Instrumentation and control

4Temperature Measurement

Principles of Temperature – ITS-90. . . . . . . . . . . . . . . . . . . . . . . . . . 121

Comparative Characteristics of Thermometers . . . . . . . . . . . . . . . 122

Temperature Differences Between ITS-90, IPTS-68 and EPT-76 . . 123

Temperature Scales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

Temperature Conversion Equations. . . . . . . . . . . . . . . . . . . . . . . . . 125

Steady-State Heat Transfer Analysis . . . . . . . . . . . . . . . . . . . . . . . . 127

Convective Heat Transfer Coefficients . . . . . . . . . . . . . . . . . . . . . . . 127

°F to °C Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

Temperature Conversion Table. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

°F to Kelvin Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

°C to °F Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

Thermocouples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

Thermocouple Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

Type E – Thermoelectric Voltage in mV. . . . . . . . . . . . . . . . . . . . 139

Type J – Thermoelectric Voltage in mV. . . . . . . . . . . . . . . . . . . . 141

Type K – Thermoelectric Voltage in mV. . . . . . . . . . . . . . . . . . . . 143

Type T – Thermoelectric Voltage in mV. . . . . . . . . . . . . . . . . . . . 145

Limits of Error for Thermocouples. . . . . . . . . . . . . . . . . . . . . . . . 147

Upper Temperature Limits for Protected Thermocouples . . . . . 147

RTDs (Resistive Temperature Detectors) . . . . . . . . . . . . . . . . . . . . . 147

RTD Material Resistivity Levels . . . . . . . . . . . . . . . . . . . . . . . . . . 148

Resistance Versus Temperature for Platinum . . . . . . . . . . . . . . . 149

new chap 4 temp.qxd 3/2/2006 8:56 AM Page 119

Wheatstone Bridge – Effect of Bridge Nonlinearities . . . . . . . . . . . 154

Wheatstone Bridge – 3-wire Measurement . . . . . . . . . . . . . . . . . . . 154

Thermistor Temperature-Resistance Relationship . . . . . . . . . . . . . 154

Resistance Tolerance Percent for Thermistors . . . . . . . . . . . . . . . . 155

Thermistor Voltage Drop Across a Wheatstone Bridge . . . . . . . . . 155

Stem Correction for a Total Immersion Thermometer . . . . . . . . . . . 155

Vapor Pressure Thermometers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156

Radiation Pyrometers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156

Planck’s Radiation Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156

Wien’s Radiation Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

Stefan-Boltzmann Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

Wien’s Displacement Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

Total Emissivities of Metals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

Total Radiation Pyrometer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160

Brightness Pyrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160

Johnson Noise Thermometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160

120 ISA Handbook of Measurement Equations and Tables


Principles of Temperature –ITS-90

Shortly after adoption of the Inter-national Practical TemperatureScale of 1968 (IPTS-68), it was real-ized the scale had many deficien-cies and limitations. Consequently,the Comité Consultatif de Ther-mométrie (CCT) – one of eight spe-cialized technical subcommittees ofthe Comité International des Poidset Mesures (CIPM) – undertook thedevelopment of a new scale. On 26-28 September 1989, the CCT recom-mended ITS-90 be adopted. Follow-ing approval by CIPM, ITS-90became the official internationaltemperature scale on 1 January1990, when it also was imple-mented at the U.S. National Insti-tute of Standards and Technology(NIST).

According to a detailed report byB.W. Mangum, of NIST’s Center forChemical Technology, NationalMeasurement Laboratory, andNIST guest scientist G.T. Furukawa,ITS-90 – when compared to IPTS-68– extends upward from 0.65 K.Also, temperatures on the newerscale are in much better agreementwith thermodynamic values. Inaddition, ITS-90’s continuity, non-uniqueness and reproducibilitythroughout its ranges are muchimproved over previous scales. Themost complete and authoritativedocument on ITS-90 from NIST isTechnical Note 1265 by Mangumand Furukawa. It is available as apdf from NIST’s web site:http://www.cstl.nist.gov/div836/836.05/papers/magnum90ITS90guide.pdf

Temperature Defining Points – IPTS-68 vs. ITS-90

Temperature Defining Point IPTS-68Kelvin ITPS-68°C ITS-90

Kelvin ITS-90°C

Triple Point of Hydrogen 13.81 -259.34 13.8033 -259.3467

Boiling (Vapor Pressure)Point of Hydrogen at 25/75Standard Atmosphere

17.042 -256.108 ~17.0 ~ -256.15

Boiling Point of Hydrogen 20.28 -252.87 ~20.3 ~ -252.85

Boiling Point of Neon 27.102 -246.048 — —

Triple Point of Neon — — 24.5561 -248.5939

Triple Point of Oxygen 54.361 -218.789 54.3584 -218.7916

Boiling Point of Oxygen 90.188 -182.962 — —

Triple Point of Water 273.16 0.01 273.16 0.01

Boiling Point of Water 373.15 100.00 — —

Freezing Point of Zinc 692.73 419.58 692.677 419.527

Freezing Point of Silver 1235.08 961.93 1234.93 961.78

Freezing Point of Gold 1337.58 1064.43 1337.77 1064.18

Chapter 4/Temperature 121


Comparative Characteristics of Thermometers

Thermometer Range°C

Resolution°C

Accuracy ofAbsolute, %

Drift in 20 khr, %

Thermocouples,Sheathed

0-250 >0.1 0.3-0.8 1.3@650°C

Sheathed type K (C/A) 250-850 >0.1 1-1.5

Sheathed type S(Pt-Rh) 0-1600 >0.1 0.1 1.7@1300°C

Platinum ResistanceThermometers

Industrial -200 to650 0.01 0.5-0.1 0.02@ 650°C

Standard -183 to631 <0.01 0.0001-0.003 0.02@

1063°C

Thermistors -200 to600 0.0005 0.03-1 0.02-0.03

Mercury-in-Glass -38 to400 0.01 0.002-0.25 0.05

Optical Pyrometer 700-3000 0.20 0.10 0

Johnson Noise Thermometer

-272 to1500

0.10 0.01-1.30 0

Transistor AbsoluteThermometer

-200 to123

0.04 0.50

Nuclear QuadrupoleResonance Thermometer

-183 to125

0.0002 0.0004 <0.01@100°C

Ultrasonic Pulse EchoThermometer

0-2000 1-2 1

Fluidic Thermometers 0-1200 0.00001 105

Quartz Crystal Thermometer

-40 to230

0.0001 <0.005 0.003@ 100°C

Eddy Current Thermometer (sodium)

150-600 0.05 1-10

Microwave Resonator 1370 0.05 1



Differences Between ITS-90, IPTS-68 and EPT-76

where

ITS or

or

E

-90 = T t

IPTS-68 = T t

PT-76 = T

90 90

68 68

76

(T90 – T68)/K

T90/K 0 1 2 3 4 5 6 7 8 9

10 -0.006 -0.003 -0.004 -0.006 -0.008 -0.008

20 -0.009 -0.008 -0.007 -0.007 -0.006 -0.005 -0.004 -0.004 -0.005 -0.006

30 -0.006 -0.007 -0.008 -0.008 -0.008 -0.007 -0.007 -0.007 -0.006 -0.006

40 -0.006 -0.006 -0.006 -0.006 -0.006 -0.007 -0.007 -0.007 -0.006 -0.006

50 -0.006 -0.005 -0.005 -0.004 -0.003 -0.002 -0.001 0.000 0.001 0.002

60 0.003 0.003 0.004 0.004 0.005 0.005 0.006 0.006 0.007 0.007

70 0.007 0.007 0.007 0.007 0.007 0.008 0.008 0.008 0.008 0.008

80 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008

90 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.009 0.009 0.009

T90/K 0 10 20 30 40 50 60 70 80 90

100 0.009 0.011 0.013 0.014 0.014 0.014 0.014 0.013 0.012 0.012

200 0.011 0.010 0.009 0.008 0.007 0.005 0.003 0.001

(T90 – T76)/mK

T90/K 0 1 2 3 4 5 6 7 8 9

0 -0.1 -0.2 -0.3 -0.4 -0.5

10 -0.6 -0.7 -0.8 -1.0 -1.1 -1.3 -1.4 -1.5 -1.8 -2.0

20 -2.2 -2.5 -2.7 -3.0 -3.2 -3.5 -3.8 -4.1



(T90 – T68)/°C

T90/°C 0 -10 -20 -30 -40 -50 -60 -70 -80 -90

-100 0.013 0.013 0.014 0.014 0.014 0.013 0.012 0.010 0.008 0.008

0 0.000 0.002 0.004 0.006 0.008 0.009 0.010 0.011 0.012 0.012

T90/°C 0 10 20 30 40 50 60 70 80 90

0 0.000 -0.002 -0.005 -0.007 -0.010 -0.013 -0.016 -0.018 -0.021 -0.024

100 -0.026 -0.028 -0.030 -0.032 -0.034 -0.036 -0.037 -0.038 -0.039 -0.039

200 -0.040 -0.040 -0.040 -0.040 -0.040 -0.040 -0.040 -0.039 -0.039 -0.039

300 -0.039 -0.039 -0.039 -0.040 -0.040 -0.041 -0.042 -0.043 -0.045 -0.046

400 -0.048 -0.051 -0.053 -0.056 -0.059 -0.062 -0.065 -0.068 -0.072 -0.075

500 -0.079 -0.083 -0.087 -0.090 -0.094 -0.098 -0.101 -0.105 -0.108 -0.112

600 -0.115 -0.118 -0.122 -0.125 -0.08 -0.03 0.02 0.06 0.11 0.16

700 0.20 0.24 0.28 0.31 0.33 0.35 0.36 0.36 0.36 0.35

800 0.34 0.32 0.29 0.25 0.22 0.18 0.14 0.10 0.06 0.03

900 -0.01 -0.03 -0.06 -0.08 -0.10 -0.12 -0.14 -0.16 -0.17 -0.18

1000 -0.19 -0.20 -0.21 -0.22 -0.23 -0.24 -0.25 -0.25 -0.26 -0.26

T90/°C 0 100 200 300 400 500 600 700 800 900

1000 -0.26 -0.30 -0.35 -0.39 -0.44 -0.49 -0.54 -0.60 -0.66

2000 -0.72 -0.79 -0.85 -0.93 -1.00 -1.07 -1.15 -1.24 -1.32 -1.41

3000 -1.50 -1.59 -1.69 -1.78 -1.89 -1.99 -2.10 -2.21 -2.32 -2.43



Temperature ConversionEquations

°Celsius to °FahrenheitDegree F = (Degree C x 1.8) + 32

°Celsius to °RankineDegree R = (Degree C + 273.15) x1.8

°Celsius to KelvinKelvin = Degree C + 273.15

°Fahrenheit to °Celsius

°Fahrenheit to °RankineDegree R = Degree F + 459.67

°Fahrenheit to Kelvin

°Rankine to °FahrenheitDegree F = Degree R - 459.67

Degree C = Degree F - 32

1.8273.1+

Degree C = Degree F - 32

1.8


17

80100

21

-40

0273 0

˚C = ˚F460

7032

-400

212

500 960 533 260 208

˚Rea

˚F ˚R K ˚C

1000 538

1340 1800 1000 727

˚F = 2(˚C)Approx.

Water Boils

Room Temp

Water Freezes

Absolute Zero

Temperature-460 -273 -2180 0

Fahrenheit Rankin Kelvin Celsius Reaumur

Relation of Temperature Scales


°Rankine to Kelvin

Kelvin to °CelsiusDegree C = Kelvin - 273.15

Kelvin to °Rankine Degree R = Kelvin x 1.8

Interpolation Values

To interpolate for accurate temper-atures between the various incre-mental changes in the followingtemperature conversion tables, theinterpolation table below providesthe values to add to the conversiontable values. Note that these valuesare to four decimal places. To usethese add-on values correctly, cal-culate the add-on value, and thenround to two decimal places.

KelvinDegree R

=1 8.

°Fahrenheit Add to °Celsius

1 0.5556

2 1.1111

3 1.6667

4 2.2222

5 2.7778

6 3.3334

7 3.8889

8 4.4445

9 5.0000

10 5.5556

20 11.1112

30 16.6668

40 22.2224

50 27.7780

60 33.3336

70 38.8892

80 44.4448

90 50.0004



Steady-State Heat TransferAnalysis

The performance of temperaturesensors can depend on all themodes of heat transfer – conduc-tion, convection, and radiation.

The steady-state heat conductionequation is:

where∇ = geometry-dependent differential operatork = thermal conductivity

For constant thermal conductivity,the conduction equation is:

The differential operators for threegeometries are:

x,y,z (Cartesian)

r,z, θ (cylindrical)

r, θ, φ (spherical)

In many applications, heat transferalong all the coordinate axes is notsignificant. In these cases the equa-tions are:

Cartesian (one-dimensional)

Cylinder (r only)

Cylinder (r,z)

Sphere (r only)

Convective Heat TransferCoefficients

Dimensionless Quantities for

Sensors of Single Cylinders or

Spheres

Nusselt number (Nu) =

Reynolds number (Re) =

Prandtl number (Pr) =

∇ =∂∂

∂∂

=∂∂

+∂∂

22

2

2

2

1

2

Tr r

rTr

T

r rTr

∂∂

+∂∂

+∂∂

=2

2

2

21

0T

r rTr

T

z

∂∂

+∂∂

=2

21

0T

r rTr

∂∂

=2

2 0T

x

∇ =∂∂

∂∂

+

∂∂

∂∂

+

∂

22

2

2

2 2

2

1

1

1

Tr r

rTr

r

T

r

sinsin

sin

θ θθ

θ

θTT

∂φ2

∇ =∂∂

+∂∂

+∂∂

+∂∂

22

2 2

2

2

2

21 1

TT

r rTr r

T T

zθ

∇ =∂∂

+∂∂

+∂∂

22

2

2

2

2

2TT

x

T

y

T

z

∇ =2 0T

∇ ⋅ =kVT 0


hDk

Duρµ

ckµ


whereh = film heat transfer coefficientD = diameter of sensork = thermal conductivity of fluidρ = fluid densityu = fluid velocityµ = fluid viscosityc = fluid specific heat capacity

General Form of the Correlations

wherea = experimental data

Nonmetals Flowing Normal to aSingle Cylinder

Nu = (0.35 + 0.47 Re0.52) Pr0.3

for 0.1 <Re <1000

Nu = 0.26 Re0.6 Pr0.3

for 1000 < Re <50,000

Nonmetals Flowing Across aSingle Sphere

Nu = 2.0 + 0.60 Re1/2 Pr1/2

Metals Flowing Normal to aSingle Cylinder

Nu = 0.8 Re0.5 Pr0.5

Metals Flowing Across a Single Sphere

Nu = 2.0 + 0.386 Re0.5 Pr0.5

Nu a a a a= +1 23 4Re Pr



Conversion Tables, °F to °C

°F °C °F °C °F °C

-500 -295.556 0 -17.778 70 21.111

-480 -284.444 1 -17.222 80 26.667

-460 -273.333 2 -16.667 90 32.222

-440 -262.222 3 -16.111 100 37.778

-420 -251.111 4 -15.556 110 43.333

-400 -240.000 5 -15.000 120 48.889

-380 -228.889 6 -14.444 130 54.444

-360 -217.778 7 -13.889 140 60.000

-340 -206.667 8 -13.333 150 65.556

-320 -195.556 9 -12.778 160 71.111

-300 -184.444 10 -12.222 170 76.667

-280 -173.333 11 -11.667 180 82.222

-260 -162.222 12 -11.111 190 87.778

-240 -151.111 13 -10.556 200 93.333

-220 -140.000 14 -10.000 210 98.889

-200 -128.889 15 -9.444 220 104.444

-180 -117.778 16 -8.889 230 110.000

-160 -106.667 17 -8.333 240 115.556

-140 -95.556 18 -7.778 250 121.111

-120 -84.444 19 -7.222 260 126.667

-100 -73.333 20 -6.667 270 132.222

-80 -62.222 30 -1.111 280 137.778

-60 -51.111 40 4.444 290 143.333

-40 -40.000 50 10.000 300 148.889

-20 -28.889 60 15.556 310 154.444



Conversion Tables, °F to °C (cont.)

°F °C °F °C °F °C

320 160.000 570 298.889 900 482.222

330 165.556 580 304.444 950 510.000

340 171.111 590 310.000 1000 537.778

350 176.667 600 315.556 1050 565.556

360 182.222 610 321.111 1100 593.333

370 187.778 620 326.667 1150 621.111

380 193.333 630 332.222 1200 648.889

390 198.889 640 337.778 1250 676.667

400 204.444 650 343.333 1300 704.444

410 210.000 660 348.889 1350 732.222

420 215.556 670 354.444 1400 760.000

430 221.111 680 360.000 1450 787.778

440 226.667 690 365.556 1500 815.556

450 232.222 700 371.111 1550 843.333

460 237.778 710 376.667 1600 871.111

470 243.333 720 382.222 1650 898.889

480 248.889 730 387.778 1700 926.667

490 254.444 740 393.333 1750 954.444

500 260.000 750 398.889 1800 982.222

510 265.556 760 404.444 1850 1010.000

520 271.111 770 410.000 1900 1037.778

530 276.667 780 415.556 1950 1065.556

540 282.222 790 421.111 2000 1093.333

550 287.778 800 426.667 2050 1121.111

560 293.333 850 454.444 2100 1148.889



Temperature Conversion Table

To Convert From To Multiply by:

°C heat unit Btu 1.8

°C heat unit Calorie 453.592

°C heat unit Joule 1899.10

°C/hr-kilocalorie °C / watt 0.859845

ft/°F m/°C 0.548640

in/°F mm/°C 45.72

Joule Calorie 0.238846

Joule/°C Btu/°F 0.000526565

kilocalorie Btu 3.968320

kilocalorie Joule 4186.80

liter-bar Joule 100.0

°C-temperature interval °F 1.8

°C-temperature interval °Rankine 1.8

°F-temperature interval °C 0.5555556

°F-temperature interval °Rankine 1.0

°F-temperature interval Kelvin 0.5555556



1

Conversion Tables, °F to Kelvin

°F K °F K °F K

-500 -22.406 0 255.372 70 294.261

-480 -11.294 1 255.928 80 299.817

-460 -0.183 2 256.483 90 305.372

-440 10.928 3 257.039 100 310.928

-420 22.039 4 257.794 110 316.483

-400 33.150 5 258.150 120 322.039

-380 44.261 6 258.706 130 327.594

-360 55.372 7 259.261 140 333.150

-340 66.483 8 259.817 150 338.706

-320 77.594 9 260.372 160 344.261

-300 88.706 10 260.928 170 349.817

-280 99.817 11 261.483 180 355.372

-260 110.928 12 262.039 190 360.928

-240 122.039 13 262.594 200 366.483

-220 133.150 14 263.150 210 372.039

-200 144.261 15 263.706 220 377.594

-180 155.372 16 264.261 230 383.150

-160 166.483 17 264.871 240 388.706

-140 177.594 18 265.372 250 394.261

-120 188.706 19 265.928 260 399.817

-100 199.817 20 266.483 270 405.372

-80 210.928 30 272.039 280 410.928

-60 222.039 40 277.594 290 416.483

-40 233.150 50 283.150 300 422.039

-20 244.261 60 288.706 310 427.594



Conversion Tables, °F to Kelvin (cont.)

°F K °F K °F K

320 433.150 570 572.709 900 755.372

330 438.706 580 577.594 950 783.150

340 444.261 590 583.150 1000 810.928

350 449.817 600 588.706 1050 838.706

360 455.372 610 594.261 1100 866.483

370 460.928 620 599.817 1150 894.261

380 466.483 630 605.372 1200 922.039

390 472.039 640 610.928 1250 949.817

400 477.594 650 616.483 1300 977.594

410 483.150 660 622.039 1350 1005.372

420 488.706 670 627.594 1400 1033.150

430 494.261 680 633.150 1450 1060.928

440 499.817 690 638.706 1500 1088.706

450 505.372 700 644.261 1550 1116.483

460 510.928 710 649.817 1600 1144.261

470 516.483 720 655.372 1650 1172.039

480 522.039 730 660.928 1700 1199.817

490 527.594 740 666.438 1750 1227.594

500 533.150 750 672.039 1800 1255.372

510 538.706 760 677.594 1850 1283.150

520 544.261 770 683.150 1900 1310.928

530 549.817 780 688.706 1950 1338.706

540 555.372 790 694.261 2000 1366.483

550 560.928 800 699.817 2050 1394.261

560 566.483 850 727.594 2100 1422.039



Conversion Tables, °C to °F

°C °F °C °F °C °F

-300 -508.0 -50 -58.0 20 68.0

-290 -490.0 -40 -40.0 25 77.0

-280 -472.0 -30 -22.0 30 86.0

-270 -454.0 -20 -4.0 40 104.0

-260 -436.0 -10 14.0 50 122.0

-250 -418.0 0 32.0 60 140.0

-240 -400.0 1 33.8 70 158.0

-230 -382.0 2 35.6 80 176.0

-220 -364.0 3 37.4 90 194.0

-210 -346.0 4 39.2 100 212.0

-200 -328.0 5 41.0 110 230.0

-190 -310.0 6 42.8 120 248.0

-180 -292.0 7 44.6 130 266.0

-170 -274.0 8 46.4 140 284.0

-160 -256.0 9 48.2 150 302.0

-150 -238.0 10 50.0 160 320.0

-140 -220.0 11 51.8 170 338.0

-130 -202.0 12 53.6 180 356.0

-120 -184.0 13 55.4 190 374.0

-110 -166.0 14 57.2 200 392.0

-100 -148.0 15 59.0 210 410.0

-90 -130.0 16 60.8 220 428.0

-80 -112.0 17 62.6 230 446.0

-70 -94.0 18 64.4 240 464.0

-60 -76.0 19 66.2 250 482.0



Conversion Tables, °C to °F (cont.)

°C °F °C °F °C °F

260 500.0 510 950.0 760 1400.0

270 518.0 520 968.0 770 1418.0

280 536.0 530 986.0 780 1436.0

290 554.0 540 1004.0 790 1454.0

300 572.0 550 1022.0 800 1472.0

310 590.0 560 1040.0 810 1490.0

320 608.0 570 1058.0 820 1508.0

330 626.0 580 1076.0 830 1526.0

340 644.0 590 1094.0 840 1544.0

350 662.0 600 1112.0 850 1562.0

360 680.0 610 1130.0 860 1580.0

370 698.0 620 1148.0 870 1598.0

380 716.0 630 1166.0 880 1616.0

390 734.0 640 1184.0 890 1634.0

400 752.0 650 1202.0 900 1652.0

410 770.0 660 1220.0 910 1670.0

420 788.0 670 1238.0 920 1688.0

430 806.0 680 1256.0 930 1706.0

440 824.0 690 1274.0 940 1724.0

450 842.0 700 1292.0 950 1742.0

460 860.0 710 1310.0 960 1760.0

470 878.0 720 1328.0 970 1778.0

480 896.0 730 1346.0 980 1796.0

490 914.0 740 1364.0 990 1814.0

500 932.0 750 1382.0 1000 1832.0



Thermocouples

The thermocouple is the most pop-ular type of sensor. Thermocouplesare based on the principle that twowires made of dissimilar materialsconnected at either end will gener-ate a potential between the twoends that is a function of the mate-rials and temperature differencebetween the two ends.

A number of material choices are incommon use. Base metal thermo-couples are useful for measuringtemperatures under 1000 degreesC. This class includes iron/constan-tan (Type J), Chromel/Alumel (TypeK) and a number of others. Nobelmetal thermocouples are useful toabout 2000 degrees C. This classincludes tungsten-rhenium alloythermocouples and others.

The potential generated is in milli-volts and is a nonlinear function oftemperature. In practice, one end isplaced near the material to be

measured and the other end is con-nected to the instrument. Since thethermocouple materials are nottypically good materials for trans-mission, wires with similar charac-teristics are used when the trans-mitting instrument is remote.

Thermocouple Types

Thermocouples come in differentcombinations of metals and cali-brations. Types J, K, T and E are thefour most common calibrations.Types R, S, C and GB are high tem-perature calibrations. Each calibra-tion has a different temperaturerange and environment. However,the maximum temperature varieswith the diameter of the wire usedin the thermocouple.

The letter type, e.g., type J, identi-fies a specific temperature-voltagerelationship, not a particular chem-ical composition. Thermocouplesof a given type may have variationsin composition as long as their

Thermocouples

Type Composition Temperature range, °C

B Pt-30% Rh versus Pt-6% Rh 0 to 1820

E Ni-Cr alloy versus a Cu-Ni alloy -270 to 1000

J Fe versus a Cu-Ni alloy -210 to 1200

K Ni-Cr alloy versus Ni-Al alloy -270 to 1372

N Ni-Cr-Si alloy versus Ni-Si-Mg alloy -270 to 1300

R Pt-13% Rh versus Pt -50 to 1768

S Pt-10% Rh versus Pt -50 to 1768

T Cu versus a Cu-Ni alloy -270 to 400


Courtesy: National Institute of Standards and Technology (NIST) ©1995 copyright by the U.S.Secretary of Commerce on behalf of the United States of America. All rights reserved.


resultant temperature-voltage rela-tionships remain within specifiedtolerances. All materials manufac-tured in compliance with the estab-lished thermoelectric voltage stan-dards are equally acceptable.

Thermocouple Circuit Analysis

Thermocouple Circuit Analysis

where:V = open-circuit voltageT1 = Temperature at one end ofwiresT2 = temperature at other end ofwiresSa = absolute Seebeck coefficientfor materialSb = absolute Seebeck coefficientfor materialT = temperature

whereSab = relative Seebeck coefficientfor materials a and b

The Relation Between Temperature Difference andVoltage

where

V = voltageT = temperature

The Basic ThermoelectricVoltage Element

A Simple Thermocouple Circuit

SVT

=∆∆

∆ = −V S T T( )2 1

S S S

S S

S S S

S S S

a b ab

ab ba

ac ab cb

ac ab bc

− == −= −= +

V S S dTTT

a b= −∫ 12 ( )


The Basic Thermoelectric Voltage Element

∆V

T1

ST2

A Simple Thermocouple Circuit

T1

Sa

Sb

T1

T2V


Solutions also require specificationof boundary conditions at inter-faces. Interfaces occur betweenregions containing different materi-als or surfaces. Since notationbecomes cumbersome if all geome-tries are considered, only the com-mon boundary conditions for cylin-drical (r only) geometry are given.

Internal; Continuity of Temperature

Tr- = Tr+

Internal; Continuity of HeatFlux

Internal; Finiteness of Temperature

Surface; Convection

Surface: Fixed Surface Temperature

TR = TF

Surface: Insulated Surface

Surface: Radiation

whereTr- = temperature at r asapproached from the interiorTr+ = temperature at r asapproached from the exteriork = thermal conductivityk1 = thermal conductivity of material interior to the interface at rk2 = thermal conductivity of material exterior to the interface at rR = radius at the surfaceh = film heat transfer coefficientθ = temperature of fluid aroundsensorθR = temperature of mediumexchanging radiative energy withthe sensorTF = fixed temperature specifiedfor surface∈ = emissivityσ = Stefan-Boltzmann constant

−∂∂

=∈ −kTr

TR R Rσ θ( )4 4

∂∂

=Tr R 0

−∂∂

= −kTr

h TR R( )θ

T r( ) ≠ ∞

kTr

kTrr r1 2

∂∂

=∂∂− +



110 6.998

120 7.685

130 8.379

140 9.081

150 9.789

160 10.503

170 11.224

180 11.951

190 12.684

200 13.421

210 14.164

220 14.912

230 15.664

240 16.420

250 17.181

260 17.945

270 18.713

280 19.484

290 20.259

300 21.036

310 21.817

320 22.600

330 23.386

340 24.174

350 24.964

360 25.757

370 26.552

380 27.348

390 28.146

400 28.946

410 29.747

420 30.550

430 31.354

440 32.159

450 32.965

460 33.772

470 34.579

480 35.387

Type E - Thermoelectric Voltage in mV

°C mV270 -9.835-260 -9.797-250 -9.718-240 -9.604-230 -9.455-220 -9.274-210 -9.063-200 -8.825-190 -8.561-180 -8.273-170 -7.963-160 -7.632-150 -7.279-140 -6.907-130 -6.516-120 -6.107-110 -5.681-100 -5.237-90 -4.777-80 -4.302-70 -3.811-60 -3.306-50 -2.787-40 -2.255-30 -1.709-20 -1.152-10 -0.5820 0.000

10 0.59120 1.19230 1.80140 2.42050 3.04860 3.68570 4.33080 4.98590 5.648

100 6.319



860 65.698

870 66.473

880 67.246

890 68.017

900 68.787

910 69.554

920 70.319

930 71.082

940 71.844

950 72.603

960 73.360

970 74.115

980 74.869

990 75.621

1000 76.373

Type E - Thermoelectric Voltage in mV (cont’d.)

°C mV490 36.196500 37.005510 37.815520 38.624530 39.434540 40.243550 41.053560 41.862570 42.671580 43.479590 44.286600 45.093610 45.900620 46.705630 47.509640 48.313650 49.116660 49.917670 50.718680 51.517690 52.315700 53.112710 53.908720 54.703730 55.497740 56.289750 57.080760 57.870770 58.659780 59.446790 60.232800 61.017810 61.801820 62.583830 63.364840 64.144850 64.922



110 5.814

120 6.360

130 6.909

140 7.459

150 8.010

160 8.562

170 9.115

180 9.669

190 10.224

200 10.779

210 11.334

220 11.889

230 12.445

240 13.000

250 13.555

260 14.110

270 14.665

280 15.219

290 15.773

300 16.327

310 16.881

320 17.434

330 17.986

340 18.538

350 19.090

360 19.642

370 20.194

380 20.745

390 21.297

400 21.848

410 22.400

420 22.952

430 23.504

440 24.057

450 24.610

460 25.164

470 25.720

480 26.276

Type J - Thermoelectric Voltage in mV

°C mV

-210 -8.095

-200 -7.890

-190 -7.659

-180 -7.403

-170 -7.123

-160 -6.821

-150 -6.500

-140 -6.159

-130 -5.801

-120 -5.426

-110 -5.037

-100 -4.633

-90 -4.215

-80 -3.786

-70 -3.344

-60 -2.893

-50 -2.431

-40 -1.961

-30 -1.482

-20 -0.995

-10 -0.501

0 0.000

10 0.507

20 1.019

30 1.537

40 2.059

50 2.585

60 3.116

70 3.650

80 4.187

90 4.726

100 5.269



830 47.431

840 48.074

850 48.715

860 49.353

870 49.989

880 50.622

890 51.251

900 51.877

910 52.500

920 53.119

930 53.735

940 54.347

950 54.956

960 55.561

970 56.164

980 56.763

990 57.360

1000 57.953

1010 58.545

1020 59.134

1030 59.721

1040 60.307

1050 60.890

1060 61.473

1070 62.054

1080 62.634

1090 63.214

1100 63.792

1110 64.370

1120 64.948

1130 65.525

1140 66.102

1150 66.679

1160 67.255

1170 67.831

1180 68.406

1190 68.980

1200 69.553

Type J - Thermoelectric Voltage in mV (cont’d.)

°C mV

490 26.834

500 27.393

510 27.953

520 28.516

530 29.080

540 29.647

550 30.216

560 30.788

570 31.362

580 31.939

590 32.519

600 33.102

610 33.689

620 34.279

630 34.873

640 35.470

650 36.071

660 36.675

670 37.284

680 37.896

690 38.512

700 39.132

710 39.755

720 40.382

730 41.012

740 41.645

750 42.281

760 42.919

770 43.559

780 44.203

790 44.848

800 45.494

810 46.141

820 46.786



70 2.851

80 3.267

90 3.682

100 4.096

110 4.509

120 4.920

130 5.328

140 5.735

150 6.138

160 6.540

170 6.941

180 7.340

190 7.739

200 8.138

210 8.539

220 8.940

230 9.343

240 9.747

250 10.153

260 10.561

270 10.971

280 11.382

290 11.795

300 12.209

310 12.624

320 13.040

330 13.457

340 13.874

350 14.293

360 14.713

370 15.133

380 15.554

390 15.975

400 16.397

410 16.820

420 17.243

430 17.667

440 18.091

Type K - Thermoelectric Voltage in mV

°C mV

-270 -6.458

-260 -6.441

-250 -6.404

-240 -6.344

-230 -6.262

-220 -6.158

-210 -6.035

-200 -5.891

-190 -5.730

-180 -5.550

-170 -5.354

-160 -5.141

-150 -4.913

-140 -4.669

-130 -4.411

-120 -4.138

-110 -3.852

-100 -3.554

-90 -3.243

-80 -2.920

-70 -2.587

-60 -2.243

-50 -1.889

-40 -1.527

-30 -1.156

-20 -0.778

-10 -0.392

0 0.000

10 0.397

20 0.798

30 1.203

40 1.612

50 2.023

60 2.436



830 34.501

840 34.908

850 35.313

860 35.718

870 36.121

880 36.524

890 36.925

900 37.326

910 37.725

920 38.124

930 38.522

940 38.918

950 39.314

960 39.708

970 40.101

980 40.494

990 40.885

1000 41.276

1010 41.665

1020 42.053

1030 42.440

1040 42.826

1050 43.211

1060 43.595

1070 43.978

1080 44.359

1090 44.740

1100 45.119

1110 45.497

1120 45.873

1130 46.249

1140 46.623

1150 46.995

1160 47.367

1170 47.737

1180 48.105

1190 48.473

1200 48.838

1210 49.202

Type K - Thermoelectric Voltage in mV (cont.)

°C mV450 18.516460 18.941470 19.366480 19.792490 20.218500 20.644510 21.071520 21.497530 21.924540 22.350550 22.776560 23.203570 23.629580 24.055590 24.480600 24.905610 25.330620 25.755630 26.179640 26.602650 27.025660 27.447670 27.869680 28.289690 28.710700 29.129710 29.548720 29.965730 30.382740 30.798750 31.213760 31.628770 32.041780 32.453790 32.865800 33.275810 33.685820 34.093



Type T - Thermoelectric Voltage in mV

°C mV-270 -6.258-260 -6.232-250 -6.180-240 -6.105-230 -6.007-220 -5.888-210 -5.753-200 -5.603-190 -5.439-180 -5.261-170 -5.070-160 -4.865-150 -4.648-140 -4.419-130 -4.177-120 -3.923-110 -3.657-100 -3.379-90 -3.089-80 -2.788-70 -2.476-60 -2.153-50 -1.819-40 -1.475-30 -1.121-20 -0.757-10 -0.3830 0.000

10 0.39120 0.79030 1.19640 1.61250 2.03660 2.46870 2.90980 3.35890 3.814

1220 49.565

1230 49.926

1240 50.286

1250 50.644

1260 51.000

1270 51.355

1280 51.708

1290 52.060

1300 52.410

1310 52.759

1320 53.106

1330 53.451

1340 53.795

1350 54.138

1360 54.479

1370 54.819



Type T - Thermoelectric Voltage in mV

°C mV

100 4.279

110 4.750

120 5.228

130 5.714

140 6.206

150 6.704

160 7.209

170 7.720

180 8.237

190 8.759

200 9.288

210 9.822

220 10.362

230 10.907

240 11.458

250 12.013

260 12.574

270 13.139

280 13.709

290 14.283

300 14.862

310 15.445

320 16.032

330 16.624

340 17.219

350 17.819

360 18.422

370 19.030

380 19.641

390 20.255

400 20.872


Source: NIST ITS-90 Database


aLimits of error are expressed in percentage of Celsius temperature. Limits of error arematerial tolerances, not accuracies.

RTDs (Resistive Temperature Detectors)

RTDs are made of metal wire, fiber, or semiconductor material thatresponds to temperature change by changing its resistance. Platinum,nickel, tungsten and other metals are used that have high resistivity, goodtemperature coefficient of resistance, good ductile or tensile strength, andchemical inertness with packaging and insulation materials. When thematerial is a semiconductor, the sensor is called a thermistor.

Recommended Upper Temperature Limits for Protected Thermocouples, °C (°F)

Type 8 Gauge 14 Gauge 20 Gauge 24 Gauge 28 Gauge

T 370 (770) 260 (500) 200 (400) 200 (400)

J 760 (1400) 590 (1100) 480 (900) 370 (700) 370 (700)

E 870 (1600) 650 (1200) 540 (1100) 430 (800) 430 (800)

K 1260 (2300) 1090 (2000) 980 (1800) 870 (1600) 870 (1600)

R or S 1480 (2700)

B 1700 (3100)

Limits of Error for Thermocouples

ThermocoupleType

TemperatureRange °C

Standarda ErrorLimit

Speciala ErrorLimit

T -59 to 93 1.0°C 0.5°C93 to 371

J 0 to 277 2.2°C 1.1°C277 to 1260

E 0 to 316 1.7°C 1.0°C316 to 817

K 0 to 277 2.2°C 1.1°C277 to 1260

R or S 0 to 538 1.5°C 0.6°C538 to 1482

B 871 to 1705 0.50% n.a.



Change in resistance can be deter-mined using a bridge circuit. Sinceresistance changes in the connec-tion wire due to ambient tempera-ture changes can also affect theresistance reading, a third wire isused from another leg in the bridgeto balance that change.

RTDs are generally more accuratethan thermocouples, but are lessrugged and cannot be used at ashigh temperatures.

All types of temperature measuringdevices suffer from slow response,since it is necessary for heat to con-duct through the protective sheath,and through any installed well.Locating the well (or unprotectedsensor) so it sees as high a veloc-ity of process material as possiblehelps reduce this lag, as does hav-ing the sensor contact the well. Abare thermocouple touching thesheath and/or well, however, gen-erates a ground and requires anisolated amplifier.

The resistivity (r) is proportional tothe length (L) and inversely propor-tional to the cross-section area (A).

whereR = resistance, ohmsr = resistivity, ohm cmL = length, cmA = cross-section area, cm2

Rr LA

=( )

RTD Material Resistivity Levels

Metal Resistivity(Ohm/CMF)

CMF = CircularMil Foot)

Copper 9.26

Gold 13.00

Nickel 36.00

Platinum 59.00

Silver 8.8

Tungsten 30.00




-200 -100 0 100 200 300 400 500 600

4.0

3.8

3.6

3.4

3.2

3.0

2.8

2.6

2.4

2.2

2.0

1.8

1.6

1.4

1.2

1.0

0.8

0.6

0.4

0.2

0.0

Basis: German Standard DIN 43760

Linear approximation for -200 to 600˚CResis

tan

ce/r

esis

tan

ce ˚C

Temperature ˚C

Resistance vs. Temperature for Platinum


Resistance Versus Temperature and Tolerance for 100 OhmPlatinum RTDs According to DIN 43760

T°C R Ohm °C Temp.Tolerance T°C R Ohm °C Temp.

Tolerance

-220 10.41 1.8 30 111.67

-210 14.36 40 115.54

-200 18.53 1.2 50 119.40

-190 22.78 60 123.40

-180 27.05 70 127.07

-170 31.28 80 130.89

-160 35.48 90 134.70

-150 39.65 100 138.50 0.6

-140 43.80 110 142.28

-130 47.93 120 146.06

-120 52.04 130 149.82

-110 56.13 140 153.57

-100 60.20 0.7 150 157.32

-90 64.25 160 161.04

-80 68.28 170 164.76

-70 72.29 180 168.47

-60 76.28 190 172.16

-50 80.25 200 175.84 1.2

-40 84.21 210 179.51

-30 88.17 220 183.17

-20 92.13 230 186.82

-10 96.07 240 190.46

0 100.00 0.3 250 194.08

10 103.90 260 197.70

20 107.79 270 201.30



Resistance Versus Temperature and Tolerance for 100 OhmPlatinum RTDs According to DIN 43760 (cont.)

T°C R Ohm °C Temp.Tolerance T°C R Ohm ° Temp.

Tolerance

280 204.88 530 290.87

290 208.46 540 294.16

300 212.03 1.8 550 297.43

310 215.58 560 300.70

320 219.13 570 303.95

330 222.66 580 307.20

340 226.18 590 310.43

350 229.69 600 313.65 3.6

360 233.19 610 316.86

370 236.67 620 320.05

380 240.15 630 323.24

390 243.61 640 326.41

400 247.06 2.4 650 329.57

410 250.50 660 332.72

420 253.93 670 335.86

430 257.34 680 338.99

440 260.75 690 342.10

450 264.14 700 345.21 4.2

460 267.52 710 348.30

470 270.89 720 351.38

480 274.25 730 354.45

490 277.60 740 357.51

500 280.93 3.0 750 360.55

510 284.26 800 375.61 4.8

520 287.57 850 390.38 5.1



Resistance Versus Temperature for 100 Ohm (Nominal) Platinum RTD According to SAMA RC21-4-1966

T °C R Ohm T °C R Ohm

-200 16.666 20 105.920

-190 20.972 30 109.799

-180 25.244 40 113.665

-170 29.483 50 117.521

-160 33.691 60 121.365

-150 37.871 70 125.197

-140 42.023 80 129.018

-130 46.151 90 132.827

-120 50.255 100 136.625

-110 54.337 110 140.412

-100 58.399 120 144.187

-90 62.441 130 147.950

-80 66.466 140 151.702

-70 70.474 150 155.442

-60 74.465 160 159.171

-50 78.442 170 162.889

-40 82.405 180 166.595

-30 86.355 190 170.289

-20 90.292 200 173.972

-10 94.216 210 177.644

0 98.129 220 181.304

10 102.030 230 184.953



Resistance Versus Temperature for 100 Ohm (Nominal) Platinum RTD According to SAMA RC21-4-1966 (cont.)

T °C R Ohm T °C R Ohm

240 188.581 430 255.512

250 192.215 440 258.919

260 195.829 450 262.315

270 199.432 460 265.699

280 203.023 470 269.072

290 206.603 480 272.434

300 210.171 490 275.784

310 213.728 500 279.122

320 217.273 510 282.449

330 220.807 520 285.784

340 224.329 530 289.068

350 227.840 540 292.361

360 231.339 550 295.642

370 234.827 560 298.911

380 238.303 570 302.169

390 241.768 580 305.416

400 245.221 590 308.651

410 248.663 600 311.875

420 252.093



Wheatstone Bridge – Effect ofBridge Nonlinearities

whereE = voltage dropEo = output voltageRT = fixed resistorRS = adjustable resistor

Wheatstone Bridge 3-WireMeasurement

Thermistor Temperature-Resistance Relationship

where R = unknown resistanceRo = known resistanceβ = KelvinsT = unknown temperatureTo = known temperature

The Steinhart and Hart Equation for NTC Thermistors

where T = temperatureR = resistanceao = 1.1252 x 10-3 K-1

a1 = 2.3476x10-4 K-1

a3 = 8.5262 x 10-8 K-1

Thermistor Temperature ErrorDue to Self-Heating

where ∆T = temperature measurementerror, °CI = sensing current, mAR = thermistor resistance, ΩDC = dissipation constant, mW/°C

∆ =TI R

DC

2

1000( )

11 11 3

3

Ta a n R a n Ro= + +( ) ( )

RR T To o

= −

β

1 1

E ER

R RR

R RoT

T

S

S=

+−

+

E ER

R RR

R RoT

T

S

S=

+−

+


E

RT

Eo

Rs

R

R

Basic Wheatstone Bridge (2-wire)

Lead 3

Lead 2

Lead 1

RL

RL

RT

Rs

Eo

R

R

E

Wheatstone Bridge for 3-Wire Measurements


Thermistor Voltage DropAcross a Wheatstone Bridge

where

Stem Correction for a TotalImmersion Thermometer

where∆T = temperature correctionK = temperature correction factorn = number of degrees on scalebetween surface of fluid and endof fluid column in the capillaryTB = bulb temperatureT = average temperature of theportion of the thermometerbetween the fluid surface and endof fluid column in the capillary

∆ = −T Kn T TB( )

KR

R R

F TRR

R

R

R

s

T

T

T

T

o

o

o

= −+

=+

=

( )1

1

resistance at a reference temperature

EE

K F To

= + ( )

Resistance Tolerance Percent for Thermistors (MIL-T-23648A)Temperature

°CType F

+ or -1% Type G

+ or -2%Type J

+ or -5%Type K

+ or -10%

-55 10 12 15 20

-15 5 6 9 14

0 3 4 7 12

25 1 2 5 10

50 3 4 7 12

75 5 6 9 14

100 7 9 12 17

125 10 12 15 20

200° 15 18 25 30

275° 20 25 35 40


aThe percent tolerance indicated with each thermistor type is the resistance at 25°C.


Vapor Pressure Thermometers

Cross Ambient Effect

wherePG = pressure on the BourdontubePB = pressure in the bulbPC = pressure in the capillary

Radiation Pyrometers

Planck’s Radiation Law

whereH(λT) = radiant power densityλ = wavelength, cmT = temperature, KC1 = 3.74 x 10-12, Wcm2

C2 = 1.44, cmK

H TC

ec T( )( )

λλ λ=

−1

5 2 1

P P PG B C= + ∆


Rs

EoE

R

R

T

Wheatstone Bridge for Thermistor Readout

Vapor

Vapor

Volatile Liquid

Volatile Liquid

Vapor Pressure Thermometers


Wien’s Radiation Law (lowertemperatures)

Stefan-Boltzmann Law (total radiation power)

whereH(T) = total radiation power perunit areaσ = 5.669 x 10-12, W/cm2 K4

T = temperature, K

Wien’s Displacement Law

where T = temperature, Kλm = wavelength where maximumradiation power density occurs

Tm

=0 2898.

λ

H T T( ) = σ 4

H TC e C T

( )/

λλ

λ=

−1

5

2



Radiation Power Density as a Function of Wavelength and

Temperature (Plank’s Law for a Blackbody)


6543210

0.15

0.14

0.13

0.12

0.11

0.10

0.09

0.08

0.07

0.06

0.05

0.04

0.03

0.02

0.01

0.00

Wavelength λ, microns

Rela

tive S

pectr

al R

ad

ian

t P

ow

er

Location of Peak

(see Wien's Displacement Law)

1300 K, 1880˚F

1200 K, 1700˚F

1100 K, 1520˚F

1000 K, 1340˚F

900 K, 1160˚F

800 K, 960˚F

700 K, 800˚F


Total Emissivities of Metals, Surface Unoxidized

Material 25°C 100°C 500°C 1000°C 1500°C 2000°C

Aluminum 0.022 0.028 0.060

Bismuth 0.048 0.061

Carbon 0.81 0.81 0.79

Chromium 0.08

Cobalt 0.13 0.23

Columbium 0.19 0.24

Copper 0.02 0.15Liquid

Gold 0.02 0.03

Iron 0.06

Lead 0.05

Mercury 0.10 0.12

Molybdenum 0.13 0.19 0.24

Nickel 0.045 0.06 0.12 0.19

Platinum 0.037 0.047 0.095 0.152 0.191

Silver 0.02 0.035

Tantalum 0.21 0.26

Tin 0.043 0.05

Tungsten 0.024 0.032 0.071 0.15 0.23 0.28

Brass 0.035 0.035

Cast Iron 0.21 0.29Liquid

Steel 0.08 0.28Liquid



Total Radiation Pyrometer

True Temperature vs. Indicated

Temperature

whereT = true temperatureTI = indicated temperature∈ = material radiation emissivity

Brightness Pyrometer

True Temperature vs. Brightness

Temperature

whereT = true temperatureTB = brightness temperature

Johnson Noise Thermometer

Relationship Between Noise Volt-

age and Absolute Temperature

where V = noise voltagek = Boltzmann’s constantT = absolute temperatureR = electrical resistance of sensor∆f = frequency band-width overwhich the noise voltage is measured

V kTR f2 4= ∆

TT

Tn

B

B=

+ ∈11 44

1λ λ.

( )

T TI= ∈( ) /1 4



Engineering

Instrumentation and control