Instrumentation and control

4
Temperature 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 Temperature
Scale 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 of
the Comité International des Poids
et Mesures (CIPM) – undertook the
development of a new scale. On 26-
28 September 1989, the CCT recom-
mended ITS-90 be adopted. Follow-
ing approval by CIPM, ITS-90
became the official international
temperature scale on 1 January
1990, when it also was imple-
mented at the U.S. National Insti-
tute of Standards and Technology
(NIST).
According to a detailed report by
B.W. Mangum, of NIST’s Center for
Chemical Technology, National
Measurement Laboratory, and
NIST guest scientist G.T. Furukawa,
ITS-90 – when compared to IPTS-68
– extends upward from 0.65 K.
Also, temperatures on the newer
scale are in much better agreement
with thermodynamic values. In
addition, ITS-90’s continuity, non-
uniqueness and reproducibility
throughout its ranges are much
improved over previous scales. The
most complete and authoritative
document on ITS-90 from NIST is
Technical Note 1265 by Mangum
and Furukawa. It is available as a
pdf from NIST’s web site:
http://www.cstl.nist.gov/div836/836.0
5/papers/magnum90ITS90guide.pdf
Temperature Defining Points – IPTS-68 vs. ITS-90
Temperature Defining Point
IPTS-68
Kelvin
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 25/75
Standard 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 of
Absolute, %
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 Resistance
Thermometers
Industrial
-200 to
650
0.01 0.5-0.1 0.02@ 650°C
Standard
-183 to
631
<0.01 0.0001-0.003
0.02@
1063°C
Thermistors
-200 to
600
0.0005 0.03-1 0.02-0.03
Mercury-in-Glass
-38 to
400
0.01 0.002-0.25 0.05
Optical Pyrometer 700-3000 0.20 0.10 0
Johnson Noise
Thermometer
-272 to
1500
0.10 0.01-1.30
0
Transistor Absolute
Thermometer
-200 to
123
0.04 0.50
Nuclear Quadrupole
Resonance
Thermometer
-183 to
125
0.0002 0.0004 <0.01@
100°C
Ultrasonic Pulse Echo
Thermometer
0-2000 1-2 1
Fluidic Thermometers 0-1200 0.00001 105
Quartz Crystal
Thermometer
-40 to
230
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 Conversion
Equations
°Celsius to °Fahrenheit
Degree F = (Degree C x 1.8) + 32
°Celsius to °Rankine
Degree R = (Degree C + 273.15) x
1.8
°Celsius to Kelvin
Kelvin = Degree C + 273.15
°Fahrenheit to °Celsius
°Fahrenheit to °Rankine
Degree R = Degree F + 459.67
°Fahrenheit to Kelvin
°Rankine to °Fahrenheit
Degree F = Degree R - 459.67
Degree C =
Degree F - 32
1.8
273.1+
Degree C =
Degree F - 32
1.8
17
80100
21
-40
0273 0
˚C = ˚F
460
70
32
-40
0
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 °Celsius
Degree 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 following
temperature conversion tables, the
interpolation table below provides
the values to add to the conversion
table values. Note that these values
are to four decimal places. To use
these add-on values correctly, cal-
culate the add-on value, and then
round to two decimal places.
Kelvin
Degree 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 Transfer
Analysis
The performance of temperature
sensors can depend on all the
modes of heat transfer – conduc-
tion, convection, and radiation.
The steady-state heat conduction
equation is:
where
∇ = geometry-dependent
differential operator
k = thermal conductivity
For constant thermal conductivity,
the conduction equation is:
The differential operators for three
geometries are:
x,y,z (Cartesian)
r,z, θ (cylindrical)
r, θ, φ (spherical)
In many applications, heat transfer
along all the coordinate axes is not
significant. In these cases the equa-
tions are:
Cartesian (one-dimensional)
Cylinder (r only)
Cylinder (r,z)
Sphere (r only)
Convective Heat Transfer
Coefficients
Dimensionless Quantities for
Sensors of Single Cylinders or
Spheres
Nusselt number (Nu) =
Reynolds number (Re) =
Prandtl number (Pr) =
∇ =
∂
∂
∂
∂




=
∂
∂
+
∂
∂
2
2
2
2
2
1
2
T
r r
r
T
r
T
r r
T
r
∂
∂
+
∂
∂
+
∂
∂
=
2
2
2
2
1
0
T
r r
T
r
T
z
∂
∂
+
∂
∂
=
2
2
1
0
T
r r
T
r
∂
∂
=
2
2
0
T
x
∇ =
∂
∂
∂
∂



 +
∂
∂
∂
∂



 +
∂
2
2
2
2
2 2
2
1
1
1
T
r r
r
T
r
r
T
r
sin
sin
sin
θ θ
θ
θ
θ
TT
∂φ2
∇ =
∂
∂
+
∂
∂
+
∂
∂
+
∂
∂
2
2
2 2
2
2
2
2
1 1
T
T
r r
T
r r
T T
zθ
∇ =
∂
∂
+
∂
∂
+
∂
∂
2
2
2
2
2
2
2
T
T
x
T
y
T
z
∇ =2
0T
∇ ⋅ =kVT 0
hD
k
Du
ρ
µ
c
k
µ

where
h = film heat transfer coefficient
D = diameter of sensor
k = thermal conductivity of fluid
ρ = fluid density
u = fluid velocity
µ = fluid viscosity
c = fluid specific heat capacity
General Form of the
Correlations
where
a = experimental data
Nonmetals Flowing Normal to a
Single 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 a
Single Sphere
Nu = 2.0 + 0.60 Re1/2 Pr1/2
Metals Flowing Normal to a
Single 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 2
3 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. Thermocouples
are based on the principle that two
wires made of dissimilar materials
connected at either end will gener-
ate a potential between the two
ends that is a function of the mate-
rials and temperature difference
between the two ends.
A number of material choices are in
common use. Base metal thermo-
couples are useful for measuring
temperatures under 1000 degrees
C. This class includes iron/constan-
tan (Type J), Chromel/Alumel (Type
K) and a number of others. Nobel
metal thermocouples are useful to
about 2000 degrees C. This class
includes tungsten-rhenium alloy
thermocouples and others.
The potential generated is in milli-
volts and is a nonlinear function of
temperature. In practice, one end is
placed near the material to be
measured and the other end is con-
nected to the instrument. Since the
thermocouple materials are not
typically good materials for trans-
mission, wires with similar charac-
teristics are used when the trans-
mitting instrument is remote.
Thermocouple Types
Thermocouples come in different
combinations of metals and cali-
brations. Types J, K, T and E are the
four most common calibrations.
Types R, S, C and GB are high tem-
perature calibrations. Each calibra-
tion has a different temperature
range and environment. However,
the maximum temperature varies
with the diameter of the wire used
in the thermocouple.
The letter type, e.g., type J, identi-
fies a specific temperature-voltage
relationship, not a particular chem-
ical composition. Thermocouples
of a given type may have variations
in 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 specified
tolerances. 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 voltage
T1 = Temperature at one end of
wires
T2 = temperature at other end of
wires
Sa = absolute Seebeck coefficient
for material
Sb = absolute Seebeck coefficient
for material
T = temperature
where
Sab = relative Seebeck coefficient
for materials a and b
The Relation Between
Temperature Difference and
Voltage
where
V = voltage
T = temperature
The Basic Thermoelectric
Voltage Element
A Simple Thermocouple
Circuit
S
V
T
=
∆
∆
∆ = −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 dTT
T
a b= −∫ 1
2( )
The Basic Thermoelectric Voltage Element
∆V
T1
S
T2
A Simple Thermocouple Circuit
T1
Sa
Sb
T1
T2V

Solutions also require specification
of boundary conditions at inter-
faces. Interfaces occur between
regions containing different materi-
als or surfaces. Since notation
becomes 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 Heat
Flux
Internal; Finiteness of
Temperature
Surface; Convection
Surface: Fixed Surface
Temperature
TR = TF
Surface: Insulated Surface
Surface: Radiation
where
Tr- = temperature at r as
approached from the interior
Tr+ = temperature at r as
approached from the exterior
k = thermal conductivity
k1 = thermal conductivity of
material interior to the interface at r
k2 = thermal conductivity of
material exterior to the interface at r
R = radius at the surface
h = film heat transfer coefficient
θ = temperature of fluid around
sensor
θR = temperature of medium
exchanging radiative energy with
the sensor
TF = fixed temperature specified
for surface
∈ = emissivity
σ = Stefan-Boltzmann constant
−
∂
∂
=∈ −k
T
r
TR R Rσ θ( )4 4
∂
∂
=
T
r
R 0
−
∂
∂
= −k
T
r
h TR R( )θ
T r( ) ≠ ∞
k
T
r
k
T
r
r 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 mV
270 -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 -0.582
0 0.000
10 0.591
20 1.192
30 1.801
40 2.420
50 3.048
60 3.685
70 4.330
80 4.985
90 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 mV
490 36.196
500 37.005
510 37.815
520 38.624
530 39.434
540 40.243
550 41.053
560 41.862
570 42.671
580 43.479
590 44.286
600 45.093
610 45.900
620 46.705
630 47.509
640 48.313
650 49.116
660 49.917
670 50.718
680 51.517
690 52.315
700 53.112
710 53.908
720 54.703
730 55.497
740 56.289
750 57.080
760 57.870
770 58.659
780 59.446
790 60.232
800 61.017
810 61.801
820 62.583
830 63.364
840 64.144
850 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 mV
450 18.516
460 18.941
470 19.366
480 19.792
490 20.218
500 20.644
510 21.071
520 21.497
530 21.924
540 22.350
550 22.776
560 23.203
570 23.629
580 24.055
590 24.480
600 24.905
610 25.330
620 25.755
630 26.179
640 26.602
650 27.025
660 27.447
670 27.869
680 28.289
690 28.710
700 29.129
710 29.548
720 29.965
730 30.382
740 30.798
750 31.213
760 31.628
770 32.041
780 32.453
790 32.865
800 33.275
810 33.685
820 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 -0.383
0 0.000
10 0.391
20 0.790
30 1.196
40 1.612
50 2.036
60 2.468
70 2.909
80 3.358
90 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 are
material tolerances, not accuracies.
RTDs (Resistive Temperature Detectors)
RTDs are made of metal wire, fiber, or semiconductor material that
responds to temperature change by changing its resistance. Platinum,
nickel, tungsten and other metals are used that have high resistivity, good
temperature coefficient of resistance, good ductile or tensile strength, and
chemical inertness with packaging and insulation materials. When the
material 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
Thermocouple
Type
Temperature
Range °C
Standarda Error
Limit
Speciala Error
Limit
T -59 to 93 1.0°C
0.5°C
93 to 371
J 0 to 277 2.2°C
1.1°C
277 to 1260
E 0 to 316 1.7°C
1.0°C
316 to 817
K 0 to 277 2.2°C
1.1°C
277 to 1260
R or S 0 to 538 1.5°C
0.6°C
538 to 1482
B 871 to 1705 0.50% n.a.

Change in resistance can be deter-
mined using a bridge circuit. Since
resistance changes in the connec-
tion wire due to ambient tempera-
ture changes can also affect the
resistance reading, a third wire is
used from another leg in the bridge
to balance that change.
RTDs are generally more accurate
than thermocouples, but are less
rugged and cannot be used at as
high temperatures.
All types of temperature measuring
devices 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 unprotected
sensor) so it sees as high a veloc-
ity of process material as possible
helps reduce this lag, as does hav-
ing the sensor contact the well. A
bare thermocouple touching the
sheath and/or well, however, gen-
erates a ground and requires an
isolated amplifier.
The resistivity (r) is proportional to
the length (L) and inversely propor-
tional to the cross-section area (A).
where
R = resistance, ohms
r = resistivity, ohm cm
L = length, cm
A = cross-section area, cm2
R
r L
A
=
( )
RTD Material Resistivity
Levels
Metal Resistivity
(Ohm/CMF)
CMF = Circular
Mil 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˚C
Resistance/resistance˚C
Temperature ˚C
Resistance vs. Temperature for Platinum

Resistance Versus Temperature and Tolerance for 100 Ohm
Platinum 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 Ohm
Platinum 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 of
Bridge Nonlinearities
where
E = voltage drop
Eo = output voltage
RT = fixed resistor
RS = adjustable resistor
Wheatstone Bridge 3-Wire
Measurement
Thermistor Temperature-
Resistance Relationship
where
R = unknown resistance
Ro = known resistance
β = Kelvins
T = unknown temperature
To = known temperature
The Steinhart and Hart
Equation for NTC Thermistors
where
T = temperature
R = resistance
ao = 1.1252 x 10-3 K-1
a1 = 2.3476x10-4 K-1
a3 = 8.5262 x 10-8 K-1
Thermistor Temperature Error
Due to Self-Heating
where
∆T = temperature measurement
error, °C
I = sensing current, mA
R = thermistor resistance, Ω
DC = dissipation constant, mW/°C
∆ =T
I R
DC
2
1000( )
1
1 11 3
3
T
a a n R a n Ro= + +( ) ( )
R
R T To o
= −





β
1 1
E E
R
R R
R
R R
o
T
T
S
S
=
+
−
+






E E
R
R R
R
R R
o
T
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 Drop
Across a Wheatstone Bridge
where
Stem Correction for a Total
Immersion Thermometer
where
∆T = temperature correction
K = temperature correction factor
n = number of degrees on scale
between surface of fluid and end
of fluid column in the capillary
TB = bulb temperature
T = average temperature of the
portion of the thermometer
between the fluid surface and end
of fluid column in the capillary
∆ = −T Kn T TB( )
K
R
R R
F T
R
R
R
R
R
s
T
T
T
T
o
o
o
= −
+
=
+
=
( )
1
1
resistance at a reference
temperature
E
E
K F T
o
= + ( )
Resistance Tolerance Percent for Thermistors (MIL-T-23648A)
Temperature
°C
Type 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
where
PG = pressure on the Bourdon
tube
PB = pressure in the bulb
PC = pressure in the capillary
Radiation Pyrometers
Planck’s Radiation Law
where
H(λT) = radiant power density
λ = wavelength, cm
T = temperature, K
C1 = 3.74 x 10-12, Wcm2
C2 = 1.44, cmK
H T
C
ec T
( )
( )
λ
λ λ
=
−
1
5 2 1
P P PG B C= + ∆
Rs
Eo
E
R
R
T
Wheatstone Bridge for Thermistor Readout
Vapor
Vapor
Volatile Liquid
Volatile Liquid
Vapor Pressure Thermometers

Wien’s Radiation Law (lower
temperatures)
Stefan-Boltzmann Law
(total radiation power)
where
H(T) = total radiation power per
unit area
σ = 5.669 x 10-12, W/cm2 K4
T = temperature, K
Wien’s Displacement Law
where
T = temperature, K
λm = wavelength where maximum
radiation power density occurs
T
m
=
0 2898.
λ
H T T( ) = σ 4
H T
C e C T
( )
/
λ
λ
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
RelativeSpectralRadiantPower
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 0.15
Liquid
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 0.29
Liquid
Steel 0.08 0.28
Liquid

Total Radiation Pyrometer
True Temperature vs. Indicated
Temperature
where
T = true temperature
TI = indicated temperature
∈ = material radiation emissivity
Brightness Pyrometer
True Temperature vs. Brightness
Temperature
where
T = true temperature
TB = brightness temperature
Johnson Noise Thermometer
Relationship Between Noise Volt-
age and Absolute Temperature
where
V = noise voltage
k = Boltzmann’s constant
T = absolute temperature
R = electrical resistance of sensor
∆f = frequency band-width over
which the noise voltage is
measured
V kTR f2
4= ∆
T
T
T
n
B
B
=
+ ∈1
1 44
1
λ
λ
.
( )
T TI= ∈( ) /1 4

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