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EXM2
Experimental methods E181101
Temperature
(thermocouples,
thermistors)
Rudolf Žitný, Ústav procesní a
zpracovatelské techniky ČVUT FS 2010
Some pictures and texts were copied
from www.wikipedia.com
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State variables- temperature
Temperature is measure of inner kinetic energy of random molecular motion. In
case of solids the kinetic energy is the energy of atom vibration, in liquids and
gases the kinetic energy includes vibrational, rotational and translational
motion. Statistically, temperature (T) is a direct measure of the mean kinetic
energy of particles (atoms, molecules). For each degree of freedom that a
particle possesses (rotational and vibrational modes), the mean kinetic energy
(Ek) is directly proportional to thermodynamic temperature
1
Ek  kT
2
where k-is universal Boltzmann constant. For more details see wikipedia.
Thermodynamic temperature is measured in Kelvins [K], that are related to
different scales, degree of Celsius scale T=C+273.15, or degree of Fahrenheit
F=1.8C+32.
Remark: you can say degree of Celcius, or degree of Fahrenheit, but never say degree of Kelvins always only Kelvins.
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Temperature measurement
Thermometers
 Glass tube (filled by mercury or organic liquid, accuracy up to 0.001 oC)
 Bimetalic (deflection of bonded metallic strips having different thermal
expansion coefficient)
 Thermocouples (different metals electrically connected generate voltage)
 RTD (Resistance Temperature Detectors – temperature dependent electrical
resistance) – thermistors (semiconductors)
 Infrared thermometers
 Thermal luminiscence (phosphor thermometers – time decay of induced light
depends upon temperature – used with optical fibres)
 Irreversible/reversible sensors (labels), liquid crystals
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Temperature measurement
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Thermocouples
Leger
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Thermocouples
Seebeck effect (electrons diffuse from hot to cold end)
Measured voltage is given by temperature T2-T1.
Cold junction temperature T2 should be 0C. Or at
least measured by different instrument (by RTD).
T1
V
T2
Different wire has no effect if T3 is the same at both ends
T1
T3
T3
V T2
It does not matter how the connection of wires is
realized (soldered, welded, mechanically connected)
T1
V T2
Usual configuration – Cu wires to voltameter.
Measured voltage is given by temperature T2-T1
T1
Exposed end
Insulated junction
T2
V
Grounded junction
Law of successive thermocouples (next slide)
T2
T1
V2
T3
V3
Thermocouple pile
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T2
T1
V 3-times greater
Example of a thermocouple
pile manufactured by
lithography
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Thermocouple types
Chromel= 90% nickel, 10% chromium
Alumel= 95% nickel, 2% aluminium, 2% manganese, 1% silicon
Nicrosil=Nickel-Chromium-Silicon
Constantan = 55% copper, 45% nickel
Type K (chromel-Alumel) ,
sensitivity 41 µV/°C
J (iron–constantan) has a
more restricted range than
type K (−40 to +750 °C), but
higher sensitivity 55 µV/°C
N (Nicrosil–Nisil) high
temperatures, exceeding
1200 °C. 39 µV/°C at 900 °C
slightly lower than type K.
T (copper–constantan) −200 to
350 °C range. Sensitivity of
about 43 µV/°C.
E (chromel–constantan) has
a high output (68 µV/°C)
which makes it well suited to
cryogenic use
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Resistivity thermometers
Specific electrical resistivity (units m) of materials depends upon
temperature. Temperature can be therefore evaluated from measured
electrical resistance of sensor (resistor) by using for example Wheatstone
bridge arrangement
Sensor
fixed resistors
V
Current
source (1mA)
There are two basic kinds of resistivity thermometers
Thermistors (resistor is a semiconductor, or a plast) high sensitivity, nonlinear, limited temperature
RTD (metallic resistor, see next slide) stable, linear,
suitable for high temperatures. R=100 .
Another classification according to sign of temperature sensitivity coef.  
1 dR
R0 dT
NTC (Negative Temp.Coef) typical for semiconductors, R=2252  is industrial standard resistance.
PTC (Positive Temp. Coef.) typical for metals, or for carbon filled plastics
Cold
Hot
sample
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RTD platinum thermometers
RTD Platinum thermometers Pt100, Pt1000 (nominal resistance 100/1000 Ohms respectively)
R  R0 (1  0.0039083T  5.77  10 7 T 2 )

Therefore coefficient of relative temperature change is approximately
1 dR
 0.0039
R0 dT
(this value slightly depends upon platinum purity, for example typical US standards =0.00392,
Europian standard =0.00385).
2-wires (reading is affected by parasitic ohmic resistance of long and tiny wires (which need not be
negligible in comparison with 100 of RTD). Example> compute resistance of Cu wire for specific
resistivity of copper 1.7E-8 .m
Parazitic resistances of leading wires
are added to the sensor resistance
V
Current source
(1mA)
V
Current source
(1mA)
3-wires
Parazitic resistances of leading wires
are partly compensated
4-wires
The most accurate
arrangement
Almost zero current flows in these two wires as
soon as internal resistance of voltameter is high
V
Current source
(1mA)
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Systematic errors in contact measurement
Pt1000 is in fact a tiny heater (at 1 mA, sensor generates RI2=0.001 W)
and the heat must be removed by a good thermal contact with measured
object.
RTD-2 wires connection (resistance of leading wires are added to the
measured sensor resistance). Specific resistance of copper is =1.7E-8
.m, resistance of wire is R=4L/( D2), L-length, D-diameter of wire.
Time delay due to thermal capacity of sensor (response time depends
upon time constant of sensor as well as upon thermal contact between fluid
and the sensor surface, see next slide)
Temperature difference between temperature of fluid and the temperature
of measuring point (junction of thermocouple wires, or Pt100 spiral). This
difference depends upon the thermal resistance fluid-sensor and thermal
resistance sensor-wall (resistance of shield). See next slide
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Time constant of sensor
Demuth
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Time constant of sensor
Time delay of sensor follows from the enthalpy balance
Enthalpy accumulation
Mc p
dTs
 S (T fluid  Ts )
dt
Heat from fluid to sensor [W]
where M-mass, cp specific heat capacity of sensor, Ts temperature of sensor, -heat transfer
coefficient, S surface of sensor, Tfluid-temperature of fluid (temperature that is to be measured).
For step change of fluid temperature solution of this equation is exponential function with time
constant 
Tfluid
Mc

p
S
Time constant is the time required by a sensor to reach 63%
of a step change temperature.
Ts

t
Heat transfer coefficient  depends upon fluid velocity (more specifically upon Reynolds number
or Rayleigh number in case of forced and natural convection, respectively). Example: for a
spherical tip of a probe and forced convection it is possible to use Whitaker’s correlation
Nu 
D
 2  0.4 Re Pr 0.4
 fluid
Re 
uD

Pr 

a
Nu-Nusselt number, D-diameter of sphere,  thermal conductivity of fluid, u-velocity of fluid,  kinematic
viscosity, a-temperature diffusivity.
Conclusion: the higher is mass of sensor the greater if time constant. The higher is velocity of fluid, the
better (the shorter is the time constant).
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Example time constant of sensors
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Tutorial time constant of sensors
Identify the time constant of a thermocouple
A/D converter
PC
NI-USB 6281
Labview
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Tutorial science direct reading
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Tutorial science direct reading
Rabin, Y., Rittel, D., 1998. A model for the time response of solid-embedded thermocouples. Experimental Mechanics 39 (2),
132–136.
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Heat conduction by shield
Scheeler
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Heat conduction by shield
Distortion of measured temperature of fluid due to heat transfer through
wires or shielding of detector. The error decreases with improved thermal
contact (fluid-surface, see above) and reduced thermal resistance of
leading wires or shield RT. For wire or a rod the thermal resistance is
RT 
4Lwire
D 2 wire
D
Lwire
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Example steady heat transfer (1/2)
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Example steady heat transfer (2/2)
2/3
0.37
toto platí jen pro malé Re, přesnější Nu  (0.4 Re  0.06 Re ) Pr
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Heat transfer - tutorial
Identify heat transfer coefficient (cross flow around cylinder)
Pt100
Cylinder H=0.075, D=0.07 [m]
cp=910, rho=2800 kg/m3
Df=0.05m
T [C]
Air cp=1000, rho=1 kg/m3,
=0.03 W/m/K
FAN (hot air)
OMEGA data logger
(thermocouples) T1,T2 , T3
Example: Re=8000, Pr=1
Nu  (0.4 Re  0.06 Re ) Pr
2/3
Nu  0.4 Re Pr 0.37  36
Watt meter
Measured 1.3.2011 1200 W
0.37
 60
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Heat transfer - tutorial
Example: velocity of air calculated from the enthalpy balance is 5 m/s
(Tnozzle=140 0C, mass flowrate of air 0.01 kg/s)
Corresponding Reynolds number (kinematic viscosity 2.10-5) is Re=17500
Nusselt number calculated for Pr=0.7 is therefore Nu  (0.4 Re  0.06 Re
80

70
60
exponential model
T [C]
) Pr 0.37  82
NuD
W
 191

mK
This is result from the
heat transfer correlation
More than 2times less is predicted
from the time constant
experiment
T  T0  (T  T0 )(1  exp(t /  ))
50
2/3

 Dc p 2800  0.07  910
W

 76.2
4
4  585
mK
40
30
20
Experiment 1.3.2011 =585 s
Probable explanation of this discrepancy:
T0=19.2, T=81 C
Velocity of air (5m/s) was calculated at the nozzle
of hair dryer. Velocity at the cylinder will be much
smaller. As soon as this velocity will be reduced
5-times (1 m/s at cylinder) the heat transfer
coefficient will be the same as that predicted from
the time constant (76 W/m/K)
10
0
0
5
10
15
t [min]
20
25
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Thermocouple - tutorial
Record time change of temperature of air compressed in syringe.
x
D
Thermocouple
P-pressure transducer Kulite XTM 140
V
p1v1  p2 v2
Example: V2/V1=0.5
p1v1  RT1
p1
v
T v
 ( 2 )  1 2
p2
v1
T2 v1
p2 v2  RT2
T1
v2  1
( )
T2
v1
=cp/cv=1.4
T1=300 K
T2=396 K
temperature increase 96 K!!