3. 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
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4. 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
122 ISA Handbook of Measurement Equations and Tables
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7. 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
Chapter 4/Temperature 125
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
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8. °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
126 ISA Handbook of Measurement Equations and Tables
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9. 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
Chapter 4/Temperature 127
hD
k
Du
ρ
µ
c
k
µ
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10. 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
128 ISA Handbook of Measurement Equations and Tables
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19. 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( )
Chapter 4/Temperature 137
The Basic Thermoelectric Voltage Element
∆V
T1
S
T2
A Simple Thermocouple Circuit
T1
Sa
Sb
T1
T2V
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20. 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
∂
∂
=
∂
∂
− +
138 ISA Handbook of Measurement Equations and Tables
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28. 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
146 ISA Handbook of Measurement Equations and Tables
Source: NIST ITS-90 Database
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29. 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.
Chapter 4/Temperature 147
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30. 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
148 ISA Handbook of Measurement Equations and Tables
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31. Chapter 4/Temperature 149
-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
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32. 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
150 ISA Handbook of Measurement Equations and Tables
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34. 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
152 ISA Handbook of Measurement Equations and Tables
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35. 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
Chapter 4/Temperature 153
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36. 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
=
+
−
+
154 ISA Handbook of Measurement Equations and Tables
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
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37. 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
Chapter 4/Temperature 155
aThe percent tolerance indicated with each thermistor type is the resistance at 25°C.
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38. 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= + ∆
156 ISA Handbook of Measurement Equations and Tables
Rs
Eo
E
R
R
T
Wheatstone Bridge for Thermistor Readout
Vapor
Vapor
Volatile Liquid
Volatile Liquid
Vapor Pressure Thermometers
new chap 4 temp.qxd 3/2/2006 8:56 AM Page 156
39. 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
Chapter 4/Temperature 157
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40. Radiation Power Density as a Function of Wavelength and
Temperature (Plank’s Law for a Blackbody)
158 ISA Handbook of Measurement Equations and Tables
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
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42. 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
160 ISA Handbook of Measurement Equations and Tables
new chap 4 temp.qxd 3/2/2006 8:56 AM Page 160