thermocouples (continued) introduction to temperature sensors isat 300 instrumentation and...
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Thermocouples (continued)
Introduction to Temperature Sensors
ISAT 300 Instrumentation and Measurement
02/21/2000
Language of Thermocouples
Temperature Range -270oC to 2320oC depends on the type of the
thermocouple Passive
Dose not require external power source Non-intrusive
Does not affect the system much Linearity
In general, it is a nonlinear function of temperature Sensitivity
From 0.011 mV/oC for type R to 0.076 mV/oC for type E
Millivolt Output of Common Thermocouples (Reference Junction at 0oC)
-20
-10
0
10
20
30
40
50
60
70
80
90
-250 250 750 1250 1750
Temperature (C)
Ou
tpu
t (m
V)
K
T
J
E
R
S
Type Materials Lead wirecolor
Operatingrange(oC)
Approximatesensitivity(mV/oC)
T Copper/constantan Blue -250 to 400 0.052
E Chromel/constantan Purple -270 to 1000 0.076
J Iron/constantan Black -210 to 760 0.050
K Chromel/alumel Yellow -270 to 1372 0.039
R Platinum/platinum-13% rhodium
Green -50 to 1768 0.011
S Platinum/platinum-10% rhodium
Green -50 to 1768 0.012
E Tungsten, 5%rhenium/tungsten,26% rhenium
White,Red trace
0 to 2320 0.020
Characteristics of Standard Thermocouples
Common Sheathed Thermocouple Probe
Place the wires and junction and ceramic insulation inside a stainless steel or inconel sheath to protect the thermocouple wires from damage or chemical contamination.
Thermopile
When n thermocouples are connected in series in a device called a thermopile
Which increases the sensitivity of the system, however, it provides a method to average several thermocouples which are distributed in a spatial region.
C 0 1 2 3 4
20 0.798 0.838 0.879 0.919 0.960
Example:
A type K thermocouple with an ice reference gives a voltage reading of 0.900 mV. What is its temperature?
Thermoelectric voltage in mV
0.040 mV
0.900
0.021 mVC 53.22
1 040.0
021.0C 22
CT
C 0 1 2 3 4
300 2.401 2.410 2.420 2.430 2.440
Example:
A type R thermocouple with an ice reference gives a voltage reading of 2.415 mV. What is its temperature?
Thermoelectric voltage in mV
2.415C 5.301
1 010.0
005.0C 301
CT
12.207
30.10
42.307
-10
0
10
20
30
40
50
60
-500 0 500 1000 1500
Temperature (C)
Ou
tpu
t Vo
ltag
e (m
V)
The Importance of 0oC Reference Junction
C 0 1 2 3 4
30 0.171 0.177 0.183 0.189 0.195
Example:
A type R thermocouple with an ice reference gives a voltage reading of 2.415 mV. What would it read
with a 30 °C reference?
Thermoelectric voltage in mV
mV 244.2mV 171.0mV 415.2 V
C 0 1 2 3 4
280 2.207 2.217 2.226 2.236 2.246
Example:
A type R thermocouple with 30 °C reference gives a voltage reading of 2.244 mV. What is its temperature?
Thermoelectric voltage in mV
0.010 mV
2.244
0.008 mVC 8.310
30 1 010.0
008.0C 280
CCT
NO!
C 0 1 2 3 4
300 2.401 2.410 2.420 2.430 2.440
Thermoelectric voltage in mV
2.415 = 2.244 + 0.171C 5.301
1 010.0
005.0C 301
CT
Example:
A type R thermocouple with 30 °C reference gives a voltage reading of 2.244 mV. What is its temperature?
Correct the voltageFIRST!
First Order System A change at the input is NOT seen immediately at the output.
Example: Move a temperature probe from cold water to hot water.
CoolBath
HotBath
CdT t
d t
T T t
Rm c
dT t
d thA T T t
CJ
C
RC
WT (t)T
p w p pw p
o
o
p
w
( ) ( ) ( )[ ( )]
, o r, ,
w h ere , in is th e h ea t cap acity o f th e p ro b e .
in is th e th erm al resis tan ce o f th e p ro b e .
is th e tem p era tu re o f p ro b e , an d is th e tem p era tu re o f w ater.
CdT t
d t
T T t
RdT t
d t CRT t
CRT
p w p
p
p w
( ) ( )
( )( )
is a tran sien t h ea t co n d u ctio n eq u atio n ,
w h ich can b e rew ritten as 1 1
A Differential Equation
Assumed that the water temperature of the hot bath (Tw) does not cool down much (non-intrusive), and can be treated as a constant.
Then this equation simply just a first-order differential equation, a time dependent temperature equation of Tp(t), with an initial condition of Tp(0)=Tpo.
Solution for This Differential Equation
Here, C is the heat capacity, R is the thermal resistance of the temperature probe, they are the probe material properties should be given or known to us.
T h e so lu tio n fo r th is d ifferen tia l eq u atio n is
N o w , if w e ap p ly th e in itia l co n d itio n to
th is so lu tio n . w e w ill g e t , w h ere , = C R .
T t C e T
T t T T e T
p
t
w
p w po
t
po
( ) .
( ) ( )( )
1
o r, w e co u ld rearran ge it as T t T
T Te
p po
w po
t( )
1
The Time Constant, Response for Varying Values of
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.5 1 1.5 2 2.5 3 3.5 4
Time
Res
po
nse
= 1.0 = 0.5
= 0.2
T t T
T Te
p po
w po
t( )
1
For t=, thermocouple reaches 63.2% of the steady-state or final value.