Workshop Thermocouple

Better Standards, Better Life 1

June, 2014

Dr. Yong-Gyoo Kim

Center for Thermometry,

Division of Physical Metrology

Korea Research Institute of Standards and Science

Thermocouple thermometry


Part I. Heat and Temperature

1. Unit and Scale of Temperature

2. Heat Transfer and Thermal Properties


1. Unit and scale of Temperature

Lord Kelvin Ludwig Boltzmann


1.1 What is temperature ?

Temperature Degree of hotness or coldness of objects

intuitively

Exactly, level of thermal energy (kT) k : Boltzmann constant

Kinetic energy due to a microscopic motion of particles, energy due to phonon ½ mv2 = ½ kT

Phonon: quantum mechanical description of an elementary vibrational motion

Heat is caused from the vibration of particles

Temperature is a quantitative description of this vibrational motion.


Temperature Kelvin Degrees Celsius

Coldest temperature achieved 100 pK −273.149 999 999 900 °C

Triple point of water 273.16 K 0.01 °C

Sun’s visible surface 5,778 K 5,505 °C

Lightening bolt’s channel 28 kK 28,000 °C

Sun’s core 16 MK 16,000,000 °C

Thermonuclear weapon peak temperature 350 MK 350,000,000 °C

Core of a high-mass star on its last day 3 GK 3,000,000,000 °C

CERN’s proton vs nucleus collisions 10 TK 10 ×1012 °C

Universe 5.391×10−44 s after Big Bang 1.417×1032 K 1.417×1032 °C

Some examples of temperature


The first thermometer

In 1594, G. Galilei A type of gas thermometer

Volume change with temperature


1.2 Unit of temperature

International unit: K or oC Absolute thermodynamic scale : Kelvin, K degree Celsius (oC) Common and practical unit 1 oC = 1 K K = 273.15 + oC

Non SI unit Fahrenheit scale: oF In Europe and USA oF = oC x 9/5 + 32

Rankine scale: oR Chemical engineering in USA oR = K x 9/5


degree Celsius (oC)

A. Celsius (Sweden ) in 1742

Ice point : 100 oC

Water boiling point : 0 oC

Divided into 100 parts

In 1744, M. Strømer

After Celsius passed away

Reverse the two fixed point value

Ice point :0 oC, boiling point : 100 oC

Currently used with Kelvin internationally


Kelvin, K

For a reversible Carnot engine, Heat efficiency is proportional to temperature

Absolute temperature ,T, is defined as above. For ideal gases, PV = constant x T At T = 0, volume of gas should be zero.

For real gases, extrapolated volume goes to zero (T = 0 K).

1

2

1

2

TT

QQ

=


Volume vs Temperature (Charles’ Law)

T[K]


1.3 Temperature scale

Before 1954, Celsius scale used Ice point and boiling point of water

After 1954, thermodynamic scale used Triple point of water (TPW) was defined as definition of

temperature scale TPW 273.16 K

Definition of temperature scale The unit of thermodynamic temperature, the kelvin,

symbol K, is defined as the fraction 1/273.16 of the thermodynamic temperature of the triple point of water

≡


Triple point cell of Water


History of temperature scale

ITS-27 Boiling point of oxygen (-182.970 oC) ~ radiation thermometer range 6 fixed-points

ITS-48 Change of Ag fixed-point value Change of interpolation equation of pyrometer Include several secondary fixed-points

IPTS-68 Down to TPW of H2 (13.81 K) 11 fixed-points Change of interpolation equation of standard thermometer

ITS-90 Current temperature scale

PLTS-2000 Down to 0.9 mK

Mise en Pratique of Kelvin (MeP-K) Current definition of Kelvin


Classification of thermometers

Primary vs. Secondary Primary : Clear equation of state

Measurement of thermodynamic temperature Secondary : Temperature-dependent parameter (voltage, current, length, etc)

Resistance thermometer, thermocouple, etc.


Standard vs. Industrial thermometer Standard : Realization of temperature scale Gas thermometer Vapor pressure thermometer Standard platinum resistance thermometer Pyrometer

Industrial : Except for the standards Thermocouple, Glass thermometer, Thermistor, etc


2. Heat Transfer and Thermal Properties Temperature measurement is just measurement of the

heat exchange between thermometer and system.


2.1 Heat transfer

3 transfer mode Conduction, Convection, Radiation


A. Conduction

transfer of thermal energy between regions of matter due to a temperature gradient In solid, liquid, gas, and plasma Vibration of solid atoms, collision or diffusion of liquid (gas) atoms

(molecules, radicals) Heat flow rate (watt, W)

k : thermal conductivity ( ) A : area ∆T : temperature gradient ∆x : distance

xTkAQ

∆∆

=∆•

KW/m ⋅


Thermal conductivity, k, of various materials


Thermal conductivity, k, of various materials

Material Thermal conductivity W/(m·K) Material Thermal conductivity

W/(m·K)

Silica Aerogel 0.004 - 0.04 Thermal epoxy 1 - 7

Air 0.025 Glass 1.1

Wood 0.04 - 0.4 Soil 1.5

Hollow Fill Fibre Insulation 0.042 Concrete, stone 1.7

Alcohols and oils 0.1 - 0.21 Ice 2

Polypropylene 0.25 Sandstone 2.4

Mineral oil 0.138 Stainless steel 12.11 ~ 45.0

Rubber 0.16 Lead 35.3

LPG 0.23 - 0.26 Aluminum 237 (pure)120—180 (alloys)

Cement, Portland 0.29 Gold 318

Epoxy (silica-filled) 0.30 Copper 401

Epoxy (unfilled) 0.12 - 0.177 Silver 429

Water (liquid) 0.6 Diamond 900 - 2320

Thermal grease 0.7 - 3 Graphene (4840±440) - (5300±480)


B. Convection

transfer of heat from one place to another by the physical movement of fluids In liquids, gases Natural (free) convection Forced convection by fan, pump, etc

Heat flow rate (watt, W) between solid and fluid

h : convection heat transfer ( W/m2K) A : area Ts : surface temperature of solid Tenvironm: temperature of fluid far from the surface

)( environms TThAQ −=∆•


Some examples of convection

Mantle convection

Atmospheric convection Foehn phenomenon

Heat sink radiator

http://upload.wikimedia.org/wikipedia/commons/6/62/Accretion-Subduction.PNG

http://upload.wikimedia.org/wikipedia/en/a/aa/Foehn1.png

http://upload.wikimedia.org/wikipedia/commons/0/08/Radiator_FxJ_v2.JPG


Convection heat transfer coefficient, h, of some phases

Process h [Wm-2 K-1]

Free Convection Gases 2 ～ 25

Liquids 50 ～ 1 000

Forced Convection Gases 25 ～ 250

Liquids 50 ～ 20 000

Convection with phase change

Boiling or condensation 2 500 ～ 100 000


C. Radiation

Energy in the form of electromagnetic waves with continuous spectrum

All matter higher than absolute zero temperature

Sunlight is thermal radiation generated by the hot plasma of the Sun.

Stefan-Boltzmann law

E : energy radiated per unit area (W/m2)

ε : emissivity

σ : Stefan-Boltzmann constant

T: Absolute temperature

4TE σε=


2.2 Thermal properties

Three important properties Thermal conductivity, heat capacity, latent heat


A. Heat capacity (C)

Heat (q) required to raise the temperature by 1 K C = q/(T2-T1)

Higher C, larger q ⇒ need more time to stabilize

For fast measurement, sensor having higher k and smaller C required.


Heat capacity of some materials

Material Per unit mass

JK-1kg-1 Per unit volume

JK-1cm-3

Copper Gold Silver Aluminum Zinc Tin Mercury Stainless steel Silicon water Ice Pyrex Alumina (Al2O3)

Magnesia (MgO) Polystyrene Silicone oil

385 129 235 903 389 227

139.3 480 712

4 179 2 040 835 800 960

1 300 1 548

3.44 2.49 2.47 2.44 2.78 1.66 1.88 3.83 1.65 4.17 1.88 1.85 3.04 3.46 1.37 1.45


B. Latent heat

Heat associated with phase change solid ⇔ liquid ⇔ gas Fixed-points use latent heat of materials


Simple melting and freezing of pure solid

For melting, Qin = latent heat For freezing, Qout = latent heat Basically, Tmelting = Tfreezing

But little difference due to impurities, solid structure During freezing, supercooling and recovery observed

Require more heat for solidification at initial to overcome the surface energy between solid and liquid

There is a critical size for nucleation of solid

time

tem

pera

ture

Melting

melting plateau

time

Freezing

freezing plateau

supercooling and recovery

tem

pera

ture


Nucleation in pure metal

Gibbs free energy change, ∆G

Critical value to solidify

Liquid Liquid

Solid

freezing

Energy G1 G2 = G1 + ∆G

SLv

SLSLvs

rGr

AGVG

γππ

γ

23 434

+∆−=

+∆−=∆

S,L: solid, liquid V: volume A : surface area γ : surface energy r : radius of solid Lv : latent heat ∆T : undercooling

m

v

Sv

Lvv

TTL

GGG∆

=

−=∆

TLTr

v

mSL

∆

=

12* γ22

23*

)(1

316

TLTG

v

mSL

∆

=∆

πγ


2.3 Errors in Use of Thermometers

Thermometer indicates the temperature of a system.

In many cases, perfect measurement is not possible. No thermal equilibrium between thermometer and system Insertion of thermometer disturbs the equilibrium.

Possible and common errors Immersion errors Heat capacity errors Settling response errors Lag errors with steadily changing temperature Radiation errors


A. Immersion errors

Thermometer stem, sheath and lead wires are acting as path for a continuous heat flow.

Heat absorbed by thermometer Heat lost from thermometer

Temperature profile along thermometer stem

A simple model for error

)exp()(eff

sysambm DLKTTT −

−=∆

• Tsys : Temperature of system • Tamb : Temperature of ambient • L : depth of immersion of sensor • Deff: effective diameter of thermometer • K : constant (~ 1)


Relative immersion error

For 1 % accuracy to 5 diameters + sensor

length For 0.01 % accuracy

to 10 diameters + sensor length

For 0.0001 % accuracy, to 15 diameters + sensor

length Highest level using fixed-

point measurement

Immersion (diameter)

For K = 1

Rel

ativ

e te

mpe

ratu

re e

rror

(%)


B. Heat capacity errors

If a thermometer is immersed into system, the temperature of system should be changed to lower or higher temperature.

This is due to heat flow to (from) thermometer from (to) system. In adiabatic condition (there is no heat flow !),

)( sTT

CCCTT ini

ts

tsmeasured −

++=

system

Ts, Cs

Tini, Ct

Tmeasured

equilibrium

• Tmeasured : Measured temperature • Ts : Temperature of system • Tini : Initial temperature of thermometer • Cs, Ct : heat capacity of system and thermometer


C. Settling response error

In practical cases, for control system, it will take time to replace heat change of thermometer.

If insufficient time is allowed, error due to response will occur.

Time

Tem

pera

ture

1/e

−−=∆

0s exp)(

ττTTT inim

• ∆Tm : temperature error • Ts : Initial temperature of system • Tini : Initial temperature of thermometer • τ : time • τ0 : 1/e time constant


Relative error

For 1 % accuracy industrial Wait 5 τ0

For 0.01 % accuracy laboratory Wait 10 τ0

For 0.0001 % accuracy, Standard lab Wait 15 τ0

Time (units of τ0)

Perc

enta

ge re

lativ

e te

mpe

ratu

re e

rror


Part II. Thermocouple Thermometry

1. Thermoelectric Effects

2. Type and Features of Thermocouples

3. Measurement Systems

4. Errors and Usage

5. Calibration and Uncertainty


1. Thermoelectric Effects Seebeck effect

Temperature difference ⇒ Electric power Peltier effect

Electric power ⇒ Temperature difference Thomson effect

Combine of above two effects


1.1 Seebeck effects

In 1821, T.J.Seebeck found

Hot Cold current

A

B

A and B are two different metallic wires.


Basic principle

For a single conductor under the temperature gradient Th side is in higher thermal energy state than Tc. So, electrons in Th side move toward Tc side. Then, number of electrons in Tc side is larger than those in Th

side. It means a non-equilibrium state. Finally, there is a driving force for the movement of electrons

in Tc side toward Th side. This is the thermoelectric voltage, in other words, Seebeck

voltage.

Th Tc


Temperature coefficient

Seebeck coefficient, S (voltage per oC) E depends on the material and temperature gradient.

Th Tc E

tES

t ∆=

=∆ 0lim


For a specific material Temperature is an intrinsic property, so it is continuous.

Th Tc E

∫= dttSE )(


Thermocouple itself is….batteries !

A series of batteries which is operated using temperature gradient.

Tem

pera

ture

Position


Circuit analysis

Two different conducting wires Single conductor can not be used as a thermocouple.

STdtSS

dtSdtS

EEE

T

TBA

T

TB

T

TA

BAnet

∆⋅∆=−=

+=

+=

∫

∫∫1

0

0

1

1

0

)(

T1 T0 Enet

EA

EB


Same wires are connected to the circuit.

STdtSS

dtSdtSdtSdtS

EEEEE

T

TBA

T

TC

T

TB

T

TA

T

TC

CBACnet

∆⋅∆=−=

+++=

+++=

∫

∫∫∫∫2

1

0

1

1

2

2

1

1

0

)(

If T1 = zero ?

T2 T0 Enet

EA

EB

T1

EC

EC


Some part is damaged.

∫∫∫

∫∫∫∫∫∫

−+−+−=

+++++=

++=

3

2

2

1

1

0

0

1

1

2

2

3

3

2

2

1

1

0

)()()( '

'

'

T

TBA

T

TBA

T

TBA

T

TB

T

TB

T

TB

T

TA

T

TA

T

TA

BAAnet

dtSSdtSSdtSS

dtSdtSdtSdtSdtSdtS

EEEE

If T1 = T2 ?

EB

T3 T0 Enet

EA

T1

EA’

T2

Let SA’ = SA + ∆S

∫∫

∫∫∫

∆+−=

−+−∆++−=

2

1

3

0

3

2

2

1

1

0

)()(

)()()(

T

TAB

T

TBA

T

TBA

T

TBABA

T

TBAnet

dtSdtSS

dtSSdtSSSdtSSE


Ideal vs Practical

For ideal and homogeneous wires E only depends on the temperature gradient and Seebeck

coefficients.

For practical thermocouples E = f(t, S, x)

t : temperature S : Seebeck coefficient x : position

Due to the thermoelectric inhomogeneity Epractical = Ehomo + Einhomo


Thermoelectric inhomogeneity

Caused from the factors affecting the Fermi energy level of material Composition change

Oxidation or evaporation

Structural change

Defects

Plastic or Elastic deformation

Produced in the local area

No temperature gradient, No effects !


Calibration uncertainty by KRISS, Type S

Type S

TC

0 2 4 6 8 10 12 14 16 18 20 22

Unc

ertIa

inty

/o C

0.1

0.2

0.3

0.4

0.5

0.6Ref TCOther factorsInhomogeneityCombined


Calibration uncertainty by KRISS, Type R

Type R

TC

0 1 2 3 4

Unc

erta

inty

/o C

0.0

0.1

0.2

0.3

0.4

0.5

0.6

Ref TCInhomogeneityOther factorsCombined


Type B

TC

0 1 2 3

Unc

erta

inty

/o C

0

1

2

3

4

5

6Ref TCInhomogeneityOther factorsCombined

Calibration uncertainty by KRISS, Type S


Change of inhomogeneity with temperature

Type S / R t/c

Little dependence on temperature

within ± 0.01 %

2002 Temperature Symposium by M. Ballico

Possible to estimate inhomogeneity at whole

temperature range.


KRISS Inhomogeneity Test System

Vertical Liquid bath Operation temperature : 180

oC ~ 200 oC Maximum immersion depth of

43 cm Stepping motor driven by

computer Bath temperature is monitored

by F250 thermometer. Emf is measured using

Keithley 2000 DMM. Ice point as reference

temperature TCs are protected using quartz

tubes.

Motor

TCs

Bath

DMM

Thermometer

Motor controller

Control PC

Ice bath


Example 1, Type S thermocouple Type S

Immersion depth /mm

0 100 200 300 400 500

Emf d

iffer

ence

(Em -

E 180

o C) /

µV

-140

-120

-100

-80

-60

-40

-20

0

0 100 200 300 400-10

-8

-6

-4

-2

0

∆E = 1.8 µV

%159.0

%1006.1423.1273

8.1

%100 ityInhomogeneC25C180 oo

=

×−

=

×−

∆=

EEE

Uncertainty at 1100 oC due to inhomogeneity (Rectangular distribution)

C0.42μV94.4

32/)5.1075600159.0(

o=

=

×=


Type B

Immersion depth /mm

0 100 200 300 400 500

Emf d

iffer

ence

(Em -

E 180

o C) /

µV

-14

-12

-10

-8

-6

-4

-2

∆E = 2.2 µV

%56.1

%1003.05.140

2.2

%100 ityInhomogeneC25C180 oo

=

×+

=

×−

∆=

EEE

Example 2, Type B thermocouple

C93.3μV5.45

32/)1.100990156.0(

o=

=

×=Uncertainty at 1500 oC due to inhomogeneity

(Rectangular distribution)


Dependency of inhomogeneity in KRISS

Type Combined Uncertainty

/oC Uncertainty from

Inhomogeneity /oC Dependency

B 3.45 2.87 83 %

B 3.91 3.42 86 %

S 0.47 0.44 93 %

S 0.40 0.36 90 %

S 0.49 0.46 93 %

S 0.53 0.50 94 %


2. Type and Features of thermocouples Letter-designated Noble metal thermocouples Base metal thermocouples

Non letter-designated Pure metal thermocouples W/Re thermocouples Others


2.1 Thermocouple Types

Temperature (oC)

-250 0 250 500 750 1000 1250 1500 1750 2000

EMF

(mV)

-20

0

20

40

60

80

100

E

J

T

KN

RS B

Temperature vs. Emf relation of commercial thermocouples


2.2 Features of Thermocouples

Type Composition

Properties + -

S R B

Pt90Rh10

Pt87Rh13

Pt70Rh30

Pt Pt Pt94Rh6

Most stable in air. S and R can be used to 1450 oC, B is to 1700 oC. Very sensitive to the metallic impurities. Should not be used in vacuum without protecting tube.

K Ni90Cr10

(Chromel) Ni95(Mn,Al,Si)5

(Alumel)

Most well-known thermocouple. In air or inert atmosphere. Severe degradation at high temperature

N Ni84.5Cr14.2Si1.3

(Nicrosil) Ni95.5(Si,Mg)4.5

(Nisil)

Alternative to the type K Enhance the high temperature stability Newest developed one

T J E

Cu Fe Ni90Cr10

Cu55Ni45

(Constantan)

T is usually used in low temperature range, below 0 oC. J and E are rarely used.


Non Letter-designated

Type Composition

Properties + -

Au/Pt Pt/Pd Au/Pd

Au Pt Au

Pt Pd Pd

Very high purity wires (5N up) Strong resistance to the composition change Most stable and accurate thermocouples

W3Re/W25Re W97Re3 W75Re25 Up to 2300 oC Specially designed ones for very high temperature. Only for inert, vacuum or hydrogen atmosphere W5Re/W26Re W95Re5 W74Re26

More than several hundreds of thermocouples


3. Measurement Systems

Thermocouple probe Reference junction Insulator and protecting tube Compensating wire

Readout


3.1 Thermocouple Probe

Sheath vs. Unsheathed Quick connector

Reference thermocouple


Color codes


3.2 Reference junction

Silicon oil

J Cold junction

Stability of ± 5 mK


3.3 Protecting tube

Temperature

Strength

Surrounding atmosphere

Material composition of protecting tube

Chemical composition of environment

For base metal TCs, metallic tube

For noble metal TCs, ceramic tube


Some insulators


3.4 Compensating wire

Economic point of view For noble metal thermocouples

Composition Type

+ - Temperature error

B S, R

K J E T N

Copper Copper Chromel Iron Chromel Copper Nicrosil

Copper Copper Alloy Alumel Constantan Constantan Constantan Nisil

0 ~100 0 ~ 200 0 ~ 200 0 ~ 200 0 ~ 200

-60 ~ 100 0 ~ 200

0 ± 5.0 ± 2.2 ± 2.2 ± 1.7 ± 1.0 ± 2.2


3.5 Readouts

Digital volt(multi)meters (0.1 µV resolution) Digital indicators (with internal reference

Junction)


4. Errors and Usage

Error tree of thermocouple


4.1 Composition change at high temperature

•Type S, 1400 oC, 1440 h

•SEM image

Negative : 95% Pt + 5% Rh

(originally 100 % Pt)

Negative leg

Positive leg


4.2 Thermocouples in different atmosphere

Type Gas Time /h Temperature change Result

Argon 10,000 - 19 ~ -28 K Completed Vacuum 1,610 - 1.5 K Failed R

Air 10,000 - 4.9 K Completed Argon 10,000 - 7 ~ - 18 K Completed

B Vacuum 2,780 - 3.2 K Failed

Test temperature: 1600 K


4.3 Effects of microstructual change of type K

•Chromel : Short-range ordering of Cr between 200 oC ~ 600 oC

•Increase of emf due to short-range ordering

Chromel

Alumel

Net emf


4.4 Effects of protecting materials

•Thermocouples in various protecting tubes at about 1000 oC

•Type S in Pt10Rh, Pt20Rh, Inconel, S.steel

•Type B in Inconel and S.steel


4.5 Annealing treatments

•Standard annealing -1450 oC, 1 h -1100 oC, 10 h

•Emfannealed-Emfas-received

• ~ 2 oC difference

Temperature /oC0 200 400 600 800 1000 1200

Tem

p. D

iff /K

0

1

2

3


4.6 Inhomogeneity of type K and N 1/4", IN Sheath, Type K, Grounded junction

Immersion depth /mm

0 100 200 300 400 500

Tem

pera

ture

/o C

130

140

150

160

170

180

190

1000 h600 h300 hAs-received

48 oC

1/4", IN Sheath, Type N, Grounded junction

Immersion depth /mm

0 100 200 300 400 500

Tem

pera

ture

/o C

172

174

176

178

180

182

1000 h600 h300 hAs-received

• 1000 oC annealing treatment with time • Type K: inhomogeneous temperature variation of about 48 oC • Type N: very small change ( ~ 1 oC)


5. Calibration and Uncertainty

Calibration method Procedures of comparison calibration Uncertainty of calibration


5.1 Calibration method

Fixed-point method At the defining fixed-points by ITS-90

Comparison method Compare with the standard (reference)


5.1.1 Fixed-point method

Most accurate method

Pd

TC wire

PtPd thermocouple at Cu Point (1084.62 oC)

Time /h.min 15:40 16:00 16:20 16:40

Emf /

µV

13242

13243

13244

13245

13246

13247

Standard deviation: ± 0.02 µV (=1 mK)

0.05 oC

Freezing cell Typical freezing curve


Calibration uncertainty of thermocouple

Temperature/oC Expanded uncertainty (k=2)

Au/Pt Pt/Pd S, R, B

231.928 (Sn) 0.02 oC 0.03 oC 0.04 oC

419.527 (Zn) 0.02 oC 0.03 oC 0.05 oC

660.323 (Al) 0.03 oC 0.03 oC 0.06 oC

961.78 (Ag) 0.03 oC 0.04 oC 0.08 oC

1084.62 (Cu) - 0.05 oC 0.09 oC

1154 (Fe/C) - 0.15 oC 0.2 oC

1324 (Co/C) - 0.65 oC 0.65 oC

1554.8 (Pd) - - 0.8 oC


Most common method Compare with Reference thermometer in

furnace or liquid-bath PRT s Thermocouples Liquid-in glass thermometers Bi-metal etc.

5.1.2 Comparison calibration


Calibration uncertainty by comparison calibration

Sensors Temperature range Expanded uncertainty (k=2)

S, R, B 0 oC ~ 1100 oC 0.2 oC

1100 oC ~ 1554 oC 2.0 oC

IPRT

-80 oC ~ 0 oC 16 mK

0 oC ~ 250 oC 16 mK

250 oC ~ 550 oC 20 mK


Type of calibration

Single point At a specific temperature

Temperature vs. temperature (or emf)

Multiple points Point to point calculation

Make a result at each calibration temperature Continuous calculation

Make a result with finite temperature interval Normally, interpolation used Above the maximum point, extrapolation applied

It is very general to calculate the deviation emf. It is used to minimize the interpolation error. Deviation emf = Measured emf – Standard emf Standard emf is from the reference table (ASTM E230, IEC 584-1)


5.2 Procedures of comparison calibration

Inspect the test item

Place the reference standard and test item into the temperature enclosure

Set the temperature enclosure to specified temperature

Confirm the temperature stable

Read the indications from reference and test item

Repeat


• Step 1 : Visual inspection


• Step 2 : Dismentle


• Step 3 : Cleaning


• Step 4 : First heat treatment


• Step 5 : Wire insertion


• Step 6 : Re-assemble


• Step 7 : Making hot junction


• Step 8 : Second heat treatment


• Step 9 : Ice point preparation


• Step 10 : Installing pyrex tubes for ice point


Weld the hot junctions Or, use the temperature

equalizing block made of Pt Install at the uniform

temperature zone

Welding

Pt block

Installation of thermocouples


From low to high temperature Measure if temperature change is below (0.05 ~ 0.1)

oC/min Repeat 10 times at each point About interval of 100 oC ~ 200 oC is suitable.

Measurement procedures


∆E = (Ex – Es)+ ∆Efit

∆E : deviation emf Ex : DUT emf Er : standard emf ∆Efit :interpolation fit

correction

Example of interpolation fit of the deviation emf

Plot the deviation emf with temperature

Temperature /oC

200 400 600 800 1000 1200

Dev

iatio

n E

mf /

µV

0

2

4

6

8

10

12

∆Ei = Ex - Er

∆Efit

∆E(=a0+a1t+a2t2+a3t3)


E’ = E + ∆E

= (c0 + c1t + ….+ c8t8) + a0+a1t+a2t2+a3t3

= ( c0+a0) + (c1+a1)t + (c2+a2)t2 + (c3+a3)t3

+ c4t4 + …. + c8t8

Making a new reference function


5.3 Uncertainty of calibration

Comparison with reference thermocouple Normally Pt/Rh-based noble thermocouples are

used as reference thermometer. Au/Pt or Pt/Pd can be used as higher grade

standards.


5.3.1 Measurement equation

Ed = (Ex – Es) + ∆Efit (1)

Ed : Deviation emf /µV Ex : Measured emf of DUT /µV Es : Standard emf of DUT /µV ∆Efit : Correction due to interpolation /µV


Measured emf of DUT

Ex = Em,x + ∆Eex + ∆Ert,x (2)

Em,x : Read emf of DUT ∆Eex : Correction due to compensation(extension) wire ∆Ert,x : Correction due to room temperature

compensation


Standard emf of DUT

Es = f(tr) (3)

tr = g(Em,r + ∆Ert,r) (4)

tr : Reference temperature from the certificate of reference thermocouple /oC

f(tr) : Standard emf from the IEC table Em,r : Measured emf of reference thermocouple ∆Ert,r : Correction due to room temperature compensation


Combined Standard Uncertainty

(5)

(6)

(7)

(8)

α : Coefficient of voltage with temperature, µV/oC β : Reverse of α, oC/µV

)()()()( 222fitsxdc EuEuEuEu ∆++=

)()()()( ,22

,2

xrtexxmx EuEuEuEu ∆+∆+=

)()()( 222rs tufuEu α+=

)()()()( ,22

,222

rrtrmr EuEugutu ∆++= ββ


5.3.2 Example of Comparison

Reference(REF): type R, DUT: type S Calibration at 8 points (230 oC, 500 oC, 600 oC, 700 oC, 800 oC, 890 oC, 980

oC, 1060 oC) 10 measurements at each point Calibration uncertainty and long term stability of REF are 0.4 oC (k =2) and ±

0.1 oC. Calibration uncertainty and long term stability of DVM(Res. 0.1 µV) are 10

µV/V (k = 2) and ± 20 µV/V. The accuracy of selector switch is ± 0.5 µV, and extension wires are not used. Two thermocouples are welded at their measuring junction. The stability of ice point (water and ice mixture) is ± 0.05 oC. The inhomogeneity of DUT at 180 oC is ± 0.078 %. The maximum deviation of interpolation is 0.15 µV. The combined standard uncertainties are calculated at each point. In this case, we calculate the uncertainty at 1060 oC.


Results of calibration

Cal. point (℃)

Reference thermocouple DUT Standard emf from IEC table

/㎶

Deviation emf /㎶ Average

/㎶ Temperature

/℃

Standard deviation

/㎶

Average /㎶

Standard deviation

/㎶

230 1 887.30 246.25 0.21 1 840.62 0.18 1839.26 1.36

500 4 465.73 499.37 0.23 4 230.18 0.27 4225.86 4.32

600 5 578.02 599.26 0.31 5 235.63 0.39 5229.98 5.65

700 6 745.01 699.80 0.24 6 279.13 0.24 6271.93 7.20

800 7 955.13 799.91 0.35 7 351.66 0.36 7342.8 8.86

890 9 217.93 900.40 0.42 8 462.70 0.40 8452.49 10.21

980 10 258.31 980.54 0.46 9 372.94 0.45 9361.89 11.05

1 060 11 328.53 1 060.84 0.58 10 304.97 0.69 10293.77 11.20


5.3.3 Standard uncertainty of DUT, u(Ex)

Standard uncertainty of emf measurement, u(Em,x)

u(EVD,x): Resolution of DVM u(EVC,x): Calibration uncertainty of DVM u(EVL,x): Long-term stability of DVM u(ERe,x): Repeatability of measurement u(ESC,x): Accuracy of selector switch u(EEN,x): Electrical noise u(EIH): Inhomogeneity of DUT u(thj): Tip temperature difference due to temperature gradient

)()()()(

)()()()()(222

,2

,2

Re,2

,2

,2

,2

,2

hjIHxENxSC

xxVLxVCxVDxm

tuEuEuEu

EuEuEuEuEu

α++++

+++=


Standard uncertainty of compensation wire, u(∆Eex) In case of using compensating or extension wires Correction through the measurement of

temperature of connecting point/ Or apply the specification Direct measurement : - 2.3 µV ± 0.3 µV u(∆Eex) = 0.15 µV

Using the specification

In this case, it is not used.

35)( CEu

o

ex ×=∆ α


Standard uncertainty of room temperature compensation, u(∆Ert,x)

Factor due to the change of reference point

Usually, use the ice temperature (0 oC)

Apply the rectangular distribution

In this case, it is ± 0.05 oC.

C

CEu

o

o

xrt

029.03

05.0)( ,

=

=∆V

CVCyu ooi

µµ

16.0/40.5029.0)(

=×=

Apply the sensitivity coefficient of type S at 0 oC


5.3.4 Standard uncertainty of REF, u(Es)

Standard uncertainty of IEC table, u(f) Internationally approved value, so it is zero.

Uncertainty reference temperature, u(tr) From the calibration certificate of reference

thermocouple tr = g(Em,r + ∆Ert,r)


5.3.4.1 Uncertainty of reference temperature, u(g)

Certificate of reference thermocouple

Normal distribution

In this case, it is 0.4 oC (k = 2). Cgu o2.0)( =


5.3.4.2 Uncertainty of reference temperature, u(tr)

Standard uncertainty of emf measurement, u(Em,r)

u(EVD,r): Resolution of DVM u(EVC,r): Calibration uncertainty of DVM u(EVL,r): Long-term stability of DVM u(ERe,r): Repeatability of measurement u(ESC,r): Accuracy of selector switch u(EEN,r): Electrical noise u(tLS): Long-term stability of reference thermocouple

)()()(

)()()()()(22

,2

,2

Re,2

,2

,2

,2

,2

LSrENrSC

rrVLrVCrVDrm

tuEuEu

EuEuEuEuEu

α+++

+++=


Room temperature compensation, u(∆Ert,r)

In this case, it is ± 0.05 oC.

C

Ctu

o

o

hj

029.03

05.0)(

=

=

CCVCVCyu

o

o

oo

i

011.0/48.13/29.5029.0)(

=

×=µµ

Coefficients at ice point and 1060 oC are different each other.

Apply the coefficient of type R thermocouple at each temperature

Note


5.3.5 Interpolation, u(∆Efit)

Uncertainty due to curve fit to get a deviation function Apply the maximum difference between the

measured and fitted value Apply the rectangular distribution

Apply the maximum difference as the half width of distribution

In this case, it is 0.15 µV. VVEu fit µµ 09.0

315.0)( ==∆


5.3.6 Combined Standard Uncertainty – uc(Ed)

V

V

EuEuEuEu fitsxdc

µµ

33.509.056.267.4

)()()()(222

222

=++=

∆++=

VV

EuEuEuEu xrtexxmx

µµ

67.416.00.067.4

)()()()(222

,22

,2

=++=

∆+∆+=

VV

tufuEu rs

µµ

α

56.2218.073.110

)()()(22

222

=×+=

+=

CC

EuEugutu

o

o

rrtrmr

218.0029.0392.001.1074.02.0

)()()()(22222

,22

,222

=

×+×+=

∆++= ββ

Note ! Sensitivity of DUT


5.3.7 Uncertainty budget – u(Ex)

Quantity Xi

Estimated xi

Std. uncertainty

u(xi)

Sensitivity coefficient

ci

Uncertainty ui(y)

Distribution Deg.

Freedom

Ex 10304.97 ㎶ 4.676 ㎶ 1 4.67 ㎶ Normal ∞

Em,x 10304.97 ㎶ 4.67 ㎶ 1 4.67 ㎶ Normal ∞

EVD,x - 0.03 ㎶ 1 0.03 ㎶ Rectang. ∞

EVC,x - 0.05 ㎶ 1 0.05 ㎶ Normal ∞

EVL,x - 0.12 ㎶ 1 0.12 ㎶ Rectang. ∞

ERe,x - 0.22 ㎶ 1 0.22 ㎶ Normal 9

ESC,x - 0.58 ㎶ 1 0.58 ㎶ Rectang. ∞

EEN,x - 0.58 ㎶ 1 0.58 ㎶ Rectang. ∞

EIH - 4.58 ㎶ 1 4.58 ㎶ Rectang. ∞

thj - 0.058 ℃ 11.73 ㎶/℃ 0.68 ㎶ Rectang. ∞

∆Eex 0 ㎶ 0 ㎶ 1 0 ㎶ Rectang. ∞

∆Ert,x 0 ㎶ 0.029 ℃ 5.40 ㎶/℃ 0.16 ㎶ Rectang. ∞


Uncertainty budget – u(Es), u(∆Efit) Quantity

Xi

Estimated xi

Std. uncertainty

u(xi)

Sensitivity coefficient

ci

Uncertainty ui(y)

Distribution Deg. Freedom

Es 10 293.77 ㎶ 2.56 ㎶ 1 2.56 ㎶ Normal ∞

f(tr) - 0 1 0 - ∞

tr - 0.218 oC 11.73 ㎶/℃ 2.56 ㎶ Normal ∞

g(tr) - 0.2 oC 1 0.2 oC Normal ∞

Em,r - 1.16 ㎶ 0.074 oC/ ㎶ 0.086 oC Normal ∞

EVD,r - 0.03 ㎶ 1 0.03 ㎶ Rectang. ∞

EVC,r - 0.06 ㎶ 1 0.06 ㎶ Normal ∞

EVL,r - 0.13 ㎶ 1 0.13 ㎶ Rectang. ∞

ERe,r - 0.18 ㎶ 1 0.18 ㎶ Normal 9

ESC,r - 0.58 ㎶ 1 0.58 ㎶ Rectang. ∞

EEN,r - 0.58 ㎶ 1 0.58 ㎶ Rectang. ∞

tLS - 0.058 ℃ 13.48 ㎶/℃ 0.78 ㎶ Rectang. ∞

∆Ert,r 0 ㎶ 0.029 ℃ 0.392 0.011 oC Rectang. ∞

∆Efit 0.14 ㎶ 0.09 ㎶ 1 0.09 ㎶ Rectang. ∞


5.3.8 Uncertainty with temperature

Calibration point /℃

Combined standard uncertainty /㎶

Expanded uncertainty (k = 2)

/㎶

Expanded uncertainty (k = 2)

/℃

246.25 2.55 5.10 0.58

499.37 3.19 6.38 0.64

599.26 3.51 7.02 0.69

699.80 3.87 7.74 0.73

799.91 4.27 8.54 0.79

900.40 4.70 9.40 0.84

980.54 5.07 10.14 0.88

1 060.84 5.33 10.66 0.91


5.3.9 Report of uncertainty

Choose the maximum uncertainty among the calculated

values

Expanded uncertainty is determined with k = 2.

In this case, U95 = 0.9 oC


Further reading T.D. McGee, “Principles and methods of temperature measurement”,

1988, John Wiley & Sons J.V.Nicholas and D.R.white, “Traceable Temperatures”, 2nd edition,

2001, John Wiley & Sons “Manual on the use of thermocouples in temperature measurement”, 4th

edition, 1993, ASTM

Workshop Thermocouple

Documents

Transcript of Workshop Thermocouple