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Chapter 9 Calibration of Temperature Sensors


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Title: Chapter 9 Calibration of Temperature Sensors

Chapter 9 Calibration of
Temperature Sensors
I recommended also the calibration of the couples
in term of the fixed points of boding or fusion
of certain pure substances
LeClwtelier (1885)
9.1 GENERAL REMARKS As seen in Chapter 4,
temperature is defined by certain standards. We
want to transfer this information to some more
rugged, faster, cheaper, smaller device that is
also temperature sensitive, and that may be
carried from the standards Laboratory to a job
site. Calibration consists of determining the
indication or output of a temperature sensor with
respect to that of a standard at a sufficient
number of known temperatures so that, with
acceptable means of interpolation, the indication
or output of the sensor will be known over the
entire temperature range of use 1.
Calibration problem areas are immediately
apparent. There must be available (1)a means
for measuring the output of the temperature
sensor, (2) a satisfactory temperature
standard, (3) controlled temperature
environments, and (4) a scheme for interpolating
between calibration points. As a result of proper
attention to application details, the means for
measuring indications or outputs of all common
temperature sensors within acceptable
uncertainties are available (see, for example,
Chapters 5-7).
A practical, realizable temperature standard has
been described in the text of the IPTS (see
Chapter 4) wherein temperature is defined by
certain fixed points, certain standard
instruments and certain standard interpolating
equations. The availability and use of
controlled-temperature environments wherein
sensor outputs are determined, and the bases of
several schemes that are useful for interpolating
between the calibration points are discussed in
the next sections.
Calibration environments can be divided into two
classes depending on the method of determining
the temperature of die test sensor. In one
case,the sensor is exposed to a fixed-paint
environment that, under certain prescribed
conditions , naturally exhibits a state of
quasi-thermal equilibrium whose temperature is
established numerically by the 1PTS without
recourse to a temperature standard. In the
other case, the sensor and a temperature standard
are expose simultaneously controlled-temperature
environment whose temperature established by the
standard instrument.
  • Fixed-Point Baths
  • Three general types of fixed-point baths are
    commercially available.
  • These are the liquid-solid (freezing-point), the
    liquid-vapor (boiling-point), and the
    solid-liquid-vapor (triple-point) baths. In these
    fixed-point baths, use is made of the
    reproducible temperature-time plateau that exists
    and signifies the coexistence of two more phases
    of a substance.
  • Provided the sensor is not contaminated by the
    fixed-point material, that sufficient immersion
    exists, that the fixed-point sample is pure and
    at a uniform temperature, the temperature
    assigned to the bath (and hence to the sensor) is

9.2.2 Triple Point of water Of the triple-point
baths, only that of water is of general interest.
This bath provides the primary defining point on
IPTS-68, and has been described is great detail
in the various texts defining the IPTS (see
Chapter 4). A pressure temperature diagram, is
give in Figure 9.1a and indicates that three
phase of water can coexist only at a pressure of
4.58 mm Hg. A cross-sector diagram of the cell
is given in Figure 9.1b. Essentially, the cell
consists of glass cylinder that has beets
evacuated at the required low pressure, charged
very high-purity gas-free water, and hermetically
The construction and preparation of the triple
point cell are described in literature 2-7.
The following is a brief review. The cell is
first chilled it ice path. The reentrant tube of
the cell serves several purposes. It is used in
thermometer well. and it is used to set up the
triple point. Freezing of a port of the
scaled-in water is accomplished by pouring
powdered dry ice (i.e. C into the recent rant
tube. When the mantle of ice, fluxes around
the recent thermometer well, reaches a thickness
of about 5 mm, the dry ice is removed?
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The cell is again placed in an ice bath. A rod,
initially at room temperature, is inserting in
the reentrant well, and this melts some of the
ice mantle that a thin layer of very pure water
forms adjacent to the well wall. When the ice
mantle is free from the reentrant tube, the
triple point is established. To assure good
thermal contact between the three-phase water and
the thermometer. the well is filled with alcohol
or mineral oil. It has been reported 6 that a
properly aged ice mantle may be kept for several
months with no appreciable drift in the
triple-point temperature.
Several triple-point baths are commercially
available. But such baths are not normally used
as routine calibration environment because of tee
time and care required in their preparation and
use. For standards work they are, of course, a
9.2.3 Freezing Point of Water The importance
of the freezing point of water (ice bath) cannot
be over-emphasized. The ice bath is used
extensively as the reference junction environment
for most thermocouple systems, and as a
calibration reference temperature for all other
temperature-sensing systems. The thermocouple
reference junction must be maintained at a
constant and known temperature, and this
temperature must be stated as a necessary part of
the calibration results.
Caldwell 10 presents useful curves effects
of wire site, thermal conduction, and immersion
depths on the reference junction temperatures of
various chromel-alumel thermocouples in ice
baths. He indicates that the most potent
variable is the size of the copper wire used to
connect the reference junctions to the measuring
He concludes that uncertainties in the reference
junction temperature of less than 0.1? are
assured by establishing at least 6 in immersion
in the ice-water mixture when using copper wires
no larger than 20 gauge.
All freezing-point baths are virtually
independent of barometric pressure variations.
For example, the ice-point temperature is
affected less than 0.001? by atmospheric pressure
variations from 28.5 to 31 in Hg. The ice bath
has already been shown in Figure 7.12. Use of
tap water in place of distilled water should act
introduce errors greater than 0.01?. It is
important, however,,that excess water be removed
periodically and more ice added so that the
reference junctions are never below the ice-water
mixture. Such water, at the bottom of the is
bath, may be as much as 4? above the ice point.
Another source of error when using an ice bath
with thermocouples is the galvanic action that
may be set up when water comes in contact with
the thermocouples wires 10, 11. Such
galvanic cells may introduce voltages large
enough to affect tare thermocouple output. The
use of insulated wires should minimize this
error. 1. Freezing Point of Metals Other
freezing-point baths that is reia6vely simple is
construction detail are commercially available
Figure 9.2 and may be used by uninitiated
personnel without great difficulty. Cooling
curves for all freezing-point baths are
characterized by a plateau of approximately zero
slopes is the temperature-time plot 12, 13.
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Profess joseph Slack, in 1790, gave the first
description 14 of this phenomenon". . . when
we freeze a liquid, a very large quantity of heat
comes out of it, while it is assuming a solid
form, the loss of which beat is not to be
perceived by the common manner of using the
thermometer . . ." The tin and zinc baths are
common examples of freezing-point baths used in
thermometry. They provide additional fixed
points on IPTS-68. Each provides an equilibrium
state that exists between the Liquid end solid
phases of a metal.
The freezing temperature is essentially
independent of atmospheric pressure variations,
is highly reproducible, and the useful
temperature-time plateau can be made to persist
for an extended period of time.
Across sectional view of a commercially available
freezing-point bath is shown in Figure 9.3. A
graphite crucible is charged with a high-purity
mortal sample, and in use dry nitrogen is
introduced to retard oxidation of the metal
sample. Detailed operating procedures are given
in the literature 7, l2-15. A brief review
of ft tin and zinc baths is included here,
however, for completeness.
9.3 Cross-sectional view of a typical
freezillg-point bath
Zinc The metal sample is first completely melted
to about 10'C above the liquids point. The
sample is then cooed until nucleation begins.
This is indicated by a gradual rise in
temperature. At this point, heat is extracted
from the sample by use of cooling rod. The quick
transfer of heat causes a thin mantle of solid
metal to form on the graphite crucible and
releases sufficient latent heat to raise the
metal to its liquids temperature. The
temperature now remains essential constant for an
extended period of time. A typical temperature
time plot of a tine plateau is given in Figure
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Tin. The operation of the do bath is similar to
that of the zinc bath except that tin tends to
super cool. The bath must be raised out of the
furnaces when the metal approaches the freezing
point and allowed to nucleate outside.
Nucleation is indicated by a gradual rise in
temperature. At this point, the cell is lowered
back into the furnace where it will reach its
liquids point. Typical temperature-tune plots
of the tin plateau ate given in Figure 9.5
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These curves further indicate that Freezing
does not occur at a fixed temperature under all
conditions, and that the plateau varies in its
time extent, such variables as purity of
material, initial temperature above melting
from which cooling begins, first heat versus
reheat, immersion of test sensor induced versus
normal cooling, and so on, all influence tine
observed freezing-point temperature and the
duration of the plateau.
For calibration work employing freezing-point
baths, accuracies ranging from 0.l to 0.5? are
obtainable. To achieve such accuracies, the
following conditions must be met the thermometer
must be protected from contamination by the
freezing-point sample. The thermometer must be
immersed in the sample sufficiently far so as to
minimize conduction heat transfer errors. The
freezing-point sample must be pure, and the
sample temperature must be essentially uniform
throughout the freezing 18, 19 Note as
already implied, that the time for taking
observation is limited by the period of freezing
after which the material must be melted again
before further observations are taken 1.
9.2.5 Boiling Point of Water The boiling
point of water (steam bath or hypsometer) also
provides one of the primary fixed points on the
IPTS. However, as is true far all
boiling-point baths, the steam-point temperature
is greatly affected by barometric pressure
variations (set Table 4. l).
Compared to the freezing -point baths, then
baths are more elaborate in construction details
(see, for example, the hypsometer in Figure 9.6)
and, for inexperience personnel, more difficult
to use. The routine determination of the
steam point is one thing, whereas the precise
determination of the temperature of equilibrium
between liquid sulfur and its vapor presents an
even greater challenge. For example, Evans 2
rotes that it is now usual procedure to bail the
sulfur actively far a period of 10 days before
making measurements.
Note that unlike the freezing-point baths, the
boiling-point baths offer a continuous plateau
with no limit in the time available for
observations, since the material can be boiled
9.2.6 Controlled-Temperature Baths Up to 1000?,
calibrations usually are made in electrically
heated Temperature-controlled stirred-liquid
baths wherein test sensors and standard
thermometers are placed and their resulting
outputs compared. In this method of
calibration, by comparison 20, the validity of
the calibration points depends on how closely the
test sensor and the standard thermometer are
brought to the same temperature. In liquid baths
this is not usually a problem, since gradients in
such environments are extremely small (under
0.1?) at given levels of immersion 21.
Many such baths are on the order of 18 in deep
so that immersion depths can be quite adequate to
minimize conduction effects. Water can be
used up to its boiling point as a satisfactory
calibration liquid. Certain non-conducting oils
are useful below their flash points. (Dow-Coming
550 synthetic oil with a flash point of about
580? is a good example). Molten salts are
frequently used between 500 and 1000? as
calibration environments. (Lavite, a heat
treating and tempering salt that melts at about
400?, is one example.)
Of the liquid metals, tin, which melts at
450?, is the one most commonly used as the
calibration medium in controlled-temperature
baths. All of these baths are available
commercially with proportional controllers that
anticipate temperature changes and activate
electric heaters accordingly to provide uniform
temperatures within 0.1? over long periods of
Electrically heated temperature-controlled
gas-environment furnaces are used almost
exclusively for calibration work in the
temperature range of 1900-2000?. For less
precise calibrations they are also used below
these temperatures in the realm of the
stirred-liquid baths.
In such gas furnaces, success in bringing test
sensors and standard to the same temperature is
not so easily achieved as in the liquid baths.
The National Bureau of Standards recommends
forming a common measuring junction between one
or more test thermo- couples and the standard
thermocouple when calibrating these sensors m a
gas furnace. In such cases, all wires must be
insulated from each outer except tit the
measuring junction if this procedure is not
applicable, feasible, or convenient, the various
test sensors can be arranged around the standard
thermometer and secured in place by wire wrapped
around the assembly.
Sometimes as an alternative, the sensors and the
standard are inserted into bolts drilled in a
large metal block that is placed in the furnace
and is intended to serve as a temperature
equalizer 22. However, gases have such low
specific heat capacities compared with liquids
and circulation of gases is usually by natural
convection currents only. Thus it is not
uncommon to find large temperature gradients in
the commercial gas furnaces. Great cut must be
exercised in obtaining calibration points in such
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A special class of controlled-temperature baths
has recently become commercially available. Such
baths employ a mass of aluminum oxide particles
that are confined in a container and can he
"fluidized' by blowing air up through the fine
solid particles (Figure 9.7). These baths offer
the advantages of a "liquid" over a gas. In
particular, the fluidized solid is characterized
by a high specific heat capacity and by low
temperature gradients. Such baths are often
safes to use than oil baths that can flash or
salt baths which corrode and can explode upon
overhearing 23?
A specially designed air furnace is used at doe
National Bureau of Standards for the routine
calibration of thermocouple up to 2282?. The
treating element of the furnace consists of an
80 nickel-20 chromium tube damped between two
water-cooled terminals in a horizontal position.
The tube, with a in inside diameter, 1 in
outside diameter. is 24 in long and is heated
electrically. The tube itself serves as the
heating element or resistor. The large current
necessary to heat the tube is obtained from and
controlled by transformers.
A large cylindrical shield of sheet metal is
mounted around the heating tube to reduce the
radiation loss. In order to minimize time lag
(see Chapter 13).no thermal insulation is used
between the heating tube and the radiation
shield. The middle part of this furnace is said
to be at a practically uniform temperature for
afoul l8 in. This furnace can be heated to 2192?
in about 10 min with 12 kW of power, and with
power off, will cool from this temperature to
572? in about the same time. Many of these
methods of calibration are treated in detail in
the various professional society references (see,
for example 19 and 24.
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9.3 INTERPOLATION METHOW It is impossible in a
practical sense to obtain enough calibration
points to define a continuous relationship
between temperature and the output of a test
sensor. Thus a suitable interpolation method
must he used between the calibration points.
Since the two independent measurements upon which
each calibration point is based are not without
their experimental uncertainties, a weighting
scheme also must be employed to minimize effects
of poor experimental points.
In this section we consider several
interpolation methods, as applied to the
calibration data of a thermocouple. Although
these examples apply to a specific temperature
sensor, they serve to illustrate general methods.
An experimental thermocouple calibration
consists of a series of voltage measurements
determined at a finite number of known
temperature if a test thermocouple were compared
with a standard temperature instrument at 100
temperatures within a10? range, there would be
little need for interpolation between the
calibration points.
However, if four to ten calibration points am all
that can be afforded in a given range of
interest, what is needed to characterize an
individual thermocouple is a continuous relation
between voltage and temperature. Efforts m
obtains such a continuous relation appear
thwarted from the start because of the small
number of discrete calibration points available.
However, interpolation between the calibration
points is possible, since the emf changes only
slowly and smoothly with temperature.
One can present raw calibration data directly
in terms of temperature T and voltage Ecouple on
a scale so chosen that the information appears
well represented by a single curve (sm. far
example, figure 9.8) or by a simple mathematical
equation. For example.,for the highest
accuracy in the range 630-1064? with the type s
thermocouple, this method is that prescribed in
the IPTS An equation is used of the form
E a bT c
where a, b, and c are constants determined by
calibration at the freezing points of gold,
silver, and antimony face (see Chapter 4).
By calibrating the thermocouple also at the
freezing point of zinc and using as equation of
the form the temperature range can be extended
down to 400? without introducing an uncertainty
of more than 0.1? in the range of 630-1064?.
However, in general this practice of directly
representing thermocouple characteristics does
not always yield results within the required
limits of uncertainty.
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Often differences between observed values and
values obtained from standard .reference tables
are used in calibration work 25 the reference
tables and the mathematical means for generating
them are presented in Section 7.8.the data of
Figure 9.8 are repotted in Figure 9.9 in terms of
differences from the proper reference
table. Difference plats are in order whenever the
range of temperature is so great that the desired
readability is precluded by the use of a T-emf
plot or whenever it is impossible to find a
single satisfactory empirical interpolating
equation for the whole T-emf range. Such
difference plats allow magnification of the
calibration data and can be fit by single
empirical equations of low degree.
The maximum spread between points taken at the
same level (replication) but obtained in random
order with respect to time and level
(randomization) is taken as the uncertainty
envelope. This information, taken from Figure
9.9, is plotted in Figure 9.10 and constitutes a
vital bit of information about the particular
thermocouple and the calibration system In lieu
of an experimental determination of the
uncertainty one must rely on judgment or on the
current literature for this information.
Usually only a single set of calibration points
is available. Typical paints would be those
taken from one shown in Figures 9.8 or 9.9.
These are shown in Figure 9.11 along with five
of" many possible methods for representing
thermocouple difference characteristic. Although
at first it appears that the most probable
relation characterizing a given thermocouple is
sensibly indeterminate from a single set of
calibration points, it is an important fact that
all experimental points must be contained within
the uncertainty envelope when the uncertainty
envelope is centered on the roost probable
interpolation equation.
If the total uncertainty were determined. and
this could only result from a very large sample
experiment, it would follow from an assumed
normal error distribution that no experimental
point cull depart from the thermocouple
characteristic (best value) by more than 1 the
uncertainty envelope. For small-sample
experiment, however, such as are usually the
case, one should expect drat a few poor
calibration points might fail m conform with the
above assertion.
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Another important fact is that overall experiment
uncertainties will be minimized by using the
leas-squares technique. Here the most probable
values far a given set of data are obtained by
weighting the relative value of each experiment
point according to the laws of probability and
then passing a precisely determined equation of
prescribed degree through the data (see Example 1
is Section 9.4).
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Making use of the least squares technique
along with the principle that all experimental
points must be contained within the uncertainty
envelope. We can begin a systematic search
for rite most probable interpolation equation.
First a least-squares equation of the first
degree is passed through the experimental data.
A check is then made to ascertain whether all
experimental points are contained within the
uncertainty envelope which is centered on the
linear interpolation equation (Figure 9.12).
We proceed, according to the results of the
foregoing cluck, to the next highest degree
equation, stopping at the lowest degree
least-squares equation that satisfies the
uncertainty requirements. For the example
given here, a third-degree interpolation equation
was required (Figure 9.13). By obtaining
voltage differences from the least-squares ht of
any set of calibration paints. the uncertainty in
the thermocouple difference characteristic will
be within one-half the uncertainty envelope.
Generally, the form of the uncertainty
envelope and the degree of the most probable
least-squares interpolation equation are strongly
dependent on the amount of calibration data
available and on the temperature range under
consideration. It is recommended that the
number of distinct calibration points available
should be at least 2(degree I). The factor is
arrived at from numerical analysis reasoning.
A distinct calibration point is arbitrarily
defined as one that is separated temperature from
all other points in the set by as much as 1/10
the difference in temperature between the maximum
and minimum temperature of the particular run.
The choice of 1/10 presupposes a maximum
practical degree of 4 for the least-squares
interpolation equation, in keeping with the
low-degree requirement of numerical analysis.
Indeed, if the data cannot be fit by a
fourth-degree interpolation equation, one should
increase the uncertainty interval and start the
fining procedure again. Difference curves often
offer greater precision in thermocouple
calibration work, for a given number of
Calibration points. That can be obtained from
the use of the raw calibration data alone.
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Although this last scheme has been particularized
for thermocouple calibration data, the same four
premises concerning (1) different plot with
respect to the reference table (2) the
determination and application of the uncertainty
envelope,(3) the least-squares technique , and
(4) the number of distinct points being at least
(degree l) may be applied successfully to many
form of experimental data over and above the
calibration of temperature sensors as ,for
example, the calibration of pressure and flow
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