx+ 2ΔRL)middotVs
Vab= Vs[(2Ro + ΔRx+ 2ΔRL -2Ro- 2ΔRL)(2(2Ro+ ΔRx+ 2ΔRL))]
Vab = (Vs4) [ΔRx (Ro + ΔRx 2 + ΔRL)]
Vab = (Vs4) [ΔRxRo (1 + ΔRx 2Ro + ΔRLRo)]
Since ΔRx and ΔRL ltlt Ro ΔRx2Ro ltlt 1 and ΔRLRo ltlt 1 the
equation for Vab can be simplified as
o
SRRx
4VVab Δ
sdot= (12)
Equation (12) has the same form as that of Equation (10) where the
uncertain ΔRL is eliminated
CHE 215 page of 21 H Muhamad 12
3 Thermistors
Thermistors are semiconductor sensors whose resistances decrease with
temperature such as FeO NiO MnO hellip The relationship of the
thermistor resistance and temperature can be written as below
⎥⎦
⎤⎢⎣
⎡⎟⎟⎠
⎞⎜⎜⎝
⎛minusβ
= oT1
T1
o eRR (13)
where Ro is the resistance of the thermistor at the ref temperature To
CHE 215 page of 21 H Muhamad 13
Generally thermistors are more sensitive than RTD They can have a
precision of plusmn 001oC as compared with plusmn 01oC for RTD In addition
the error due to lead wire is insignificant since the resistance of the
thermistor is very high compared to that of the lead wire However the
suitable temperature range for thermistors is narrower from -100 to
400oC while RTD can cover from -100 to 1000 oC
4 Thermocouple
A thermocouple consists of two dissimilar metal wires twisted together
to form a junction that can act as a temperature sensor For example
copper wire and constantan wire (55 copper plus 45 nickel)
bull Seebeck effect
The use of a thermocouple as a temperature sensor is based on the
principle of the Seebeck effect The Seebeck effect states that an emf is
generated in the thermocouple when the junction is heated or cooled
Junction copper A
Constantan B
CHE 215 page of 21 H Muhamad 14
VAB is finite when the junction is at a temperature different from that at
the terminals A and B
bull Law of intermediate metals
Junction copper A
iron
Constantan B
When another metal (iron) is added to the thermocouple circuit as shown
in the above sketch two more junctions are formed at points A and B
As long as the junctions at A and B are kept at the same temperature the
emf generated by the main junction isnrsquot altered ie the temperature
reading doesnrsquot change
bull Law of intermediate temperatures
hot junction copper cold junction
E
constantan
CHE 215 page of 21 H Muhamad 15
For the same thermocouple ie the same two dissimilar metal junctions
the emf generated at different temperatures are additive
E3 = E1 + E2
Where E1 is the emf for the cold junction at 0oC and the hot junction at
50 oC E2 is the emf for the cold junction at 50oC and hot junction at 100
oC E3 is the emf for the cold junction at 0oC and hot junction at 100 oC
Precautions for use of TC
bull Extension wire should have similar properties as those of the TC
otherwise the two junctions of the extension wires and the TC wires
should be kept at the same temperature
bull Extension wire should be thick (having a low resistance) so to
minimize the error associated with the wire heating since the wire
resistance R = ρLS where ρ is the resistivity of the wire L is the
length and S is the cross-sectional area of the wire
5 Correction for temperature measurement under high-velocity
For temperature measurements of a flow at high speed usually gas flow
the effect of the stagnation point at the tip of the temperature sensor on
CHE 215 page of 21 H Muhamad 16
the reading could be significant At the stagnation point the stagnation
temperature Ts is
cp
S gCu
TT2
2α+= infin (14)
Where Tinfin is the temperature of the bulk gas uinfin is the velocity of gas the
flow Cp is the specific heat of the gas
The temperature registered by the sensor (the measured temperature) is
usually different than the stagnation temperature due to the effect of the
shield intruding in the flow path The measured temperature is called the
recovery temperature It is strongly dependent on the configuration of
the sensor and the shield The relative difference between the measured
temperature by the sensor Tr and the stagnation temperature TS is
known as the recovery factor r
infinminusinfinminus
=TTTTr
s
r (15)
7 Temperature measurements by radiation
The temperature of an object can be determined from the total thermal
radiation emitted from the object For an ideal body the total energy
emitted is proportional to the fourth power of the temperature
CHE 215 page of 21 H Muhamad 17
However most practical objects are non-ideal bodies and a correction
must be made to obtain the true temperature of the target This
correction is done by the emissivity of the non-ideal body as below
(16) 4TE σε=
Where E is the energy emitted by the object at the temperature T (in K
or oR) ɛ is the emissivity of the object (ɛ le 10) and σ is the Stefan-
Boltzmann constant
σ = 174x10-9 BTU(hft2oR4) or 5669x10-8 W(m2K4)
When an object is an ideal body the emissivity ɛ is equal to 10 and
Equation (16) is then known as the Stefan-Boltzmann equation
CHE 215 page of 21 H Muhamad 18
71 Optical Pyrometer
The optical pyrometer is simply a photometer that matches the energy
emitted from a reference source with the incoming one from the target
source As an example in the laboratory of this course the target source
is an incandescent lamp whose tungsten filament temperature can be
varied by adjusting the current through it (by adjusting a knob on the
optical pyrometer) When the brightness of the reference filament in the
optical pyrometer matches the brightness of the target filament being
measured the image of the reference filament blends into the colour of
the background of the viewing field in the optical pyrometer At this
point the intensity of the energy emitted from the target is equal to that
emitted from the reference and hence the temperature of the target (light
bulb) can be read from the display on a digital readout
2 Total Radiation Pyrometer
The total radiation pyrometer is the most commonly used pyrometer for
continuous non-contacting measurement of temperature Radiation (both
infrared and visible) passes through a lens and is then concentrated on a
heat-sensing element which produces an electric signal This sensing
element or detector may be a thermopile a thin thermistor flake or a
CHE 215 page of 21 H Muhamad 19
resistance thermometer Thermopiles are the most commonly used
Ambient temperature compensation may be required since the body of
the pyrometer is heated by the target radiation and the thermopile is
sensitive to the body heat
The current (or voltage) produced by the sensing detector is sent to a
potentiometer or a millivoltmeter where the current can be read The
total radiation pyrometer can be used to measure low temperature
However temperatures measured are also subject to errors
bull if the source is not an ideal body Error = (1 - ɛ14)
bull if the optical system gets dirty and adsorbs too much radiation
bull If part of the radiant energy is absorbed before it reaches the
instruments such as absorption by smoke and dust Gases such as
carbon dioxide sulphur dioxide and water vapour absorb infrared
radiation
The emissivity of a material (usually written ε or e) is the relative ability
of its surface to emit energy by radiation It is the ratio of energy
radiated by a particular material to energy radiated by a black body at
CHE 215 page of 21 H Muhamad 20
CHE 215 page of 21 H Muhamad 21
the same temperature A true black body would have an ε = 1 while any
real object would have ε lt 1 Emissivity is a dimensionless quantity
In general the duller and blacker a material is the closer its emissivity is
to 1 The more reflective a material is the lower its emissivity Highly
polished silver has an emissivity of about 002[1]
2 At some other temperature
Rx = Ro +ΔR
Va = Ro(Ro+Ro)middotVs = Vs2
Vb = Ro(Ro+Rx)middotVs = Ro(Ro + Ro + ΔR)middotVs = Ro( 2Ro + ΔR)middotVs
Vab= Vs2 - Ro( 2Ro + ΔR)middotVs = Vs[12 ndash Ro(2Ro + ΔR)]
Vab= Vs[(2Ro + ΔR-2Ro)(2(2Ro+ ΔR))]= Vs[(ΔRRo)(2(2+ ΔRRo))]
o
oSR2R1
RR4
VVabΔ+Δ
sdot=
Since ΔR ltlt Ro ΔR2Ro ltlt 1 Vab can be simplified as
o
SR
R4
VVab Δsdot= (10)
b) With lead wire
(in ldquoExperimental Methods for Engineersrdquo J Holman)
CHE 215 page of 21 H Muhamad 9
RL 1 At the calibrated temperature
Ro Rx (RL + Rx) = Ro
Vs Va = Ro(Ro+Ro)middotVs = Vs2
Ro Ro Vb = Ro(Ro+Ro)middotVs = Vs2
Vab = Va ndash Vb = 0
b) At some other temperature
(RL + Rx) = Ro +ΔRx+ ΔRL for the RTD wire and the lead wire
Va = Ro(Ro+Ro)middotVs = Vs2
Vb = Ro(Ro + Ro + ΔRx+ ΔRL)middotVs
Vab= Vs2 - Ro(2 Ro + ΔRx+ ΔRL)middotVs
Vab= Vs[(2Ro + ΔRx+ ΔRL -2Ro)(2(2Ro+ ΔRx+ ΔRL))]
Vab = (Vs4) [((ΔRx+ ΔRL )Ro) (1+ ΔRx 2Ro + ΔRL 2Ro)]
Since ΔRx and ΔRL ltlt Ro ΔRx2Ro ltlt 1 and ΔRL2Ro ltlt 1 the
equation for Vab can be simplified as
( )o
LSR
RRx4
VVab Δ+Δsdot= (11)
CHE 215 page of 21 H Muhamad 10
ΔRL is not known not calibrated and uncontrollable since it is exposed
to the outside environment that is subject to sporadic changes This is a
source of error in the temperature measurement by RTD
c) Lead wire compensation
(in ldquoExperimental Methods for Engineersrdquo J Holman)
RL 1 At the calibrated temperature
Ro Rx (RL + Rx) = Ro (RL + RD) = Ro
Vs Va = Ro(Ro+Ro)middotVs = Vs2
Ro RL Vb = Ro(Ro+Ro)middotVs = Vs2
RD Vab = Va ndash Vb = 0
CHE 215 page of 21 H Muhamad 11
b) At some other temperature
(RL + Rx) = Ro +ΔRx+ ΔRL for the RTD wire and the lead wire
(RL + RD) = Ro + ΔRL for the dummy wire
Va = Ro(Ro+Ro)middotVs = Vs2
Vb = (Ro+ΔRL) [(Ro+ΔRL) + (Ro + ΔRx+ ΔRL)]middotVs
Vab= Vs2 - (Ro+ΔRL)(2 Ro + ΔRx+ 2ΔRL)middotVs
Vab= Vs[(2Ro + ΔRx+ 2ΔRL -2Ro- 2ΔRL)(2(2Ro+ ΔRx+ 2ΔRL))]
Vab = (Vs4) [ΔRx (Ro + ΔRx 2 + ΔRL)]
Vab = (Vs4) [ΔRxRo (1 + ΔRx 2Ro + ΔRLRo)]
Since ΔRx and ΔRL ltlt Ro ΔRx2Ro ltlt 1 and ΔRLRo ltlt 1 the
equation for Vab can be simplified as
o
SRRx
4VVab Δ
sdot= (12)
Equation (12) has the same form as that of Equation (10) where the
uncertain ΔRL is eliminated
CHE 215 page of 21 H Muhamad 12
3 Thermistors
Thermistors are semiconductor sensors whose resistances decrease with
temperature such as FeO NiO MnO hellip The relationship of the
thermistor resistance and temperature can be written as below
⎥⎦
⎤⎢⎣
⎡⎟⎟⎠
⎞⎜⎜⎝
⎛minusβ
= oT1
T1
o eRR (13)
where Ro is the resistance of the thermistor at the ref temperature To
CHE 215 page of 21 H Muhamad 13
Generally thermistors are more sensitive than RTD They can have a
precision of plusmn 001oC as compared with plusmn 01oC for RTD In addition
the error due to lead wire is insignificant since the resistance of the
thermistor is very high compared to that of the lead wire However the
suitable temperature range for thermistors is narrower from -100 to
400oC while RTD can cover from -100 to 1000 oC
4 Thermocouple
A thermocouple consists of two dissimilar metal wires twisted together
to form a junction that can act as a temperature sensor For example
copper wire and constantan wire (55 copper plus 45 nickel)
bull Seebeck effect
The use of a thermocouple as a temperature sensor is based on the
principle of the Seebeck effect The Seebeck effect states that an emf is
generated in the thermocouple when the junction is heated or cooled
Junction copper A
Constantan B
CHE 215 page of 21 H Muhamad 14
VAB is finite when the junction is at a temperature different from that at
the terminals A and B
bull Law of intermediate metals
Junction copper A
iron
Constantan B
When another metal (iron) is added to the thermocouple circuit as shown
in the above sketch two more junctions are formed at points A and B
As long as the junctions at A and B are kept at the same temperature the
emf generated by the main junction isnrsquot altered ie the temperature
reading doesnrsquot change
bull Law of intermediate temperatures
hot junction copper cold junction
E
constantan
CHE 215 page of 21 H Muhamad 15
For the same thermocouple ie the same two dissimilar metal junctions
the emf generated at different temperatures are additive
E3 = E1 + E2
Where E1 is the emf for the cold junction at 0oC and the hot junction at
50 oC E2 is the emf for the cold junction at 50oC and hot junction at 100
oC E3 is the emf for the cold junction at 0oC and hot junction at 100 oC
Precautions for use of TC
bull Extension wire should have similar properties as those of the TC
otherwise the two junctions of the extension wires and the TC wires
should be kept at the same temperature
bull Extension wire should be thick (having a low resistance) so to
minimize the error associated with the wire heating since the wire
resistance R = ρLS where ρ is the resistivity of the wire L is the
length and S is the cross-sectional area of the wire
5 Correction for temperature measurement under high-velocity
For temperature measurements of a flow at high speed usually gas flow
the effect of the stagnation point at the tip of the temperature sensor on
CHE 215 page of 21 H Muhamad 16
the reading could be significant At the stagnation point the stagnation
temperature Ts is
cp
S gCu
TT2
2α+= infin (14)
Where Tinfin is the temperature of the bulk gas uinfin is the velocity of gas the
flow Cp is the specific heat of the gas
The temperature registered by the sensor (the measured temperature) is
usually different than the stagnation temperature due to the effect of the
shield intruding in the flow path The measured temperature is called the
recovery temperature It is strongly dependent on the configuration of
the sensor and the shield The relative difference between the measured
temperature by the sensor Tr and the stagnation temperature TS is
known as the recovery factor r
infinminusinfinminus
=TTTTr
s
r (15)
7 Temperature measurements by radiation
The temperature of an object can be determined from the total thermal
radiation emitted from the object For an ideal body the total energy
emitted is proportional to the fourth power of the temperature
CHE 215 page of 21 H Muhamad 17
However most practical objects are non-ideal bodies and a correction
must be made to obtain the true temperature of the target This
correction is done by the emissivity of the non-ideal body as below
(16) 4TE σε=
Where E is the energy emitted by the object at the temperature T (in K
or oR) ɛ is the emissivity of the object (ɛ le 10) and σ is the Stefan-
Boltzmann constant
σ = 174x10-9 BTU(hft2oR4) or 5669x10-8 W(m2K4)
When an object is an ideal body the emissivity ɛ is equal to 10 and
Equation (16) is then known as the Stefan-Boltzmann equation
CHE 215 page of 21 H Muhamad 18
71 Optical Pyrometer
The optical pyrometer is simply a photometer that matches the energy
emitted from a reference source with the incoming one from the target
source As an example in the laboratory of this course the target source
is an incandescent lamp whose tungsten filament temperature can be
varied by adjusting the current through it (by adjusting a knob on the
optical pyrometer) When the brightness of the reference filament in the
optical pyrometer matches the brightness of the target filament being
measured the image of the reference filament blends into the colour of
the background of the viewing field in the optical pyrometer At this
point the intensity of the energy emitted from the target is equal to that
emitted from the reference and hence the temperature of the target (light
bulb) can be read from the display on a digital readout
2 Total Radiation Pyrometer
The total radiation pyrometer is the most commonly used pyrometer for
continuous non-contacting measurement of temperature Radiation (both
infrared and visible) passes through a lens and is then concentrated on a
heat-sensing element which produces an electric signal This sensing
element or detector may be a thermopile a thin thermistor flake or a
CHE 215 page of 21 H Muhamad 19
resistance thermometer Thermopiles are the most commonly used
Ambient temperature compensation may be required since the body of
the pyrometer is heated by the target radiation and the thermopile is
sensitive to the body heat
The current (or voltage) produced by the sensing detector is sent to a
potentiometer or a millivoltmeter where the current can be read The
total radiation pyrometer can be used to measure low temperature
However temperatures measured are also subject to errors
bull if the source is not an ideal body Error = (1 - ɛ14)
bull if the optical system gets dirty and adsorbs too much radiation
bull If part of the radiant energy is absorbed before it reaches the
instruments such as absorption by smoke and dust Gases such as
carbon dioxide sulphur dioxide and water vapour absorb infrared
radiation
The emissivity of a material (usually written ε or e) is the relative ability
of its surface to emit energy by radiation It is the ratio of energy
radiated by a particular material to energy radiated by a black body at
CHE 215 page of 21 H Muhamad 20
CHE 215 page of 21 H Muhamad 21
the same temperature A true black body would have an ε = 1 while any
real object would have ε lt 1 Emissivity is a dimensionless quantity
In general the duller and blacker a material is the closer its emissivity is
to 1 The more reflective a material is the lower its emissivity Highly
polished silver has an emissivity of about 002[1]
RL 1 At the calibrated temperature
Ro Rx (RL + Rx) = Ro
Vs Va = Ro(Ro+Ro)middotVs = Vs2
Ro Ro Vb = Ro(Ro+Ro)middotVs = Vs2
Vab = Va ndash Vb = 0
b) At some other temperature
(RL + Rx) = Ro +ΔRx+ ΔRL for the RTD wire and the lead wire
Va = Ro(Ro+Ro)middotVs = Vs2
Vb = Ro(Ro + Ro + ΔRx+ ΔRL)middotVs
Vab= Vs2 - Ro(2 Ro + ΔRx+ ΔRL)middotVs
Vab= Vs[(2Ro + ΔRx+ ΔRL -2Ro)(2(2Ro+ ΔRx+ ΔRL))]
Vab = (Vs4) [((ΔRx+ ΔRL )Ro) (1+ ΔRx 2Ro + ΔRL 2Ro)]
Since ΔRx and ΔRL ltlt Ro ΔRx2Ro ltlt 1 and ΔRL2Ro ltlt 1 the
equation for Vab can be simplified as
( )o
LSR
RRx4
VVab Δ+Δsdot= (11)
CHE 215 page of 21 H Muhamad 10
ΔRL is not known not calibrated and uncontrollable since it is exposed
to the outside environment that is subject to sporadic changes This is a
source of error in the temperature measurement by RTD
c) Lead wire compensation
(in ldquoExperimental Methods for Engineersrdquo J Holman)
RL 1 At the calibrated temperature
Ro Rx (RL + Rx) = Ro (RL + RD) = Ro
Vs Va = Ro(Ro+Ro)middotVs = Vs2
Ro RL Vb = Ro(Ro+Ro)middotVs = Vs2
RD Vab = Va ndash Vb = 0
CHE 215 page of 21 H Muhamad 11
b) At some other temperature
(RL + Rx) = Ro +ΔRx+ ΔRL for the RTD wire and the lead wire
(RL + RD) = Ro + ΔRL for the dummy wire
Va = Ro(Ro+Ro)middotVs = Vs2
Vb = (Ro+ΔRL) [(Ro+ΔRL) + (Ro + ΔRx+ ΔRL)]middotVs
Vab= Vs2 - (Ro+ΔRL)(2 Ro + ΔRx+ 2ΔRL)middotVs
Vab= Vs[(2Ro + ΔRx+ 2ΔRL -2Ro- 2ΔRL)(2(2Ro+ ΔRx+ 2ΔRL))]
Vab = (Vs4) [ΔRx (Ro + ΔRx 2 + ΔRL)]
Vab = (Vs4) [ΔRxRo (1 + ΔRx 2Ro + ΔRLRo)]
Since ΔRx and ΔRL ltlt Ro ΔRx2Ro ltlt 1 and ΔRLRo ltlt 1 the
equation for Vab can be simplified as
o
SRRx
4VVab Δ
sdot= (12)
Equation (12) has the same form as that of Equation (10) where the
uncertain ΔRL is eliminated
CHE 215 page of 21 H Muhamad 12
3 Thermistors
Thermistors are semiconductor sensors whose resistances decrease with
temperature such as FeO NiO MnO hellip The relationship of the
thermistor resistance and temperature can be written as below
⎥⎦
⎤⎢⎣
⎡⎟⎟⎠
⎞⎜⎜⎝
⎛minusβ
= oT1
T1
o eRR (13)
where Ro is the resistance of the thermistor at the ref temperature To
CHE 215 page of 21 H Muhamad 13
Generally thermistors are more sensitive than RTD They can have a
precision of plusmn 001oC as compared with plusmn 01oC for RTD In addition
the error due to lead wire is insignificant since the resistance of the
thermistor is very high compared to that of the lead wire However the
suitable temperature range for thermistors is narrower from -100 to
400oC while RTD can cover from -100 to 1000 oC
4 Thermocouple
A thermocouple consists of two dissimilar metal wires twisted together
to form a junction that can act as a temperature sensor For example
copper wire and constantan wire (55 copper plus 45 nickel)
bull Seebeck effect
The use of a thermocouple as a temperature sensor is based on the
principle of the Seebeck effect The Seebeck effect states that an emf is
generated in the thermocouple when the junction is heated or cooled
Junction copper A
Constantan B
CHE 215 page of 21 H Muhamad 14
VAB is finite when the junction is at a temperature different from that at
the terminals A and B
bull Law of intermediate metals
Junction copper A
iron
Constantan B
When another metal (iron) is added to the thermocouple circuit as shown
in the above sketch two more junctions are formed at points A and B
As long as the junctions at A and B are kept at the same temperature the
emf generated by the main junction isnrsquot altered ie the temperature
reading doesnrsquot change
bull Law of intermediate temperatures
hot junction copper cold junction
E
constantan
CHE 215 page of 21 H Muhamad 15
For the same thermocouple ie the same two dissimilar metal junctions
the emf generated at different temperatures are additive
E3 = E1 + E2
Where E1 is the emf for the cold junction at 0oC and the hot junction at
50 oC E2 is the emf for the cold junction at 50oC and hot junction at 100
oC E3 is the emf for the cold junction at 0oC and hot junction at 100 oC
Precautions for use of TC
bull Extension wire should have similar properties as those of the TC
otherwise the two junctions of the extension wires and the TC wires
should be kept at the same temperature
bull Extension wire should be thick (having a low resistance) so to
minimize the error associated with the wire heating since the wire
resistance R = ρLS where ρ is the resistivity of the wire L is the
length and S is the cross-sectional area of the wire
5 Correction for temperature measurement under high-velocity
For temperature measurements of a flow at high speed usually gas flow
the effect of the stagnation point at the tip of the temperature sensor on
CHE 215 page of 21 H Muhamad 16
the reading could be significant At the stagnation point the stagnation
temperature Ts is
cp
S gCu
TT2
2α+= infin (14)
Where Tinfin is the temperature of the bulk gas uinfin is the velocity of gas the
flow Cp is the specific heat of the gas
The temperature registered by the sensor (the measured temperature) is
usually different than the stagnation temperature due to the effect of the
shield intruding in the flow path The measured temperature is called the
recovery temperature It is strongly dependent on the configuration of
the sensor and the shield The relative difference between the measured
temperature by the sensor Tr and the stagnation temperature TS is
known as the recovery factor r
infinminusinfinminus
=TTTTr
s
r (15)
7 Temperature measurements by radiation
The temperature of an object can be determined from the total thermal
radiation emitted from the object For an ideal body the total energy
emitted is proportional to the fourth power of the temperature
CHE 215 page of 21 H Muhamad 17
However most practical objects are non-ideal bodies and a correction
must be made to obtain the true temperature of the target This
correction is done by the emissivity of the non-ideal body as below
(16) 4TE σε=
Where E is the energy emitted by the object at the temperature T (in K
or oR) ɛ is the emissivity of the object (ɛ le 10) and σ is the Stefan-
Boltzmann constant
σ = 174x10-9 BTU(hft2oR4) or 5669x10-8 W(m2K4)
When an object is an ideal body the emissivity ɛ is equal to 10 and
Equation (16) is then known as the Stefan-Boltzmann equation
CHE 215 page of 21 H Muhamad 18
71 Optical Pyrometer
The optical pyrometer is simply a photometer that matches the energy
emitted from a reference source with the incoming one from the target
source As an example in the laboratory of this course the target source
is an incandescent lamp whose tungsten filament temperature can be
varied by adjusting the current through it (by adjusting a knob on the
optical pyrometer) When the brightness of the reference filament in the
optical pyrometer matches the brightness of the target filament being
measured the image of the reference filament blends into the colour of
the background of the viewing field in the optical pyrometer At this
point the intensity of the energy emitted from the target is equal to that
emitted from the reference and hence the temperature of the target (light
bulb) can be read from the display on a digital readout
2 Total Radiation Pyrometer
The total radiation pyrometer is the most commonly used pyrometer for
continuous non-contacting measurement of temperature Radiation (both
infrared and visible) passes through a lens and is then concentrated on a
heat-sensing element which produces an electric signal This sensing
element or detector may be a thermopile a thin thermistor flake or a
CHE 215 page of 21 H Muhamad 19
resistance thermometer Thermopiles are the most commonly used
Ambient temperature compensation may be required since the body of
the pyrometer is heated by the target radiation and the thermopile is
sensitive to the body heat
The current (or voltage) produced by the sensing detector is sent to a
potentiometer or a millivoltmeter where the current can be read The
total radiation pyrometer can be used to measure low temperature
However temperatures measured are also subject to errors
bull if the source is not an ideal body Error = (1 - ɛ14)
bull if the optical system gets dirty and adsorbs too much radiation
bull If part of the radiant energy is absorbed before it reaches the
instruments such as absorption by smoke and dust Gases such as
carbon dioxide sulphur dioxide and water vapour absorb infrared
radiation
The emissivity of a material (usually written ε or e) is the relative ability
of its surface to emit energy by radiation It is the ratio of energy
radiated by a particular material to energy radiated by a black body at
CHE 215 page of 21 H Muhamad 20
CHE 215 page of 21 H Muhamad 21
the same temperature A true black body would have an ε = 1 while any
real object would have ε lt 1 Emissivity is a dimensionless quantity
In general the duller and blacker a material is the closer its emissivity is
to 1 The more reflective a material is the lower its emissivity Highly
polished silver has an emissivity of about 002[1]
ΔRL is not known not calibrated and uncontrollable since it is exposed
to the outside environment that is subject to sporadic changes This is a
source of error in the temperature measurement by RTD
c) Lead wire compensation
(in ldquoExperimental Methods for Engineersrdquo J Holman)
RL 1 At the calibrated temperature
Ro Rx (RL + Rx) = Ro (RL + RD) = Ro
Vs Va = Ro(Ro+Ro)middotVs = Vs2
Ro RL Vb = Ro(Ro+Ro)middotVs = Vs2
RD Vab = Va ndash Vb = 0
CHE 215 page of 21 H Muhamad 11
b) At some other temperature
(RL + Rx) = Ro +ΔRx+ ΔRL for the RTD wire and the lead wire
(RL + RD) = Ro + ΔRL for the dummy wire
Va = Ro(Ro+Ro)middotVs = Vs2
Vb = (Ro+ΔRL) [(Ro+ΔRL) + (Ro + ΔRx+ ΔRL)]middotVs
Vab= Vs2 - (Ro+ΔRL)(2 Ro + ΔRx+ 2ΔRL)middotVs
Vab= Vs[(2Ro + ΔRx+ 2ΔRL -2Ro- 2ΔRL)(2(2Ro+ ΔRx+ 2ΔRL))]
Vab = (Vs4) [ΔRx (Ro + ΔRx 2 + ΔRL)]
Vab = (Vs4) [ΔRxRo (1 + ΔRx 2Ro + ΔRLRo)]
Since ΔRx and ΔRL ltlt Ro ΔRx2Ro ltlt 1 and ΔRLRo ltlt 1 the
equation for Vab can be simplified as
o
SRRx
4VVab Δ
sdot= (12)
Equation (12) has the same form as that of Equation (10) where the
uncertain ΔRL is eliminated
CHE 215 page of 21 H Muhamad 12
3 Thermistors
Thermistors are semiconductor sensors whose resistances decrease with
temperature such as FeO NiO MnO hellip The relationship of the
thermistor resistance and temperature can be written as below
⎥⎦
⎤⎢⎣
⎡⎟⎟⎠
⎞⎜⎜⎝
⎛minusβ
= oT1
T1
o eRR (13)
where Ro is the resistance of the thermistor at the ref temperature To
CHE 215 page of 21 H Muhamad 13
Generally thermistors are more sensitive than RTD They can have a
precision of plusmn 001oC as compared with plusmn 01oC for RTD In addition
the error due to lead wire is insignificant since the resistance of the
thermistor is very high compared to that of the lead wire However the
suitable temperature range for thermistors is narrower from -100 to
400oC while RTD can cover from -100 to 1000 oC
4 Thermocouple
A thermocouple consists of two dissimilar metal wires twisted together
to form a junction that can act as a temperature sensor For example
copper wire and constantan wire (55 copper plus 45 nickel)
bull Seebeck effect
The use of a thermocouple as a temperature sensor is based on the
principle of the Seebeck effect The Seebeck effect states that an emf is
generated in the thermocouple when the junction is heated or cooled
Junction copper A
Constantan B
CHE 215 page of 21 H Muhamad 14
VAB is finite when the junction is at a temperature different from that at
the terminals A and B
bull Law of intermediate metals
Junction copper A
iron
Constantan B
When another metal (iron) is added to the thermocouple circuit as shown
in the above sketch two more junctions are formed at points A and B
As long as the junctions at A and B are kept at the same temperature the
emf generated by the main junction isnrsquot altered ie the temperature
reading doesnrsquot change
bull Law of intermediate temperatures
hot junction copper cold junction
E
constantan
CHE 215 page of 21 H Muhamad 15
For the same thermocouple ie the same two dissimilar metal junctions
the emf generated at different temperatures are additive
E3 = E1 + E2
Where E1 is the emf for the cold junction at 0oC and the hot junction at
50 oC E2 is the emf for the cold junction at 50oC and hot junction at 100
oC E3 is the emf for the cold junction at 0oC and hot junction at 100 oC
Precautions for use of TC
bull Extension wire should have similar properties as those of the TC
otherwise the two junctions of the extension wires and the TC wires
should be kept at the same temperature
bull Extension wire should be thick (having a low resistance) so to
minimize the error associated with the wire heating since the wire
resistance R = ρLS where ρ is the resistivity of the wire L is the
length and S is the cross-sectional area of the wire
5 Correction for temperature measurement under high-velocity
For temperature measurements of a flow at high speed usually gas flow
the effect of the stagnation point at the tip of the temperature sensor on
CHE 215 page of 21 H Muhamad 16
the reading could be significant At the stagnation point the stagnation
temperature Ts is
cp
S gCu
TT2
2α+= infin (14)
Where Tinfin is the temperature of the bulk gas uinfin is the velocity of gas the
flow Cp is the specific heat of the gas
The temperature registered by the sensor (the measured temperature) is
usually different than the stagnation temperature due to the effect of the
shield intruding in the flow path The measured temperature is called the
recovery temperature It is strongly dependent on the configuration of
the sensor and the shield The relative difference between the measured
temperature by the sensor Tr and the stagnation temperature TS is
known as the recovery factor r
infinminusinfinminus
=TTTTr
s
r (15)
7 Temperature measurements by radiation
The temperature of an object can be determined from the total thermal
radiation emitted from the object For an ideal body the total energy
emitted is proportional to the fourth power of the temperature
CHE 215 page of 21 H Muhamad 17
However most practical objects are non-ideal bodies and a correction
must be made to obtain the true temperature of the target This
correction is done by the emissivity of the non-ideal body as below
(16) 4TE σε=
Where E is the energy emitted by the object at the temperature T (in K
or oR) ɛ is the emissivity of the object (ɛ le 10) and σ is the Stefan-
Boltzmann constant
σ = 174x10-9 BTU(hft2oR4) or 5669x10-8 W(m2K4)
When an object is an ideal body the emissivity ɛ is equal to 10 and
Equation (16) is then known as the Stefan-Boltzmann equation
CHE 215 page of 21 H Muhamad 18
71 Optical Pyrometer
The optical pyrometer is simply a photometer that matches the energy
emitted from a reference source with the incoming one from the target
source As an example in the laboratory of this course the target source
is an incandescent lamp whose tungsten filament temperature can be
varied by adjusting the current through it (by adjusting a knob on the
optical pyrometer) When the brightness of the reference filament in the
optical pyrometer matches the brightness of the target filament being
measured the image of the reference filament blends into the colour of
the background of the viewing field in the optical pyrometer At this
point the intensity of the energy emitted from the target is equal to that
emitted from the reference and hence the temperature of the target (light
bulb) can be read from the display on a digital readout
2 Total Radiation Pyrometer
The total radiation pyrometer is the most commonly used pyrometer for
continuous non-contacting measurement of temperature Radiation (both
infrared and visible) passes through a lens and is then concentrated on a
heat-sensing element which produces an electric signal This sensing
element or detector may be a thermopile a thin thermistor flake or a
CHE 215 page of 21 H Muhamad 19
resistance thermometer Thermopiles are the most commonly used
Ambient temperature compensation may be required since the body of
the pyrometer is heated by the target radiation and the thermopile is
sensitive to the body heat
The current (or voltage) produced by the sensing detector is sent to a
potentiometer or a millivoltmeter where the current can be read The
total radiation pyrometer can be used to measure low temperature
However temperatures measured are also subject to errors
bull if the source is not an ideal body Error = (1 - ɛ14)
bull if the optical system gets dirty and adsorbs too much radiation
bull If part of the radiant energy is absorbed before it reaches the
instruments such as absorption by smoke and dust Gases such as
carbon dioxide sulphur dioxide and water vapour absorb infrared
radiation
The emissivity of a material (usually written ε or e) is the relative ability
of its surface to emit energy by radiation It is the ratio of energy
radiated by a particular material to energy radiated by a black body at
CHE 215 page of 21 H Muhamad 20
CHE 215 page of 21 H Muhamad 21
the same temperature A true black body would have an ε = 1 while any
real object would have ε lt 1 Emissivity is a dimensionless quantity
In general the duller and blacker a material is the closer its emissivity is
to 1 The more reflective a material is the lower its emissivity Highly
polished silver has an emissivity of about 002[1]
b) At some other temperature
(RL + Rx) = Ro +ΔRx+ ΔRL for the RTD wire and the lead wire
(RL + RD) = Ro + ΔRL for the dummy wire
Va = Ro(Ro+Ro)middotVs = Vs2
Vb = (Ro+ΔRL) [(Ro+ΔRL) + (Ro + ΔRx+ ΔRL)]middotVs
Vab= Vs2 - (Ro+ΔRL)(2 Ro + ΔRx+ 2ΔRL)middotVs
Vab= Vs[(2Ro + ΔRx+ 2ΔRL -2Ro- 2ΔRL)(2(2Ro+ ΔRx+ 2ΔRL))]
Vab = (Vs4) [ΔRx (Ro + ΔRx 2 + ΔRL)]
Vab = (Vs4) [ΔRxRo (1 + ΔRx 2Ro + ΔRLRo)]
Since ΔRx and ΔRL ltlt Ro ΔRx2Ro ltlt 1 and ΔRLRo ltlt 1 the
equation for Vab can be simplified as
o
SRRx
4VVab Δ
sdot= (12)
Equation (12) has the same form as that of Equation (10) where the
uncertain ΔRL is eliminated
CHE 215 page of 21 H Muhamad 12
3 Thermistors
Thermistors are semiconductor sensors whose resistances decrease with
temperature such as FeO NiO MnO hellip The relationship of the
thermistor resistance and temperature can be written as below
⎥⎦
⎤⎢⎣
⎡⎟⎟⎠
⎞⎜⎜⎝
⎛minusβ
= oT1
T1
o eRR (13)
where Ro is the resistance of the thermistor at the ref temperature To
CHE 215 page of 21 H Muhamad 13
Generally thermistors are more sensitive than RTD They can have a
precision of plusmn 001oC as compared with plusmn 01oC for RTD In addition
the error due to lead wire is insignificant since the resistance of the
thermistor is very high compared to that of the lead wire However the
suitable temperature range for thermistors is narrower from -100 to
400oC while RTD can cover from -100 to 1000 oC
4 Thermocouple
A thermocouple consists of two dissimilar metal wires twisted together
to form a junction that can act as a temperature sensor For example
copper wire and constantan wire (55 copper plus 45 nickel)
bull Seebeck effect
The use of a thermocouple as a temperature sensor is based on the
principle of the Seebeck effect The Seebeck effect states that an emf is
generated in the thermocouple when the junction is heated or cooled
Junction copper A
Constantan B
CHE 215 page of 21 H Muhamad 14
VAB is finite when the junction is at a temperature different from that at
the terminals A and B
bull Law of intermediate metals
Junction copper A
iron
Constantan B
When another metal (iron) is added to the thermocouple circuit as shown
in the above sketch two more junctions are formed at points A and B
As long as the junctions at A and B are kept at the same temperature the
emf generated by the main junction isnrsquot altered ie the temperature
reading doesnrsquot change
bull Law of intermediate temperatures
hot junction copper cold junction
E
constantan
CHE 215 page of 21 H Muhamad 15
For the same thermocouple ie the same two dissimilar metal junctions
the emf generated at different temperatures are additive
E3 = E1 + E2
Where E1 is the emf for the cold junction at 0oC and the hot junction at
50 oC E2 is the emf for the cold junction at 50oC and hot junction at 100
oC E3 is the emf for the cold junction at 0oC and hot junction at 100 oC
Precautions for use of TC
bull Extension wire should have similar properties as those of the TC
otherwise the two junctions of the extension wires and the TC wires
should be kept at the same temperature
bull Extension wire should be thick (having a low resistance) so to
minimize the error associated with the wire heating since the wire
resistance R = ρLS where ρ is the resistivity of the wire L is the
length and S is the cross-sectional area of the wire
5 Correction for temperature measurement under high-velocity
For temperature measurements of a flow at high speed usually gas flow
the effect of the stagnation point at the tip of the temperature sensor on
CHE 215 page of 21 H Muhamad 16
the reading could be significant At the stagnation point the stagnation
temperature Ts is
cp
S gCu
TT2
2α+= infin (14)
Where Tinfin is the temperature of the bulk gas uinfin is the velocity of gas the
flow Cp is the specific heat of the gas
The temperature registered by the sensor (the measured temperature) is
usually different than the stagnation temperature due to the effect of the
shield intruding in the flow path The measured temperature is called the
recovery temperature It is strongly dependent on the configuration of
the sensor and the shield The relative difference between the measured
temperature by the sensor Tr and the stagnation temperature TS is
known as the recovery factor r
infinminusinfinminus
=TTTTr
s
r (15)
7 Temperature measurements by radiation
The temperature of an object can be determined from the total thermal
radiation emitted from the object For an ideal body the total energy
emitted is proportional to the fourth power of the temperature
CHE 215 page of 21 H Muhamad 17
However most practical objects are non-ideal bodies and a correction
must be made to obtain the true temperature of the target This
correction is done by the emissivity of the non-ideal body as below
(16) 4TE σε=
Where E is the energy emitted by the object at the temperature T (in K
or oR) ɛ is the emissivity of the object (ɛ le 10) and σ is the Stefan-
Boltzmann constant
σ = 174x10-9 BTU(hft2oR4) or 5669x10-8 W(m2K4)
When an object is an ideal body the emissivity ɛ is equal to 10 and
Equation (16) is then known as the Stefan-Boltzmann equation
CHE 215 page of 21 H Muhamad 18
71 Optical Pyrometer
The optical pyrometer is simply a photometer that matches the energy
emitted from a reference source with the incoming one from the target
source As an example in the laboratory of this course the target source
is an incandescent lamp whose tungsten filament temperature can be
varied by adjusting the current through it (by adjusting a knob on the
optical pyrometer) When the brightness of the reference filament in the
optical pyrometer matches the brightness of the target filament being
measured the image of the reference filament blends into the colour of
the background of the viewing field in the optical pyrometer At this
point the intensity of the energy emitted from the target is equal to that
emitted from the reference and hence the temperature of the target (light
bulb) can be read from the display on a digital readout
2 Total Radiation Pyrometer
The total radiation pyrometer is the most commonly used pyrometer for
continuous non-contacting measurement of temperature Radiation (both
infrared and visible) passes through a lens and is then concentrated on a
heat-sensing element which produces an electric signal This sensing
element or detector may be a thermopile a thin thermistor flake or a
CHE 215 page of 21 H Muhamad 19
resistance thermometer Thermopiles are the most commonly used
Ambient temperature compensation may be required since the body of
the pyrometer is heated by the target radiation and the thermopile is
sensitive to the body heat
The current (or voltage) produced by the sensing detector is sent to a
potentiometer or a millivoltmeter where the current can be read The
total radiation pyrometer can be used to measure low temperature
However temperatures measured are also subject to errors
bull if the source is not an ideal body Error = (1 - ɛ14)
bull if the optical system gets dirty and adsorbs too much radiation
bull If part of the radiant energy is absorbed before it reaches the
instruments such as absorption by smoke and dust Gases such as
carbon dioxide sulphur dioxide and water vapour absorb infrared
radiation
The emissivity of a material (usually written ε or e) is the relative ability
of its surface to emit energy by radiation It is the ratio of energy
radiated by a particular material to energy radiated by a black body at
CHE 215 page of 21 H Muhamad 20
CHE 215 page of 21 H Muhamad 21
the same temperature A true black body would have an ε = 1 while any
real object would have ε lt 1 Emissivity is a dimensionless quantity
In general the duller and blacker a material is the closer its emissivity is
to 1 The more reflective a material is the lower its emissivity Highly
polished silver has an emissivity of about 002[1]
3 Thermistors
Thermistors are semiconductor sensors whose resistances decrease with
temperature such as FeO NiO MnO hellip The relationship of the
thermistor resistance and temperature can be written as below
⎥⎦
⎤⎢⎣
⎡⎟⎟⎠
⎞⎜⎜⎝
⎛minusβ
= oT1
T1
o eRR (13)
where Ro is the resistance of the thermistor at the ref temperature To
CHE 215 page of 21 H Muhamad 13
Generally thermistors are more sensitive than RTD They can have a
precision of plusmn 001oC as compared with plusmn 01oC for RTD In addition
the error due to lead wire is insignificant since the resistance of the
thermistor is very high compared to that of the lead wire However the
suitable temperature range for thermistors is narrower from -100 to
400oC while RTD can cover from -100 to 1000 oC
4 Thermocouple
A thermocouple consists of two dissimilar metal wires twisted together
to form a junction that can act as a temperature sensor For example
copper wire and constantan wire (55 copper plus 45 nickel)
bull Seebeck effect
The use of a thermocouple as a temperature sensor is based on the
principle of the Seebeck effect The Seebeck effect states that an emf is
generated in the thermocouple when the junction is heated or cooled
Junction copper A
Constantan B
CHE 215 page of 21 H Muhamad 14
VAB is finite when the junction is at a temperature different from that at
the terminals A and B
bull Law of intermediate metals
Junction copper A
iron
Constantan B
When another metal (iron) is added to the thermocouple circuit as shown
in the above sketch two more junctions are formed at points A and B
As long as the junctions at A and B are kept at the same temperature the
emf generated by the main junction isnrsquot altered ie the temperature
reading doesnrsquot change
bull Law of intermediate temperatures
hot junction copper cold junction
E
constantan
CHE 215 page of 21 H Muhamad 15
For the same thermocouple ie the same two dissimilar metal junctions
the emf generated at different temperatures are additive
E3 = E1 + E2
Where E1 is the emf for the cold junction at 0oC and the hot junction at
50 oC E2 is the emf for the cold junction at 50oC and hot junction at 100
oC E3 is the emf for the cold junction at 0oC and hot junction at 100 oC
Precautions for use of TC
bull Extension wire should have similar properties as those of the TC
otherwise the two junctions of the extension wires and the TC wires
should be kept at the same temperature
bull Extension wire should be thick (having a low resistance) so to
minimize the error associated with the wire heating since the wire
resistance R = ρLS where ρ is the resistivity of the wire L is the
length and S is the cross-sectional area of the wire
5 Correction for temperature measurement under high-velocity
For temperature measurements of a flow at high speed usually gas flow
the effect of the stagnation point at the tip of the temperature sensor on
CHE 215 page of 21 H Muhamad 16
the reading could be significant At the stagnation point the stagnation
temperature Ts is
cp
S gCu
TT2
2α+= infin (14)
Where Tinfin is the temperature of the bulk gas uinfin is the velocity of gas the
flow Cp is the specific heat of the gas
The temperature registered by the sensor (the measured temperature) is
usually different than the stagnation temperature due to the effect of the
shield intruding in the flow path The measured temperature is called the
recovery temperature It is strongly dependent on the configuration of
the sensor and the shield The relative difference between the measured
temperature by the sensor Tr and the stagnation temperature TS is
known as the recovery factor r
infinminusinfinminus
=TTTTr
s
r (15)
7 Temperature measurements by radiation
The temperature of an object can be determined from the total thermal
radiation emitted from the object For an ideal body the total energy
emitted is proportional to the fourth power of the temperature
CHE 215 page of 21 H Muhamad 17
However most practical objects are non-ideal bodies and a correction
must be made to obtain the true temperature of the target This
correction is done by the emissivity of the non-ideal body as below
(16) 4TE σε=
Where E is the energy emitted by the object at the temperature T (in K
or oR) ɛ is the emissivity of the object (ɛ le 10) and σ is the Stefan-
Boltzmann constant
σ = 174x10-9 BTU(hft2oR4) or 5669x10-8 W(m2K4)
When an object is an ideal body the emissivity ɛ is equal to 10 and
Equation (16) is then known as the Stefan-Boltzmann equation
CHE 215 page of 21 H Muhamad 18
71 Optical Pyrometer
The optical pyrometer is simply a photometer that matches the energy
emitted from a reference source with the incoming one from the target
source As an example in the laboratory of this course the target source
is an incandescent lamp whose tungsten filament temperature can be
varied by adjusting the current through it (by adjusting a knob on the
optical pyrometer) When the brightness of the reference filament in the
optical pyrometer matches the brightness of the target filament being
measured the image of the reference filament blends into the colour of
the background of the viewing field in the optical pyrometer At this
point the intensity of the energy emitted from the target is equal to that
emitted from the reference and hence the temperature of the target (light
bulb) can be read from the display on a digital readout
2 Total Radiation Pyrometer
The total radiation pyrometer is the most commonly used pyrometer for
continuous non-contacting measurement of temperature Radiation (both
infrared and visible) passes through a lens and is then concentrated on a
heat-sensing element which produces an electric signal This sensing
element or detector may be a thermopile a thin thermistor flake or a
CHE 215 page of 21 H Muhamad 19
resistance thermometer Thermopiles are the most commonly used
Ambient temperature compensation may be required since the body of
the pyrometer is heated by the target radiation and the thermopile is
sensitive to the body heat
The current (or voltage) produced by the sensing detector is sent to a
potentiometer or a millivoltmeter where the current can be read The
total radiation pyrometer can be used to measure low temperature
However temperatures measured are also subject to errors
bull if the source is not an ideal body Error = (1 - ɛ14)
bull if the optical system gets dirty and adsorbs too much radiation
bull If part of the radiant energy is absorbed before it reaches the
instruments such as absorption by smoke and dust Gases such as
carbon dioxide sulphur dioxide and water vapour absorb infrared
radiation
The emissivity of a material (usually written ε or e) is the relative ability
of its surface to emit energy by radiation It is the ratio of energy
radiated by a particular material to energy radiated by a black body at
CHE 215 page of 21 H Muhamad 20
CHE 215 page of 21 H Muhamad 21
the same temperature A true black body would have an ε = 1 while any
real object would have ε lt 1 Emissivity is a dimensionless quantity
In general the duller and blacker a material is the closer its emissivity is
to 1 The more reflective a material is the lower its emissivity Highly
polished silver has an emissivity of about 002[1]
Generally thermistors are more sensitive than RTD They can have a
precision of plusmn 001oC as compared with plusmn 01oC for RTD In addition
the error due to lead wire is insignificant since the resistance of the
thermistor is very high compared to that of the lead wire However the
suitable temperature range for thermistors is narrower from -100 to
400oC while RTD can cover from -100 to 1000 oC
4 Thermocouple
A thermocouple consists of two dissimilar metal wires twisted together
to form a junction that can act as a temperature sensor For example
copper wire and constantan wire (55 copper plus 45 nickel)
bull Seebeck effect
The use of a thermocouple as a temperature sensor is based on the
principle of the Seebeck effect The Seebeck effect states that an emf is
generated in the thermocouple when the junction is heated or cooled
Junction copper A
Constantan B
CHE 215 page of 21 H Muhamad 14
VAB is finite when the junction is at a temperature different from that at
the terminals A and B
bull Law of intermediate metals
Junction copper A
iron
Constantan B
When another metal (iron) is added to the thermocouple circuit as shown
in the above sketch two more junctions are formed at points A and B
As long as the junctions at A and B are kept at the same temperature the
emf generated by the main junction isnrsquot altered ie the temperature
reading doesnrsquot change
bull Law of intermediate temperatures
hot junction copper cold junction
E
constantan
CHE 215 page of 21 H Muhamad 15
For the same thermocouple ie the same two dissimilar metal junctions
the emf generated at different temperatures are additive
E3 = E1 + E2
Where E1 is the emf for the cold junction at 0oC and the hot junction at
50 oC E2 is the emf for the cold junction at 50oC and hot junction at 100
oC E3 is the emf for the cold junction at 0oC and hot junction at 100 oC
Precautions for use of TC
bull Extension wire should have similar properties as those of the TC
otherwise the two junctions of the extension wires and the TC wires
should be kept at the same temperature
bull Extension wire should be thick (having a low resistance) so to
minimize the error associated with the wire heating since the wire
resistance R = ρLS where ρ is the resistivity of the wire L is the
length and S is the cross-sectional area of the wire
5 Correction for temperature measurement under high-velocity
For temperature measurements of a flow at high speed usually gas flow
the effect of the stagnation point at the tip of the temperature sensor on
CHE 215 page of 21 H Muhamad 16
the reading could be significant At the stagnation point the stagnation
temperature Ts is
cp
S gCu
TT2
2α+= infin (14)
Where Tinfin is the temperature of the bulk gas uinfin is the velocity of gas the
flow Cp is the specific heat of the gas
The temperature registered by the sensor (the measured temperature) is
usually different than the stagnation temperature due to the effect of the
shield intruding in the flow path The measured temperature is called the
recovery temperature It is strongly dependent on the configuration of
the sensor and the shield The relative difference between the measured
temperature by the sensor Tr and the stagnation temperature TS is
known as the recovery factor r
infinminusinfinminus
=TTTTr
s
r (15)
7 Temperature measurements by radiation
The temperature of an object can be determined from the total thermal
radiation emitted from the object For an ideal body the total energy
emitted is proportional to the fourth power of the temperature
CHE 215 page of 21 H Muhamad 17
However most practical objects are non-ideal bodies and a correction
must be made to obtain the true temperature of the target This
correction is done by the emissivity of the non-ideal body as below
(16) 4TE σε=
Where E is the energy emitted by the object at the temperature T (in K
or oR) ɛ is the emissivity of the object (ɛ le 10) and σ is the Stefan-
Boltzmann constant
σ = 174x10-9 BTU(hft2oR4) or 5669x10-8 W(m2K4)
When an object is an ideal body the emissivity ɛ is equal to 10 and
Equation (16) is then known as the Stefan-Boltzmann equation
CHE 215 page of 21 H Muhamad 18
71 Optical Pyrometer
The optical pyrometer is simply a photometer that matches the energy
emitted from a reference source with the incoming one from the target
source As an example in the laboratory of this course the target source
is an incandescent lamp whose tungsten filament temperature can be
varied by adjusting the current through it (by adjusting a knob on the
optical pyrometer) When the brightness of the reference filament in the
optical pyrometer matches the brightness of the target filament being
measured the image of the reference filament blends into the colour of
the background of the viewing field in the optical pyrometer At this
point the intensity of the energy emitted from the target is equal to that
emitted from the reference and hence the temperature of the target (light
bulb) can be read from the display on a digital readout
2 Total Radiation Pyrometer
The total radiation pyrometer is the most commonly used pyrometer for
continuous non-contacting measurement of temperature Radiation (both
infrared and visible) passes through a lens and is then concentrated on a
heat-sensing element which produces an electric signal This sensing
element or detector may be a thermopile a thin thermistor flake or a
CHE 215 page of 21 H Muhamad 19
resistance thermometer Thermopiles are the most commonly used
Ambient temperature compensation may be required since the body of
the pyrometer is heated by the target radiation and the thermopile is
sensitive to the body heat
The current (or voltage) produced by the sensing detector is sent to a
potentiometer or a millivoltmeter where the current can be read The
total radiation pyrometer can be used to measure low temperature
However temperatures measured are also subject to errors
bull if the source is not an ideal body Error = (1 - ɛ14)
bull if the optical system gets dirty and adsorbs too much radiation
bull If part of the radiant energy is absorbed before it reaches the
instruments such as absorption by smoke and dust Gases such as
carbon dioxide sulphur dioxide and water vapour absorb infrared
radiation
The emissivity of a material (usually written ε or e) is the relative ability
of its surface to emit energy by radiation It is the ratio of energy
radiated by a particular material to energy radiated by a black body at
CHE 215 page of 21 H Muhamad 20
CHE 215 page of 21 H Muhamad 21
the same temperature A true black body would have an ε = 1 while any
real object would have ε lt 1 Emissivity is a dimensionless quantity
In general the duller and blacker a material is the closer its emissivity is
to 1 The more reflective a material is the lower its emissivity Highly
polished silver has an emissivity of about 002[1]
VAB is finite when the junction is at a temperature different from that at
the terminals A and B
bull Law of intermediate metals
Junction copper A
iron
Constantan B
When another metal (iron) is added to the thermocouple circuit as shown
in the above sketch two more junctions are formed at points A and B
As long as the junctions at A and B are kept at the same temperature the
emf generated by the main junction isnrsquot altered ie the temperature
reading doesnrsquot change
bull Law of intermediate temperatures
hot junction copper cold junction
E
constantan
CHE 215 page of 21 H Muhamad 15
For the same thermocouple ie the same two dissimilar metal junctions
the emf generated at different temperatures are additive
E3 = E1 + E2
Where E1 is the emf for the cold junction at 0oC and the hot junction at
50 oC E2 is the emf for the cold junction at 50oC and hot junction at 100
oC E3 is the emf for the cold junction at 0oC and hot junction at 100 oC
Precautions for use of TC
bull Extension wire should have similar properties as those of the TC
otherwise the two junctions of the extension wires and the TC wires
should be kept at the same temperature
bull Extension wire should be thick (having a low resistance) so to
minimize the error associated with the wire heating since the wire
resistance R = ρLS where ρ is the resistivity of the wire L is the
length and S is the cross-sectional area of the wire
5 Correction for temperature measurement under high-velocity
For temperature measurements of a flow at high speed usually gas flow
the effect of the stagnation point at the tip of the temperature sensor on
CHE 215 page of 21 H Muhamad 16
the reading could be significant At the stagnation point the stagnation
temperature Ts is
cp
S gCu
TT2
2α+= infin (14)
Where Tinfin is the temperature of the bulk gas uinfin is the velocity of gas the
flow Cp is the specific heat of the gas
The temperature registered by the sensor (the measured temperature) is
usually different than the stagnation temperature due to the effect of the
shield intruding in the flow path The measured temperature is called the
recovery temperature It is strongly dependent on the configuration of
the sensor and the shield The relative difference between the measured
temperature by the sensor Tr and the stagnation temperature TS is
known as the recovery factor r
infinminusinfinminus
=TTTTr
s
r (15)
7 Temperature measurements by radiation
The temperature of an object can be determined from the total thermal
radiation emitted from the object For an ideal body the total energy
emitted is proportional to the fourth power of the temperature
CHE 215 page of 21 H Muhamad 17
However most practical objects are non-ideal bodies and a correction
must be made to obtain the true temperature of the target This
correction is done by the emissivity of the non-ideal body as below
(16) 4TE σε=
Where E is the energy emitted by the object at the temperature T (in K
or oR) ɛ is the emissivity of the object (ɛ le 10) and σ is the Stefan-
Boltzmann constant
σ = 174x10-9 BTU(hft2oR4) or 5669x10-8 W(m2K4)
When an object is an ideal body the emissivity ɛ is equal to 10 and
Equation (16) is then known as the Stefan-Boltzmann equation
CHE 215 page of 21 H Muhamad 18
71 Optical Pyrometer
The optical pyrometer is simply a photometer that matches the energy
emitted from a reference source with the incoming one from the target
source As an example in the laboratory of this course the target source
is an incandescent lamp whose tungsten filament temperature can be
varied by adjusting the current through it (by adjusting a knob on the
optical pyrometer) When the brightness of the reference filament in the
optical pyrometer matches the brightness of the target filament being
measured the image of the reference filament blends into the colour of
the background of the viewing field in the optical pyrometer At this
point the intensity of the energy emitted from the target is equal to that
emitted from the reference and hence the temperature of the target (light
bulb) can be read from the display on a digital readout
2 Total Radiation Pyrometer
The total radiation pyrometer is the most commonly used pyrometer for
continuous non-contacting measurement of temperature Radiation (both
infrared and visible) passes through a lens and is then concentrated on a
heat-sensing element which produces an electric signal This sensing
element or detector may be a thermopile a thin thermistor flake or a
CHE 215 page of 21 H Muhamad 19
resistance thermometer Thermopiles are the most commonly used
Ambient temperature compensation may be required since the body of
the pyrometer is heated by the target radiation and the thermopile is
sensitive to the body heat
The current (or voltage) produced by the sensing detector is sent to a
potentiometer or a millivoltmeter where the current can be read The
total radiation pyrometer can be used to measure low temperature
However temperatures measured are also subject to errors
bull if the source is not an ideal body Error = (1 - ɛ14)
bull if the optical system gets dirty and adsorbs too much radiation
bull If part of the radiant energy is absorbed before it reaches the
instruments such as absorption by smoke and dust Gases such as
carbon dioxide sulphur dioxide and water vapour absorb infrared
radiation
The emissivity of a material (usually written ε or e) is the relative ability
of its surface to emit energy by radiation It is the ratio of energy
radiated by a particular material to energy radiated by a black body at
CHE 215 page of 21 H Muhamad 20
CHE 215 page of 21 H Muhamad 21
the same temperature A true black body would have an ε = 1 while any
real object would have ε lt 1 Emissivity is a dimensionless quantity
In general the duller and blacker a material is the closer its emissivity is
to 1 The more reflective a material is the lower its emissivity Highly
polished silver has an emissivity of about 002[1]
For the same thermocouple ie the same two dissimilar metal junctions
the emf generated at different temperatures are additive
E3 = E1 + E2
Where E1 is the emf for the cold junction at 0oC and the hot junction at
50 oC E2 is the emf for the cold junction at 50oC and hot junction at 100
oC E3 is the emf for the cold junction at 0oC and hot junction at 100 oC
Precautions for use of TC
bull Extension wire should have similar properties as those of the TC
otherwise the two junctions of the extension wires and the TC wires
should be kept at the same temperature
bull Extension wire should be thick (having a low resistance) so to
minimize the error associated with the wire heating since the wire
resistance R = ρLS where ρ is the resistivity of the wire L is the
length and S is the cross-sectional area of the wire
5 Correction for temperature measurement under high-velocity
For temperature measurements of a flow at high speed usually gas flow
the effect of the stagnation point at the tip of the temperature sensor on
CHE 215 page of 21 H Muhamad 16
the reading could be significant At the stagnation point the stagnation
temperature Ts is
cp
S gCu
TT2
2α+= infin (14)
Where Tinfin is the temperature of the bulk gas uinfin is the velocity of gas the
flow Cp is the specific heat of the gas
The temperature registered by the sensor (the measured temperature) is
usually different than the stagnation temperature due to the effect of the
shield intruding in the flow path The measured temperature is called the
recovery temperature It is strongly dependent on the configuration of
the sensor and the shield The relative difference between the measured
temperature by the sensor Tr and the stagnation temperature TS is
known as the recovery factor r
infinminusinfinminus
=TTTTr
s
r (15)
7 Temperature measurements by radiation
The temperature of an object can be determined from the total thermal
radiation emitted from the object For an ideal body the total energy
emitted is proportional to the fourth power of the temperature
CHE 215 page of 21 H Muhamad 17
However most practical objects are non-ideal bodies and a correction
must be made to obtain the true temperature of the target This
correction is done by the emissivity of the non-ideal body as below
(16) 4TE σε=
Where E is the energy emitted by the object at the temperature T (in K
or oR) ɛ is the emissivity of the object (ɛ le 10) and σ is the Stefan-
Boltzmann constant
σ = 174x10-9 BTU(hft2oR4) or 5669x10-8 W(m2K4)
When an object is an ideal body the emissivity ɛ is equal to 10 and
Equation (16) is then known as the Stefan-Boltzmann equation
CHE 215 page of 21 H Muhamad 18
71 Optical Pyrometer
The optical pyrometer is simply a photometer that matches the energy
emitted from a reference source with the incoming one from the target
source As an example in the laboratory of this course the target source
is an incandescent lamp whose tungsten filament temperature can be
varied by adjusting the current through it (by adjusting a knob on the
optical pyrometer) When the brightness of the reference filament in the
optical pyrometer matches the brightness of the target filament being
measured the image of the reference filament blends into the colour of
the background of the viewing field in the optical pyrometer At this
point the intensity of the energy emitted from the target is equal to that
emitted from the reference and hence the temperature of the target (light
bulb) can be read from the display on a digital readout
2 Total Radiation Pyrometer
The total radiation pyrometer is the most commonly used pyrometer for
continuous non-contacting measurement of temperature Radiation (both
infrared and visible) passes through a lens and is then concentrated on a
heat-sensing element which produces an electric signal This sensing
element or detector may be a thermopile a thin thermistor flake or a
CHE 215 page of 21 H Muhamad 19
resistance thermometer Thermopiles are the most commonly used
Ambient temperature compensation may be required since the body of
the pyrometer is heated by the target radiation and the thermopile is
sensitive to the body heat
The current (or voltage) produced by the sensing detector is sent to a
potentiometer or a millivoltmeter where the current can be read The
total radiation pyrometer can be used to measure low temperature
However temperatures measured are also subject to errors
bull if the source is not an ideal body Error = (1 - ɛ14)
bull if the optical system gets dirty and adsorbs too much radiation
bull If part of the radiant energy is absorbed before it reaches the
instruments such as absorption by smoke and dust Gases such as
carbon dioxide sulphur dioxide and water vapour absorb infrared
radiation
The emissivity of a material (usually written ε or e) is the relative ability
of its surface to emit energy by radiation It is the ratio of energy
radiated by a particular material to energy radiated by a black body at
CHE 215 page of 21 H Muhamad 20
CHE 215 page of 21 H Muhamad 21
the same temperature A true black body would have an ε = 1 while any
real object would have ε lt 1 Emissivity is a dimensionless quantity
In general the duller and blacker a material is the closer its emissivity is
to 1 The more reflective a material is the lower its emissivity Highly
polished silver has an emissivity of about 002[1]
the reading could be significant At the stagnation point the stagnation
temperature Ts is
cp
S gCu
TT2
2α+= infin (14)
Where Tinfin is the temperature of the bulk gas uinfin is the velocity of gas the
flow Cp is the specific heat of the gas
The temperature registered by the sensor (the measured temperature) is
usually different than the stagnation temperature due to the effect of the
shield intruding in the flow path The measured temperature is called the
recovery temperature It is strongly dependent on the configuration of
the sensor and the shield The relative difference between the measured
temperature by the sensor Tr and the stagnation temperature TS is
known as the recovery factor r
infinminusinfinminus
=TTTTr
s
r (15)
7 Temperature measurements by radiation
The temperature of an object can be determined from the total thermal
radiation emitted from the object For an ideal body the total energy
emitted is proportional to the fourth power of the temperature
CHE 215 page of 21 H Muhamad 17
However most practical objects are non-ideal bodies and a correction
must be made to obtain the true temperature of the target This
correction is done by the emissivity of the non-ideal body as below
(16) 4TE σε=
Where E is the energy emitted by the object at the temperature T (in K
or oR) ɛ is the emissivity of the object (ɛ le 10) and σ is the Stefan-
Boltzmann constant
σ = 174x10-9 BTU(hft2oR4) or 5669x10-8 W(m2K4)
When an object is an ideal body the emissivity ɛ is equal to 10 and
Equation (16) is then known as the Stefan-Boltzmann equation
CHE 215 page of 21 H Muhamad 18
71 Optical Pyrometer
The optical pyrometer is simply a photometer that matches the energy
emitted from a reference source with the incoming one from the target
source As an example in the laboratory of this course the target source
is an incandescent lamp whose tungsten filament temperature can be
varied by adjusting the current through it (by adjusting a knob on the
optical pyrometer) When the brightness of the reference filament in the
optical pyrometer matches the brightness of the target filament being
measured the image of the reference filament blends into the colour of
the background of the viewing field in the optical pyrometer At this
point the intensity of the energy emitted from the target is equal to that
emitted from the reference and hence the temperature of the target (light
bulb) can be read from the display on a digital readout
2 Total Radiation Pyrometer
The total radiation pyrometer is the most commonly used pyrometer for
continuous non-contacting measurement of temperature Radiation (both
infrared and visible) passes through a lens and is then concentrated on a
heat-sensing element which produces an electric signal This sensing
element or detector may be a thermopile a thin thermistor flake or a
CHE 215 page of 21 H Muhamad 19
resistance thermometer Thermopiles are the most commonly used
Ambient temperature compensation may be required since the body of
the pyrometer is heated by the target radiation and the thermopile is
sensitive to the body heat
The current (or voltage) produced by the sensing detector is sent to a
potentiometer or a millivoltmeter where the current can be read The
total radiation pyrometer can be used to measure low temperature
However temperatures measured are also subject to errors
bull if the source is not an ideal body Error = (1 - ɛ14)
bull if the optical system gets dirty and adsorbs too much radiation
bull If part of the radiant energy is absorbed before it reaches the
instruments such as absorption by smoke and dust Gases such as
carbon dioxide sulphur dioxide and water vapour absorb infrared
radiation
The emissivity of a material (usually written ε or e) is the relative ability
of its surface to emit energy by radiation It is the ratio of energy
radiated by a particular material to energy radiated by a black body at
CHE 215 page of 21 H Muhamad 20
CHE 215 page of 21 H Muhamad 21
the same temperature A true black body would have an ε = 1 while any
real object would have ε lt 1 Emissivity is a dimensionless quantity
In general the duller and blacker a material is the closer its emissivity is
to 1 The more reflective a material is the lower its emissivity Highly
polished silver has an emissivity of about 002[1]
However most practical objects are non-ideal bodies and a correction
must be made to obtain the true temperature of the target This
correction is done by the emissivity of the non-ideal body as below
(16) 4TE σε=
Where E is the energy emitted by the object at the temperature T (in K
or oR) ɛ is the emissivity of the object (ɛ le 10) and σ is the Stefan-
Boltzmann constant
σ = 174x10-9 BTU(hft2oR4) or 5669x10-8 W(m2K4)
When an object is an ideal body the emissivity ɛ is equal to 10 and
Equation (16) is then known as the Stefan-Boltzmann equation
CHE 215 page of 21 H Muhamad 18
71 Optical Pyrometer
The optical pyrometer is simply a photometer that matches the energy
emitted from a reference source with the incoming one from the target
source As an example in the laboratory of this course the target source
is an incandescent lamp whose tungsten filament temperature can be
varied by adjusting the current through it (by adjusting a knob on the
optical pyrometer) When the brightness of the reference filament in the
optical pyrometer matches the brightness of the target filament being
measured the image of the reference filament blends into the colour of
the background of the viewing field in the optical pyrometer At this
point the intensity of the energy emitted from the target is equal to that
emitted from the reference and hence the temperature of the target (light
bulb) can be read from the display on a digital readout
2 Total Radiation Pyrometer
The total radiation pyrometer is the most commonly used pyrometer for
continuous non-contacting measurement of temperature Radiation (both
infrared and visible) passes through a lens and is then concentrated on a
heat-sensing element which produces an electric signal This sensing
element or detector may be a thermopile a thin thermistor flake or a
CHE 215 page of 21 H Muhamad 19
resistance thermometer Thermopiles are the most commonly used
Ambient temperature compensation may be required since the body of
the pyrometer is heated by the target radiation and the thermopile is
sensitive to the body heat
The current (or voltage) produced by the sensing detector is sent to a
potentiometer or a millivoltmeter where the current can be read The
total radiation pyrometer can be used to measure low temperature
However temperatures measured are also subject to errors
bull if the source is not an ideal body Error = (1 - ɛ14)
bull if the optical system gets dirty and adsorbs too much radiation
bull If part of the radiant energy is absorbed before it reaches the
instruments such as absorption by smoke and dust Gases such as
carbon dioxide sulphur dioxide and water vapour absorb infrared
radiation
The emissivity of a material (usually written ε or e) is the relative ability
of its surface to emit energy by radiation It is the ratio of energy
radiated by a particular material to energy radiated by a black body at
CHE 215 page of 21 H Muhamad 20
CHE 215 page of 21 H Muhamad 21
the same temperature A true black body would have an ε = 1 while any
real object would have ε lt 1 Emissivity is a dimensionless quantity
In general the duller and blacker a material is the closer its emissivity is
to 1 The more reflective a material is the lower its emissivity Highly
polished silver has an emissivity of about 002[1]
71 Optical Pyrometer
The optical pyrometer is simply a photometer that matches the energy
emitted from a reference source with the incoming one from the target
source As an example in the laboratory of this course the target source
is an incandescent lamp whose tungsten filament temperature can be
varied by adjusting the current through it (by adjusting a knob on the
optical pyrometer) When the brightness of the reference filament in the
optical pyrometer matches the brightness of the target filament being
measured the image of the reference filament blends into the colour of
the background of the viewing field in the optical pyrometer At this
point the intensity of the energy emitted from the target is equal to that
emitted from the reference and hence the temperature of the target (light
bulb) can be read from the display on a digital readout
2 Total Radiation Pyrometer
The total radiation pyrometer is the most commonly used pyrometer for
continuous non-contacting measurement of temperature Radiation (both
infrared and visible) passes through a lens and is then concentrated on a
heat-sensing element which produces an electric signal This sensing
element or detector may be a thermopile a thin thermistor flake or a
CHE 215 page of 21 H Muhamad 19
resistance thermometer Thermopiles are the most commonly used
Ambient temperature compensation may be required since the body of
the pyrometer is heated by the target radiation and the thermopile is
sensitive to the body heat
The current (or voltage) produced by the sensing detector is sent to a
potentiometer or a millivoltmeter where the current can be read The
total radiation pyrometer can be used to measure low temperature
However temperatures measured are also subject to errors
bull if the source is not an ideal body Error = (1 - ɛ14)
bull if the optical system gets dirty and adsorbs too much radiation
bull If part of the radiant energy is absorbed before it reaches the
instruments such as absorption by smoke and dust Gases such as
carbon dioxide sulphur dioxide and water vapour absorb infrared
radiation
The emissivity of a material (usually written ε or e) is the relative ability
of its surface to emit energy by radiation It is the ratio of energy
radiated by a particular material to energy radiated by a black body at
CHE 215 page of 21 H Muhamad 20
CHE 215 page of 21 H Muhamad 21
the same temperature A true black body would have an ε = 1 while any
real object would have ε lt 1 Emissivity is a dimensionless quantity
In general the duller and blacker a material is the closer its emissivity is
to 1 The more reflective a material is the lower its emissivity Highly
polished silver has an emissivity of about 002[1]
resistance thermometer Thermopiles are the most commonly used
Ambient temperature compensation may be required since the body of
the pyrometer is heated by the target radiation and the thermopile is
sensitive to the body heat
The current (or voltage) produced by the sensing detector is sent to a
potentiometer or a millivoltmeter where the current can be read The
total radiation pyrometer can be used to measure low temperature
However temperatures measured are also subject to errors
bull if the source is not an ideal body Error = (1 - ɛ14)
bull if the optical system gets dirty and adsorbs too much radiation
bull If part of the radiant energy is absorbed before it reaches the
instruments such as absorption by smoke and dust Gases such as
carbon dioxide sulphur dioxide and water vapour absorb infrared
radiation
The emissivity of a material (usually written ε or e) is the relative ability
of its surface to emit energy by radiation It is the ratio of energy
radiated by a particular material to energy radiated by a black body at
CHE 215 page of 21 H Muhamad 20
CHE 215 page of 21 H Muhamad 21
the same temperature A true black body would have an ε = 1 while any
real object would have ε lt 1 Emissivity is a dimensionless quantity
In general the duller and blacker a material is the closer its emissivity is
to 1 The more reflective a material is the lower its emissivity Highly
polished silver has an emissivity of about 002[1]
CHE 215 page of 21 H Muhamad 21
the same temperature A true black body would have an ε = 1 while any
real object would have ε lt 1 Emissivity is a dimensionless quantity
In general the duller and blacker a material is the closer its emissivity is
to 1 The more reflective a material is the lower its emissivity Highly
polished silver has an emissivity of about 002[1]