NIST Measurement Services:

Liquid-In-Glass

Thermometer Calibration

Service

NIST

Special

Publication

250-23

Jacquelyn Wise

U.S. Department of Commerce

National Institute of Standards and Technology
Center for Basic Standards

The Center for Basic Standards develops and maintains the scientific competencies and laboratory facilities nec- essary to preserve and continue to refine the base physical quantities upon which the Nation's measurement

system is constructed. The Center is responsible for the standards of voltage, current, resistance and

impedance, temperature, vacuum, leak rate, pressure, mass, length, time and frequency. The Center collaborates closely with the standardizing laboratories of other countries to ensure that measures used in international

trade are fully compatible. The Center also performs research at the frontiers of physics in order to improve

measurement capability and quantitative understanding of basic physical processes that underlie measurement

science.

Electricity Division

Maintains and improves the national standards of electrical measurements; conducts experiments to realize the

electrical units in terms of the mechanical units; develops stable electrical standards and improved methods for the dissemination of the units of electrical measurements; determines fundamental physical constants related to

electrical units; develops instrumentation for precise electrical measurements directly referenced to the national

standards; implements techniques for their use and puts them into practical applications; assists in applying scientific and technological development to measurement problems, especially in other areas of NBS research.

Temperature and Pressure Division

Maintains and improves the national standards of temperature and pressure; conducts research towards the development of new concepts for these standards; calibrates practical standards for the U.S. scientific and technical community in terms of the primary standards; develops methods and devices to assist user groups in the

assessment and enhancement of the accuracy of their measurements of temperature and pressure; prepares

and promulgates evaluations and descriptions of temperature and pressure measurement processes; coordi- nates these standards and measurement methods nationally and internationally; and determines the accuracy of the national standards of temperature and pressure with respect to fundamental thermodynamic relations. Length and Mass Division

Develops and uses the competence necessary to implement a more accurate measurement system for length

and mass; applies research, utilizing the most advanced technology available, to the improvement of our present

standards and devises new standards and new methods for their transfer. Time and Frequency Division

Maintains, develops, and improves the national standards for time (which are coordinated with the United States

Naval Observatory) and frequency, and the time scales based on these standards; carries out research in areas

of importance to the further fundamental improvement of frequency standards and their applications focusing on

microwave and laser devices, atomic and molecular resonances, and the measurement of fundamental physical

phenomena and constants; adapts time and frequency standard devices and concepts to special scientific and

technological demands; develops time and frequency measurement methods in the radio frequency, microwave,

infrared, and visible radiation regions; coordinates the national time and frequency standards, time scales, and

measurement methods nationally and internationally in conjunction with the United States Naval Observatory;

operates time and frequency dissemination services, such as radio stations and broadcasts, for the purpose of

traceability to the national standards of time and frequency.

Quantum Physics Division

Engages in research in atomic and molecular physics at the forefront of the field, and performs basic, highly accurate measurements and theoretical analyses that help establish a reliable foundation for scientific and technological measurement and data.

Quantum Metrology Division

Engages in forefront research in quantum metrology; contributes to new determinations of the fundamental

physical constants, and the extension and refinement of the electromagnetic scale and devises, where possible,

tests of basic symmetries and invariances.
NIST MEASUREMENT SERVICES:

Liquid-In-Glass Thermometer Calibration Service

Jacquelyn Wise

Temperature and Pressure Division

Center for Basic Standards

National Measurement Laboratory

National Institute of Standards and Technology

Gaithersburg, MD 20899

U.S. DEPARTMENT OF COMMERCE, C. William Verity, Secretary

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY, Ernest Ambler, Director

(formerly National Bureau of Standards)

September 1988

NOTE: As of 23 August 1988, the National Bureau of Standards (NBS) became the National Institute of

Standards and Technology (NIST) when President

Reagan signed into law the Omnibus Trade and

Competitiveness Act.
Library of Congress Catalog Card Number: 88-600580

National Institute of Standards and Technology

Special Publication 250-23, 128 pages (Sept. 1988)

CODEN: XNBSAV

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1988

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402-9325
PREFACE

Calibrations and related measurement services of the National Bureau of

Standards provide the means for makers and users of measuring tools to

achieve levels of measurement accuracy that are necessary to attain

quality, productivity and competitiveness. These requirements include the

highest levels of accuracy that are possible on the basis of the most

modern advances in science and technology as well as the levels of accuracy

that are necessary in the routine production of goods and services. More

than 300 different calibrations, measurement assurance services and special

tests are available from NBS to support the activities of public and

private organizations. These services enable users to link their

measurements to the reference standards maintained by NBS and, thereby, to

the measurement systems of other countries throughout the world. NBS

Special Publication 250, NBS Calibration Services Users Guide , describes

the calibrations and related services that are offered, provides essential

information for placing orders for these services and identifies expert

persons to be contacted for technical assistance.

NBS Special Publication 250 has recently been expanded by the addition of

supplementary publications that provide detailed technical descriptions of

specific NBS calibration services and, together with the NBS Calibration

Services Users Guide, they constitute a topical series. Each technical

supplement on a particular calibration service includes:

o specifications for the service

o design philosophy and theory

o description of the NBS measurement system

o NBS operational procedures

o measurement uncertainty assessment

error budget

systematic errors random errors

o NBS internal quality control procedures

The new publications will present more technical detail than the

information that can be included in NBS Reports of Calibration. In general

they will also provide more detail than past publications in the scientific

and technical literature; such publications, when they exist, tend to

focus upon a particular element of the topic and other elements may have

been published in different places at different times. The new series will

integrate the description of NBS calibration technologies in a form that is more readily accessible and more useful to the technical user to achieve

high quality measurements.
The present publication, SP 250-23, NBS Measurement Services: Liquid-inGlass Thermometer Calibration Service, by Jacquelyn A. Wise, is one of

approximately 20 documents in the new series published or in preparation by

the Center for Basic Standards. It describes calibration technology and

procedures utilized in connection with NBS Service Identification Numbers

from 31010C to 31161S listed in the NBS Calibration Services Users Guide

1986-88/Revised (pages 47 and 48). Inquiries concerning the contents of

these documents may be directed to the author (s) or to one of the technical

contact persons identified in the Users Guide.

Suggestions for improving the effectiveness and usefulness of the new

series would be very much appreciated at NBS. Likewise, suggestions

concerning the need for new calibration services, special tests and

measurement assurance programs are always welcome.

Joe D. Simmons, Acting Chief

Office of Physical Measurement Services

Katharine Gebbie, Acting Director

Center for Basic Standards

iv
TABLE OF CONTENTS

1.0 Description of Service 1

1 . 1 General 1 1.2 Types of Thermometers Accepted for Calibration at NBS ... 1 1.3 Procedures For Submitting A Thermometer for Calibration . . 2 1.4 Shipping Instructions 2

2.0 Design Philosophy and Theory 3

2.1 General Description of Liquid- in-Glass Thermometers .... 3 2.2 Three Immersion Depths for Liquid- in-Glass Thermometers . . 4

2.3 Materials of Construction 6 2.4 Scale Design and Workmanship 7 2.5 Scale Dimensions 8 2.6 Reference Point 9

3.0 Temperature Scale and Primary Standard Thermometer 10

3.1 International Practical Temperature Scale 10

3.2 Standard Platinum Resistance Thermometer 12

3.3 AC Bridge 14

4.0 Description of the Measurement System 14

4.1 Laboratory Environment 14

4.2 Calibration Baths 15

4.2.1 Ice Bath . 16

4.2.2 Steam Bath 17

4.2.3 Water and Oil Baths 20

4.2.4 Tin Bath 23

4.2.5 Cryostat 24

4.2.6 Liquid Nitrogen and Liquid Oxygen Points 26

5.0 Operational Procedures 28

5.1 Examination and Preparation of Thermometers for

Calibration 28

5.2 Number and Choice of Calibration Points 30

5.3 Types of Thermometers and How They Are Calibrated 31

5.3.1 Total- immersion Thermometers 31

5.3.2 Partial- immersion Thermometers 32

5.3.3 ASTM Thermometers 32

5.3.4 Calorimetric Thermometers 33

v
5.3.5 Beckmann Thermometers 33

5.3.6 Clinical Standard Thermometers 35

5.3.7 Kinematic Viscosity Thermometers 35

5.3.8 Low- temperature Thermometers 35

5.4 Stem- temperature Measurement 36

5.5 Checking the Standard Platinum Resistance Thermometer

at the Triple Point of Water 37

5.6 Use of Ice Bath 38

5.7 Placement of Thermometers in Calibration Baths 40

5.8 Placement of Faden and Auxiliary Thermometers for

Measurement of Stem Temperatures 41

5.9 Regulating the Bath, Reading Sequence, and Recording Data . 49

6.0 Calculations 51

6.1 Computation of Bath Temperature 51

6.2 Determining Corrections of Thermometers Being Calibrated . 58

6.3 Stem-Temperature Corrections 59

6.3.1 Emergent Stem- temperature Correction using Two

Auxiliary Thermometers 64

6.3.2 Emergent Stem- temperature Correction using Two

Faden Thermometers 64

6.3.3 Emergent Stem- temperature Correction using One

Auxiliary Thermometer 66

6.3.4 Emergent Stem- temperature Correction using One

Faden Thermometer 66

6.3.5 Too-deep Immersion Correction 67

6.3.6 Faden Correction 68

6.3.7 Emergent Stem- temperature Correction for

Calorimetric Thermometers 69

6.3.8 Emergent Stem- temperature Correction for Beckmann

Thermometers 70

7.0 Documentation 70

7.1 Report of Calibration 70

8.0 Internal Quality Control 78

8.1 Use of Check Standards 79

8.2 Comparison of Corrections and Evaluation of Data on Check Standards 79

9.0 Assessment of Uncertainties 81

9.1 Current Tolerance and Uncertainty Values 81

9.2 Evaluation of Uncertainties 88

vi
10.0 Glass Changes and Recalibration of Thermometers 115

10.1 Glass Changes 115

10.1.1 Temporary Changes 116

10.1.2 Permanent Changes 117

10.2 Recalibration of Liquid- in-Glass Thermometers 118

11.0 Future 119

12.0 Bibliography 119

vii

1.0 Description of Service

1.1 General

This service provides calibrations for a variety of thermometers covering

the range from -196 to +538 °C. The majority of the thermometers are liquid- in-glass but other types are calibrated as well; thermistors,

industrial platinum resistance thermometers, thermocouples, and digital

thermometer systems. The customer's thermometers are calibrated in

constant temperature baths in terms of the National Bureau of Standards

(NBS) primary standard, a calibrated platinum resistance thermometer. The

primary standard maintains calibrations traceable to the International

Practical Temperature Scale (1968), referred to as IPTS-68, with an accuracy of approximately 5 mK at the lower temperature range and 2 mK at

the higher range. The customer is provided a Report of Calibration or Report of Test which contains results of the calibration and other

important information related to his particular thermometer.

Typical uncertainties for the most accurate liquid- in-glass thermometers in

four temperature ranges are listed below. A more detailed discussion of

uncertainties is given in Section 9.

TYPE OF THERMOMETER RANGE UNCERTAINTY

(Total Immersion)

Mercury- in-Glass 0 to 300 °C 0.1 to 0.5 °C

(Graduated in 0 . 5 to 2 °C) 300 to 500 °C 0.5 to 1.0 °C

Mercury-in-Glass 0 to 100 °C 0.03 to 0.05 °C

(Graduated in 0.1 to 0.2 °C)

Organic Liquid- in-Glass

(Graduated in 1 °C) -200 to 0 °C 0.2 to 0.5 °C

Twice a year NBS offers a 5-day Precision Thermometry Seminar. One full day

is devoted to liquid- in-glass thermometry and includes lectures as well as "hands-on" laboratory experience.

1.2 Types of Thermometers Accepted for Calibration at NBS

Not all liquid- in-glass thermometers are acceptable for calibration at

NBS. In general, the thermometer must be of an acceptable design and

workmanship and be compatible with the existing calibration facilities.

The type known as laboratory or chemical thermometers, consisting of a solid stem with graduation lines and numbers permanently etched or placed

on the stem, are regularly accepted. Other types such as Beckmann, calorimetric, and enclosed scale (Einschluss) laboratory thermometers are also

regularly accepted. Industrial or mechanical type thermometers with

special mountings may be accepted for test if they can be inserted in the

comparison baths, or if the thermometer can be detached easily from the

mounting

1
Any thermometer, such as a household thermometer, consisting of a paper,

plastic or metal mounting containing the scale graduations and attached to

the unmarked glass thermometer by metal clips, is not acceptable for

calibration. Maximum self -registering mercury- in-glass clinical thermometers are no longer tested at NBS.

It is advisable to contact the NBS liquid- in-glass thermometry laboratory

if there is any doubt about the acceptability of a thermometer for calibration. Every effort will be made to assist you in selecting an appropriate

thermometer for a particular measurement application.

1.3 Procedures for Submitting A Thermometer for Calibration

Calibrations are conducted in accordance with policies described in NBS

Special Publication 250. The cost will depend on the number of calibration

points requested, the temperature range, and the quantity of thermometers

submitted. NBS should be contacted for information about tests not

specifically outlined in the above publication. If the required

measurements appear feasible, and, in the opinion of NBS, are sufficiently

important to justify the work, such tests will be undertaken for a special

fee determined by the nature of the work and time involved.

A letter or purchase order requesting the test may be sent to NBS either

with the thermometer or separately. However, no calibration will begin

until both the thermometer and letter or purchase order have been received. The request should include the quantity and serial numbers of the

thermometers, the calibration points required, and the suggested method for

return shipment. If the customer wants his thermometer insured for return

shipment, a statement to that effect must appear on the request with a value assigned; otherwise, the thermometer will be returned uninsured.

NBS will assign a test number to each calibration request and acknowledge

the receipt of the thermometer. The acknowledgment will state the estimated cost of the calibration and the estimated completion date. Any difficulties with the calibration that may be anticipated will also be mentioned

in the acknowledgment, as well as the name of an NBS contact who can answer

further questions that may arise.

1.4 Shipping Instructions

Thermometers should be packed firmly in their individual cases to assure

safe shipment. A rigid material, such as wooden slats or corrugated paper, can be wrapped around the thermometer case as an additional safeguard

against breakage. The package should contain enough packing material to

absorb any shock that it may receive. Each shipment should include a packing list stating the number of thermometers shipped, the name of the

company submitting them, and, if applicable, the company's purchase order

number. The thermometers should be sent to:

2
National Bureau of Standards

Route 270 and Quince Orchard Road

Gaithersburg, Maryland 20899

Attention: Jacquelyn Wise

Thermometers will be returned via the method requested by the customer. If

no preference is stated, NBS will select a best method. The thermometers

will be packed in the same boxes and manner in which they were received,

unless the boxes were damaged when they arrived. Shipping charges, both to

and from NBS will be paid by the customer. All reasonable care will be

taken in handling thermometers at NBS, but the risk of damage either in

shipment or during calibration must be assumed by the customer.

2.0 Design Philosophy and Theory

2.1 General Description of Liquid- in-Glass Thermometers

The liquid- in-glass thermometer works on the principle of thermal expansion. As the temperature of the thermometer increases, the liquid and the

glass of the thermometer expand with different expansion coefficients,

causing the liquid to advance up the capillary tube. The top of the liquid

column, known as the meniscus, will eventually come to rest when the

temperature of the thermometer is in equilibrium with the temperature of

its environment. The temperature of the thermometer can then be read from

the scale on the stem.

The principal features of a typical liquid- in-glass thermometer are shown

in Figure 1. However, all of the features shown would not necessarily be

incorporated in any one thermometer.

CONTRACTION EXPANSION

SCALE LINE SCALE

Fig. 1. Principal features of a solid-stem liquid-in-glass thermometer.

3
The bulb of the thermometer is a thin glass-walled reservoir for the

thermometer liquid. It contains a volume equivalent to a specific number

of degrees of the scale depending upon the expansion coefficients of the

thermometric liquid and the bulb glass. For example, for mercury in a bulb

made of "normal" glass, the bulb volume is equivalent to approximately

6,222 times the volume of a 1 degree length of the capillary on the scale

for Celsius thermometers, or 11,200 times the volume of a 1 degree length

of the capillary on the scale for Fahrenheit thermometers. For organic

thermometric liquids with expansion coefficients higher than that of

mercury, the bulb volumes are correspondingly smaller.

The stem of a thermometer is the glass capillary through which the

thermometric liquid advances or retreats with changes in temperature. It can be a heavy glass stem with a very small capillary in the center or it can be an enclosed scale stem, in which a very small capillary tube is

attached to a glass scale and enclosed in a glass sleeve.

The main scale is graduated in degrees or multiples or submultiples of

degrees. Frequently, the main scale is the only scale on the thermometer.

However, some thermometers have an additional short scale, known as an auxiliary scale, when a suitable reference temperature, such as the ice

point, is not included in the range of the main scale. The reference

temperature is used to check the calibration of the thermometer as a function of time or use.

The expansion chamber is an enlargement at the top of the capillary bore.

In gas-filled thermometers, it prevents an excessive buildup of internal

pressure when the liquid advances toward the top of the scale. An expansion chamber should have a volume equal to or greater than the volume of a

20 mm length of uniform capillary. Smaller enlargements do not qualify as expansion chambers.

The contraction chamber is an enlargement of the capillary bore located

below the main scale or between the main scale and an auxiliary scale. It serves to reduce the length of capillary needed to reach the main scale

from the reference point or to prevent contraction of the entire liquid

column into the bulb.

2.2 Three Immersion Depths for Liquid- in-Glass Thermometers

Liquid-in-glass thermometers are designed to be used at one of the three

immersion depths illustrated in Figure 2.

A total- immersion thermometer is designed to indicate temperatures

correctly when the bulb and all but about 12 mm of the liquid column are immersed in the bath medium and exposed to the temperature being measured.

The top 12 mm of the liquid column should be above the bath medium so that

the thermometer can be read and the mercury does not distill at high

temperatures. The meniscus should never be at or below the surface of the

bath medium.

4
TOTAL IMMERSION PARTIAL IMMERSION COMPLETE IMMERSION

Fig. 2. Three ways a liquid- in-glass thermometer can be used.

A partial- immersion thermometer is designed to indicate temperatures

correctly when the bulb and a specified portion of the stem are exposed to

the temperature being measured. The remaining portion of the stem will be

at the ambient temperature, which is usually different from the temperature

being measured. The segment of the stem from the immersion line to the

meniscus of the liquid column will be referred to throughout the text as the "emergent-stem." Partial- immersion thermometers must be clearly marked

"partial immersion" or the equivalent (for example, "76 mm immersion"), or have a conspicuous line permanently placed on the stem to indicate the

proper depth of immersion. (The immersion depth is from the bottom of the

bulb.) The immersion line must be at least 13 mm above the top of the

bulb. There are some special purpose partial- immersion thermometers that

need not be marked with an immersion line. These include thermometers made

for use in a specific manner or in a particular instrument, such as a viscometer or a flash-point tester where the thermometer is always mounted

in a specific arrangement for that instrument.

A complete- immersion thermometer is designed to indicate temperature

correctly when the whole thermometer, including the expansion chamber, is

subjected to the temperature being measured. Thermometers made in the

United States are generally not designed to be used at complete immersion.

5
A thermometer is designed to be used at only one of the above immersion

depths and it is normally calibrated at that depth. If the thermometer is

used at immersion depths other than that at which it was calibrated and

intended to be used, the temperature reading will be in error. This error

can be as large as several degrees. However, if a total- immersion

thermometer must be used at partial immersion or a partial- immersion

thermometer must be used at total immersion, a stem- temperature correction

can be computed (see Sections 5.8 and 6.3) and applied to the thermometer

reading to obtain the correct temperature reading. No such stemtemperature correction can be made for complete- immersion thermometers used

at total or partial immersion, or for total- or partial- immersion thermometers used at complete immersion. This is due to the additional error produced by different pressures on the thin-walled bulb and expansion

chamber when the thermometer is completely immersed as opposed to having

the bulb at a more shallow depth and the expansion chamber above the bath.

2 . 3 Materials of Construction

The cleanliness of the thermometer bulb, bore, and liquid filling have a pronounced effect on the performance of a thermometer. The proper choice

of thermometer glass is also important for good performance. The thermometer, and especially the bulb, must be made of glass suitable for use in the

temperature range indicated on the stem. Several types of glass commonly

used in the manufacture of thermometer bulbs are listed in Table 1 along

with Thompson's [1] estimate of reasonable upper temperature limits for

each type. Thompson's estimates are based on the work of Liberatore and

Whitcome [2]. Significant changes in bulb volume may occur if the bulb is

heated for long periods of time at temperatures within 130 °C of the strain

point of the bulb glass, i.e., the temperature at which the glass has a viscosity of 10 1A - 5 poises [3]. Thermometers may be used intermittently,

to within approximately 70 celsius degrees of the strain point. It should

be noted that the use of a glass with a high strain point, such as borosilicate glass, results in better thermometer performance and stability

even in thermometers used at temperatures much lower than the exposure

limits given in Table 1.

The thermometer must also be adequately annealed to enable the bulb volume

to remain reasonably stable with continued use. This is especially true

for a thermometer graduated above 300 °C. The quality of the thermometer

glass and the adequacy of the annealing process may be determined from the

stability of the reference-point readings. A method for testing bulb

stability is described in The American Society for Testing and Materials

Method E-77 [4]

All high- temperature thermometers should be filled with a dry inert gas

such as nitrogen under sufficient pressure to prevent separation of the

mercury at any temperature indicated on the scale. Total-immersion

thermometers graduated above 150 °C must be filled with gas to minimize the

distillation of mercury from the top of the column. An expansion chamber

at the top of the capillary or a specified length of uniform capillary

above the highest graduation is essential for thermometers containing a

6
TABLE 1

TEMPERATURE EXPOSURE LIMITS FOR VARIOUS THERMOMETER GLASSES [1]

Strain Exposure Limits

Point

Continuous Intermittent

°C °C °F °C °F

Corning normal 7560 500 370 700 430* 805*

Kimble R6 490 360 680 420 790

Jena 16 III 495 365 690 425 795

Corning borosilicate 8800 529 400 750 460 860

Jena borosilicate 2954 548 420 790 480 900

Corning 1720 668 540 1005 600 1110

Jena Supremax 2955 665 535 995 595 1100

[1] Data taken from Ref. [1].

*405 °C or 760 °F if Corning Standard Thermometer 0041 glass is

used for the stem.

gas. The gas must have an adequate area for compression when the mercury

is advanced toward the top of the scale; otherwise, excessive pressure in

the capillary will break the thermometer.

For thermometers graduated below 150 °C, a gas filling is optional but

strongly recommended. The mercury column of a vacuous thermometer will

tend to separate easily if the thermometer is inverted or subjected to a sudden shock.

2.4 Scale Design and Workmanship

Solid- stem thermometers must have the graduation marks placed directly on

the stem and opposite the enamel backing. If the thermometer is of the

enclosed- scale type, the graduated scale must be securely fastened to

prevent relative displacement between the scale and the capillary, or a datum line should be conveniently located to indicate whether the scale is

in its original position. The graduation marks should be clear cut,

straight, of uniform width, and in a plane perpendicular to the axis of the

thermometer

The scale should be graduated in 0.1, 0.2, or 0.5 degree intervals or in

decimal multiples. The divisions should be numbered in such a manner that

the identification of any graduation is not unnecessarily difficult.

Thermometers with scales graduated in 0.25 degree intervals, or submultiples, can look very much like thermometers graduated in 0.2 degree

7
intervals or decimal multiples and can be read incorrectly. If the

thermometers are graduated in 0.1 or 0.2 degree intervals (or decimal

multiples) , every fifth mark should be longer than the intermediate ones and a number should appear at every tenth mark. Thermometers graduated in

0.5 degree intervals (or decimal multiples) require three lengths of

graduation marks. These consist of alternating short and intermediate

marks, with every tenth line distinctly longer than the others. A number

should appear at every 10th or 20th mark. Examples are given in Figure 3.

0.1 0.2 0.5

Fig. 3. Scale graduations for thermometers in intervals of 0 . 1 , 0.2,

and 0 . 5 degree

The scale must not be extended to temperatures beyond which the particular

thermometer glass is suited. A thermometer made of borosilicate glass, for

example, should never be graduated to 500 °C. It would be ruined in a short time if used at that temperature.

2.5 Scale Dimensions

Although optimum line width depends in some measure on the intended use of

a particular thermometer, coarse graduation marks do not represent good

design. If the thermometer indications are to be observed precisely (for

example to 0.1 of a division), the width of the graduation marks should not

exceed 0.2 of the interval between the center lines of the graduations. In

instances where the thermometer must be read quickly or in poor light, and

less precision is expected, somewhat wider lines may be acceptable.

The graduation marks must not be too closely spaced. The closest permissible spacing depends on the fineness and clearness of the marks. In no case should the distance between center lines of adjacent graduation marks

on a solid-stem thermometer be less than 0.4 mm. The minimum permissible

interval between graduation marks for an enclosed- scale thermometer is

0.3 mm if the lines are ruled on a milk-glass scale; otherwise, the minimum

8
is also 0.4 nun. The minimum in no case represents good design, and welldesigned thermometers will have graduation intervals considerably larger

than the specified minimum.

In order for a thermometer to be usable over the entire range of the scale

the graduation marks must not be placed too close to any enlargement in the

capillary. Appreciable errors may result if any of the following

conditions exist.

(1) There is insufficient immersion of the mercury in the main bulb or a capillary enlargement;

(2) the graduation marks have been placed over parts of the capillary that

have been changed by manufacturing operations ; or

(3) the graduations are so close to the top of the thermometer that

excessive gas pressure results when the mercury is raised to this

level

The distances given below are considered minimum limits commensurate with

good thermometer design:

(a) A 13 mm length of uniform capillary between the bulb and the immersion

line or the lowest graduation, if the graduation is not above 100 °C; a 30 mm length if the graduation is above 100 °C.

(b) A 5 mm length of uniform capillary between an enlargement and the

graduation next below, except at the top of the thermometer.

(c) A 10 mm length of uniform capillary between an enlargement, other than

the bulb, and the graduation next above, if the graduation is not above

100 °C; a 30 mm length if the graduation is above 100 °C.

(d) A 10 mm length of uniform capillary above the highest graduation, if

there is an expansion chamber; a 30 mm length if there is no expansion

chamber

These dimensions are shown in Figure 4.

2.6 Reference Point

Thermometers graduated above 150 °C, or precision thermometers with an expected accuracy of better than 0.1 °C when calibrated for actual

temperature measurement, must have a reference point. The effects of

changes in the bulb volume on the thermometer indications may be followed

throughout the life of the thermometer by periodic testing at the reference

point. From the reference point observations, the thermometer corrections

can be kept current (see Section 10.2). If a suitable reference point,

either the ice or steam point, is not included in the range of the main

scale, a short auxiliary scale containing a fixed point should be

provided. To prevent the thermometer from being unduly long, a contraction

chamber may be introduced between the auxiliary scale and the main scale.

9
1 3 MM 5 MM 10 MM

10 MM ( GRADUATION ABOVE IS LESS THAN 100°C)

'30 MM (GRADUATION ABOVE IS G HEATER THAN 100°C)

Fig. 4. Minimum distances for scale placement on a liquid- in-glass

thermometer

Any auxiliary scale must have graduations identical to those on the main

scale, both dimensionally and in terms of temperature, and they must extend

for a short interval both above and below the reference point. Similarly,

when the main scale ends near a reference point, the graduations must be

continued for a short interval beyond the reference temperature.

Reference points are not needed on thermometers intended for differential

measurements (such as calorimetric thermometers), nor on thermometers

graduated below 150 °C, if they are not to be calibrated to an accuracy of

better than 0.1 °C.

3.0 Temperature Scale and Primary Standard Thermometer

3.1 International Practical Temperature Scale

The scale to which measurements of temperature should ultimately be

referred is the Kelvin Thermodynamic Temperature Scale (KTTS) . Values of

temperature expressed on the KTTS are designated by the symbol T. The unit

of temperature is the Kelvin, symbol K, which is a base unit of the Systeme

Internationale (SI), and is defined as "the fraction 1/273.16 of the

thermodynamic temperature of the triple point of water."

10
Because of the difficulties that are encountered in the practical

realization of the KTTS , it has been necessary to define and utilize

practical temperature scales. The International Temperature Scale and

defining text was first adopted in 1927 and later revised in 1948. The

Eleventh General Conference of Weights and Measures in 1960 changed the name of the scale to the International Practical Temperature Scale (IPTS)

of 1948 and adopted a revised text of the scale, although numerically the

scale was not changed. In 1968, in accordance with the power given to it

by Resolution 8 of the Thirteenth General Conference of Weights and

Measures, the International Committee of Weights and Measures adopted the

International Practical Temperature Scale of 1968 [5], henceforth referred

to as IPTS-68. The IPTS-68 replaced the International Practical

Temperature Scale of 1948 and may be expressed either as a Kelvin scale or

as a Celsius scale.

The present Celsius scale has its zero 0.01 K below the triple point of

water (the ice point, which is essentially 0 °C, can be realized by pure

ice in equilibrium with pure water saturated with air at one standard

atmosphere) . The value of a temperature expressed on the Thermodynamic

Celsius Temperature Scale is designated by the symbol t and is related to

the value on the KTTS by:

t = T - 273.15 K.

The unit of the Celsius Scale is the degree Celsius, symbol °C, which by

definition is equal in magnitude to the Kelvin.

Values of temperature expressed on the International Practical Kelvin Scale

are designated by the symbol T68 , and values of temperature expressed on

the International Practical Celsius Temperature Scale are designated by the

symbol t68 . The relationship between T68 and t6

is:

t68 = T68 - 273.15 K.

The units of T68 and t68 , like the thermodynamic scales, are the Kelvin,

symbol K, and degree Celsius, symbol °C.

The IPTS-68 was designed to be in agreement within the uncertainty of the

KTTS at the time. The IPTS-68 is intended to provide scientific and

industrial laboratories throughout the world with a common basis for

stating temperatures. Calibrations of thermometers at NBS , therefore, are made with reference to values of temperature on the IPTS-68.

Although values of temperature on the IPTS-68 are expressed in degrees

Celsius, thermometers that are graduated on the Fahrenheit Scale can be

calibrated with reference to the IPTS-68 by using the conversion formula:

(temperature value in °F) = (9/5) (temperature value in °C) + 32.

The National Bureau of Standards has been performing calibrations with

reference to the IPTS-68 since July, 1969. All Reports of Calibration and

Reports of Test issued after that date clearly indicate this scale.

11
In the range of temperature normally covered by liquid- in-glass thermometry, the IPTS-68 is defined by the following fixed points:

(1) The equilibrium between the liquid and vapor phases of oxygen

(condensation point of oxygen at one standard atmosphere) at

-182.962 °C,

(2) The equilibrium between solid, liquid, and vapor phases of water

(triple point of water) at 0.01 °C,

(3) The equilibrium between the liquid and vapor phases of water at one standard atmosphere (normal boiling point of water) at 100 °C,

(4) The equilibrium between the solid and liquid phases of tin (freezing

point of tin at one standard atmosphere) at 231.9681 °C. (This point

may be used as an alternative to the boiling point of water.)

(5) The equilibrium between solid and liquid phases of zinc (freezing point

of zinc at one standard atmosphere) at 419.58 °C.

Additionally, the temperatures on the IPTS-68 in the range of -182.96 to

+630.7 °C are defined in terms of a standard platinum resistance

thermometer that has been calibrated at the above fixed points, with

interpolations and extrapolations between and beyond these points being

accomplished by employing specified equations [5].

At NBS , liquid- in-glass thermometer indications, except at the ice point,

are compared directly with temperatures measured with a standard platinum

resistance thermometer and an NBS-built Cutkosky AC resistance bridge [6]

(see Figure 5)

3.2 Standard Platinum Resistance Thermometer

A standard platinum resistance thermometer (SPRT) has a resistor made of

platinum of sufficient purity that the finished thermometer will have a value of the resistance at 100 °C divided by the resistance at 0 °C

[R(100)/R(0) ] not less than 1.3925 or alpha, defined as (R(100)-R(0))/100R(0) , not less than 0.003925. The typical SPRT has an ice-point resistance of about 25.5 ohms and is called a 25-ohm thermometer;

its resistor is wound from about 61 cm of 0.075 mm diameter wire.

The insulation material that supports the resistor and leads must not

contaminate the platinum during the annealing of the assembled thermometer

nor when subjected for extended periods of time to temperatures to which

the thermometer is normally exposed. The insulation resistance between

the leads must be greater than 5 X 109 ohms at 500 °C if the error introduced by insulation leakage in the leads of a 25-ohm thermometer is to be

less than the equivalent of 1 micro ohm. For SPRT's the most commonly used

insulation is mica.

12
Fig. 5. Standard platinum resistance thermometer and Cutkosky

AC resistance bridge used for calibrating liquid- inglass thermometers.

The configuration of the resistor is inevitably the result of compromise

between conflicting requirements. The resistor must be free to expand and

contract without constraint from its support. This characteristic is the

so called "strain-free" construction. If the platinum were not free to

expand, the resistance of the platinum would not only be a function of

temperature but would also relate to the strain that results from the

differential expansion of the platinum and its support.

The sensing elements of all SPRT's have four leads. The four leads define

the resistor precisely by permitting measurements that eliminate the effect

of the resistance of the leads. The resistor winding is made as noninductive as possible, often bifilar.

Because the junction of the leads is electrically a part of the measured

resistor, the leads extending immediately from the resistor must also be of

high purity platinum; the lengths of these leads are often as short as

8 mm. Either gold or platinum wire is employed in continuing these leads

within the thermometer. Gold does not seem to contaminate the resistor and

is easily worked. Measurement of the resistor may be facilitated if the

four leads are made of the same material with the length and diameter the same so that the leads have about equal resistances at any temperature.

This statement is also applicable to leads that are external to the

protecting envelope.

13
The hermetic seal through the soft glass envelope at the thermometer head

has been made using short lengths of tungsten wire, to the ends of which

platinum lead wires are welded. The external platinum leads are soft

soldered to copper leads that are mechanically secured to the head. More

recently the hermetic seal has been made using commercially available

"electronic- type" metal- to- glass seals. Coaxial leads are required when an

AC bridge is used to determine the resistance of the SPRT.

3.3 AC Bridge

If the current is reversed sufficiently rapidly, it is usually said that

the bridge is an "AC" bridge. Bridges operating at 400 hertz have been

built at the NBS based on a design by Cutkosky [6]. These bridges were designed for use with SPRT's. The bridge uses an inductive ratio divider

that eliminates the need for calibrating the bridge because the initial

uncertainty of the divider is about 2 parts in 108 and appears to be

stable. Additionally, the bridge requires only one manual resistance

balance, the phase angle balance is automatic, and incorporates a built-in

phase - sensitive null detector which can easily resolve 1 micro ohm in

25 ohms. A small error (usually less than 10 micro ohms) may be introduced

in measuring a 25 -ohm SPRT unless coaxial leads are used between the bridge

and the thermometer head. (The heads of SPRT's have been modified to

contain two BNC coaxial connectors. The two leads from one end of the SPRT

coil were connected to the center "female" contacts of the BNC receptacles

and the two leads from the other end of the SPRT were connected to the

outer shells or the shield contacts.) For precision measurements the

length of the pair of coaxial leads should not be greater that 15 meters to

limit the dielectric losses of the shunt capacitance. Preliminary measurements on 25 -ohm SPRT's indicate that, if the leads do not affect the

measurements, the accuracy of the measured value in ohms of a thermometer

element is limited by the accuracy to which the reference standard resistor

is known. However, in the accurate determination of the resistance ratio,

R(t)/R(0), the stability, rather than the accuracy, of the reference

standard is the important requirement.

4.0 Description of the Measurement System

4 . 1 Laboratory Environment

The laboratory should be maintained at a constant temperature and

humidity. Many thermometers that are submitted for calibration will be

intended for use at partial immersion. In this case it is important that

the emergent stem remain at a constant temperature while the thermometer is

being tested. For example, if there is a one degree change in the

laboratory temperature, an error of approximately 0.01 °C can result in the

calibration of a partial- immersion thermometer with 50 degrees of stem

emerging from the bath. The temperature of the calibration laboratory at

NBS is maintained at 23 °C ± 1 degree. The humidity is maintained near 50%

to keep any electronic components in the laboratory from being adversely

affected.

14
The calibration baths that use oil as the medium are operated under a hood

which is isolated from the ventilation system of the building and exhausted

directly outside.

The thermometers submitted for calibration and the standard platinum

resistance thermometers are stored in map cases which have corrugated paper

placed on the bottom of each drawer to keep the thermometers from rolling

into each other when the drawer is opened. Immediately before and after

calibration, thermometers are stored vertically in a thermometer rack

designed especially for this purpose.

4.2 Calibration Baths

In most instances, the liquid- in-glass thermometer scale corrections are determined by comparing its scale indications in a series of stirred liquid

comparison baths with the temperature of the bath medium measured by a standard platinum resistance thermometer.

All electrically heated constant temperature comparison baths at NBS have

the heating coils isolated from the volume where the thermometers are placed. There is an unrestricted path of flow for the bath medium, which

is stirred at a sufficient rate to maintain a uniform temperature throughout the bath. Heat loss from the baths is minimized by a 5 to 7 cm thickness of insulation around the bath and an insulated cover. A holder

containing the thermometers is fitted into the top cover. This holder can

be rotated, enabling each thermometer to appear in the field of view of a vertically adjustable 10 power telescope attached to each bath. The

telescope is always kept perpendicular to the thermometers being read.

The comparison baths used to calibrate thermometers above 0 °C are manually

controlled by adjusting the current to the heating coils through a rheostat. For calibration below 0 °C the temperature is automatically

controlled.

All baths at NBS were evaluated to determine the temperature gradient

throughout the medium. This was done by placing three standard platinum

resistance thermometers at various locations and depths in the medium. The

thermometers were read simultaneously and the maximum difference between

the three readings at each temperature was considered to be caused by the

gradient. In addition to the temperature gradient throughout the medium,

there are large variable gradients in liquid baths in the region close to

the surface, due to large heat loses at the surface because of radiation

and evaporation. The depth to which the surface conditions affect the

temperature regulation depends upon the bath liquid and the operating

temperature. Obviously, thermometers must be immersed deep enough to avoid

this unregulated region. Henceforth, this unregulated region of the bath

will be referred to as the "unknown temperature region." The depth of such

region will be given with the description of each bath.

A discussion of the NBS calibration baths is given in the following

sections

15
4.2.1 Ice Bath

An ice bath (see Figure 6) is a fixed-point apparatus used to determine the

reference point on liquid- in-glass thermometers at 0 °C. No standard

thermometer is needed to realize the temperature of the ice and water

mixture. If it is made properly, the uncertainty of the medium is no greater than 0.005 °C.

Fig. 6. Ice point bath.

The ice bath is perhaps the most valuable and essential reference

temperature apparatus in the liquid- in-glass thermometer calibration

laboratory, because all liquid- in-glass thermometers suffer changes in bulb

volume (due to thermal expansion and other factors) . Recalibration at the

ice point is sufficient in most cases to correct for such changes (see

Section 5.2, NBS Monograph 150 [7]).

The ice bath at NBS consists of a glass Dewar flask approximately 36 cm

deep and 8 cm in diameter. The outside of the flask is covered with

16
electrical or waterproof adhesive tape and enclosed in a metal sleeve to

protect the operator in the event that it should break. The flask is

supported by a structure that will not allow it to tip over easily. A clip

is placed above the flask to hold the thermometer perpendicular to the

telescope. A siphon is placed in the bottom of the flask to remove excess water that will form due to the melting of the ice during the day. A small

soft mallet, which is used to gently tap the thermometers before reading,

is available.

A still and storage tank are used to keep the laboratory supplied with an adequate amount of distilled water. The distilled water that is produced

is frozen to form blocks of distilled water ice. The freezer and con- tainers used for this purpose are not used for anything else and kept as clean and free from impurities as possible. The containers are washed

thoroughly with soap and water and rinsed two or three times with distilled

water before being used initially.

An ice shaver is used to shave the ice to the proper size. The ice chips

should be approximately 2 to 5 mm in diameter. These particles are smaller

than those produced by crushing or chipping the ice.

The shaved ice and air saturated distilled water are placed in the Dewar

flask and allowed to reach a constant temperature, a process which takes

approximately 15 to 30 minutes. After this time, any excess water should

be siphoned off and additional ice added. When the ice bath is ready for

use, there should be no floating ice in the flask and no excess water on

the surface. There should be as much ice as can be forced into the flask

and sufficient distilled water to fill the small crevices between the ice

chips. Failure to follow this procedure can lead to vertical or radial

temperature gradients which can result in a calibration error as large as 0.01 °C in the ice point.

Whenever the ice bath is used, care should be taken not to contaminate the

ice or water. Plastic gloves should be worn by the operator or hands

washed often while taking ice points. It is important that impurities,

such as salt from the hands, not be allowed to come in contact with the

ice. This will cause a depression of the freezing point and result in an error in subsequent ice-point determinations.

4.2.2 Steam Bath

Although the ice point at 0 °C is most often the reference point, the steam

point at 100 °C is sometimes used. The steam bath or hypsometer used at

NBS and its schematic drawing are shown as Figures 7 and 8, respectively.

This bath is used only if the 100 °C mark is too close (less than 50 mm) to

the bulb or contraction chamber to permit adequate immersion of these large

volumes of mercury in an oil bath. Approximately 1,000 ml of distilled

water is placed in the boiler. A Fisher burner is ignited under the boiler

and in approximately one hour the bath is ready to be used.

Steam produced from the boiler circulates within a double-walled steam

jacket permitting free circulation of steam around the thermometers

17
Fig. 7. Steam point bath.

suspended within this space. Water condenses and drips from the

thermometer. A provision is made both for relieving any excess pressure in

the space surrounding the thermometers and for determining the excess pressure by means of a small differential manometer.

When the steam bath is used as a comparison bath, the temperature of the

steam is determined at the time of test with a standard platinum resistance

thermometer

The steam bath can also be used as a fixed-point apparatus. In this case a barometer is used, since the temperature of the steam depends on the

prevailing atmospheric pressure. The usual adjustments must be made to the

barometer reading, including any necessary corrections for the value of

local acceleration of gravity, for the difference in height between the

steam bath and the barometer, and for any excess pressure above atmospheric

in the steam jacket. After the corrected pressure reading is obtained, the

temperature of the steam can be derived from the values given in Table 2

18
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19
Fig. 8. Schematic drawing of the steam point bath.

With a barometer accurate to 0.1 mm mercury, this procedure is capable of an accuracy of 0.002 to 0.003 °C. The Fortin type barometer will usually

suffice for all but the most exacting measurements.

4.2.3 Water and Oil Baths

The designs are the same for both the water and the oil baths that are used

at NBS . A photograph of an oil bath is shown as Figure 9 and a drawing is

given as Figure 10. The baths consist of two cylindrical wells of

different diameters with connecting passages at the top and bottom. The

heating coil and stirrer are located in the smaller well, leaving the

larger well unobstructed for the insertion of the thermometers. The fluid

20
Fig. 9. Oil bath.

is forced past the heating coils, through the bottom opening into the

larger well, around the thermometers, and back into the smaller well

through the connecting passage at the top.

For calibration in the range of +1 to +95 °C, distilled water is used as the bath medium. Distilled water is preferable to tap water, since no chemical deposits will form at the top of the bath. Water is plentiful,

clean, and does not produce harmful vapors. Some distilled water is added

each day before the bath is used, since some of the water will escape

through the overflow tube due to expansion when heated. The level of the

water should be no more than 10 mm below the top of the thermometer holder

(see figure 10)

For calibration from approximately +1 to 22 °C, the bath water is cooled by

adding ice made from distilled water to bring the temperature of the bath

below the lowest calibration point. When the ice has melted, the stirrer

is turned on and the water is heated to bring the meniscus of the

thermometer under test to within one scale division of the calibration

point. No heat is added to the water when calibrating in this range, since

the temperature of the bath will rise at a steady rate, due to heat from

the room. Measured gradients in the water bath do not exceed 0.01 °C. The

unknown temperature region is 25 mm deep.

21
PULLEY

BEARING

INSULATION-^

HEATING

COILS

AIR SPACE

SPACE

BETWEEN

TUBES

BEARING

THERMOMETER

HOLDER

INSULATION

SUPPORT

Fig. 10. Drawing of water and oil baths

Two oil baths are maintained at NBS . One, called the low temperature oil

bath, is used to calibrate thermometers in the range of +95 to +200 °C. An

oil purchased from EXXON, known as Zerice 46 1

, is used. Before starting,

1 Certain commercial equipment, instruments, or materials are identified in this paper in order to adequately specify the experimental

procedures. Such identification does not imply recommendation or endorsement by the National Bureau of Standards, nor does it imply that the

materials or equipment identified are necessarily the best available for

the purpose

22
the oil level is first raised to within 25 mm of the top of the bath by

hand pumping oil from an overflow collection pan under the bath. As

thermometers are calibrated at the higher temperatures, the bath oil will

expand and leave through the overflow tube and is collected in the pan

below the bath. The temperature gradients in the low temperature oil bath

range from 0.01 °C at 100 °C to 0.025 °C at 200 °C. The unknown

temperature region is 50 mm deep.

For calibration in the range of +200 to +300 °C the high temperature oil

bath is used. The bath medium is an oil called Extra Hecla from Mobil Oil

Corporation. The oil that exits from the overflow tube is collected in an overflow collection pan. Before the bath is used, oil is poured into the

bath to within 70 mm from the top of the bath. Temperature gradients in

the high temperature oil bath are no greater than 0.05 °C. The unknown

temperature region is 50 mm deep.

4.2.4 Tin Bath

The tin bath is used to calibrate thermometers in the range of +300 to

+538 °C. The medium is 99.9% pure tin, conforming to Federal Specification

QQ-T-371C, Grade A, and can be purchased from Nathan Trotter, Philadelphia,

Pennsylvania

A picture and drawing of the tin bath are shown as Figures 11 and 12,

respectively. It consists of two coaxial cylinders arranged in such a way

as to permit the molten tin to circulate between the walls of the two

cylinders and through the inner cylinder by means of openings at the top

and bottom. The stirring propeller is situated near the bottom of the

inner cylinder, leaving the majority of the space for the reentrant tubes

(not shown in the drawing) into which the thermometers are inserted. The

heater coils are wound on the outside of the outer cylinder. The gradients

in the tin bath range from 0.1 to 0.2 °C. The unknown temperature region

is 76 mm deep.

The evening before the tin bath is to be used, a clock is set to automatically turn the bath on in the early morning hours. This is necessary,

since it takes approximately four hours for the bath to reach a temperature

of 350 °C. If a temperature above 500 °C is needed, the clock should be

set to turn the bath on at 3:00 am.

Before the tin bath can be used, oxidized tin, formed when the bath was

last used, must be removed. To do this, the reentrant tube holder is

removed and placed on the hook attached near the top of the stirring

shaft. The oxide of tin is at the top of the bath and can be removed

easily with special implements stored near the bath. Some residue, which

will cling to the reentrant tubes, is removed and this must be done

immediately after the tubes are withdrawn from the bath. Fresh tin is

added to bring the level of the molten tin within 2 to 3 cm from the top of

the inner cylinder. When all of the oxide of tin has been removed and the

level raised, the tubes are placed back into the molten tin bath. The

stirrer is turned on and the current to the heater coil is adjusted to

control the bath at the desired temperature.

23
V

Fig. 11 . Tin bath.

4.2.5 Cryostat

Calibrations from -1 to -110 °C are made in the cryostat shown as Figure 13. A vertical section drawing is shown as Figure 14. The cryostat

consists of an inner Dewar flask, D, which contains the bath liquid. This

flask is surrounded by liquid nitrogen contained in the outer Dewar flask,

C. The rate of heat transfer between the bath liquid and the liquid

nitrogen is controlled by the presence or absence of gas or air in the

space between the walls of the inner Dewar flask. When the lowest

temperature desired for the day is reached, the rate of heat transfer is

retarded by evacuating the gas or air through the side tube, M, which is

connected to a vacuum system. Vigorous stirring of the bath liquid is

maintained by the propeller, I, which circulates the liquid around the

walls of the stirrer tube, P, similar to the flow of the molten tin in the

tin bath. The temperature of the bath is thermostatically controlled by

24
0 10 20

STIR DRIVE

Fig. 12. Drawing of tin bath.

heater coils, J, wound on the outside of the stirrer tube. The

thermometers are immersed inside the stirrer tube, thus shielding them from

the heater coils

The bath liquid is a five-component mixture containing by weight 14.5% of

chloroform, 25.3% of methylene chloride, 33.4% of ethyl bromide, 10.4% of

transdichloroethy lene , and 16.4% of trichloroethylene . This mixture

freezes at approximately -150 °C, but readily absorbs moisture and becomes

cloudy at somewhat higher temperatures. For this reason calibrations are not performed in this bath below -110 °C. Another liquid that has been

25
Fig. 13. Cryostat.

used as the bath medium is 2 -methylpentane . Measured gradients in the

cryostat did not exceed 0.01 °C. The unknown temperature region is 25 mm

deep

4.2.6 Liquid Nitrogen and Liquid Oxygen Points

A comparison measurement can be made at approximately -196 °C (boiling

point of nitrogen) and -183 °C (boiling point of oxygen). A silvered Dewar

flask with a narrow transparent vertical strip is used as a container for

the liquid nitrogen or oxygen. The liquid is agitated by bubbling nitrogen

or oxygen gas in the corresponding liquid through a glass tube with an outlet near the bottom of the flask. The apparatus, shown with

thermometers inserted, is pictured in Figure 15.

26

Fig. 15. Apparatus used to calibrate thermometers at the boiling

point of nitrogen and oxygen.

5.0 Operational Procedures

5.1 Examination and Preparation of Thermometers for Calibration

Every thermometer submitted for calibration is examined under a 15 to 20

power microscope for defects. One reason for this visual inspection is to

detect a separated mercury column or small droplets of mercury that may be

at the top of the thermometer. This can occur because of rough handling

that may be encountered during shipping. All of the separated mercury must

be reunited with the main column before the thermometer can be calibrated.

There are three ways that the mercury can be reunited.

a) The bulb of the thermometer may be cooled in a solution of common salt,

ice, and water (or other cooling agent) to bring the mercury down slowly

into the bulb. If the salt solution does not provide sufficient cooling,

carbon dioxide snow (dry ice) may be used. Since the temperature of the

28
dry ice is approximately -78 °C, and mercury freezes at approximately

-40 °C, the mercury will solidify. The lower half of the bulb is cooled

and never the stem or mercury column. Moderate tapping of the bulb on a rubber pad or stopper or similar soft spongy object, or the application of

centrifugal force, by swinging the thermometer in a short arc, usually

serves to unite the mercury into the bulb. In the event that the mercury

has solidified, care must be taken to warm the top of the bulb first, so that pressures in the bulb, due to expanding mercury, may be relieved.

b) If there is a contraction chamber above the bulb or an expansion chamber

at the top of the thermometer, the separated portion of the mercury is

first driven into either chamber by warming or cooling the bulb. The

thermometer is then tapped laterally against the hand to shatter the

separated portion into droplets. The thermometer is next heated or cooled

to drive the main column into the contraction chamber or the expansion

chamber to pick up the droplets. If the bulb is heated, it should be done

uniformly. Great care is necessary to avoid filling the expansion chamber

completely with mercury, which might produce pressures large enough to

burst the bulb. The expansion chamber should never be more than 2/3 full.

This procedure should not be used if the thermometer requires heating above

260 °C.

c) As a last resort, especially for thermometers with no expansion

chambers, small separated portions of the column or droplets of mercury at

the top can be converted to mercury vapor by placing the top of the

thermometer in an oil bath (200 to 250 °C) . The vapor condenses in the

cooler capillary, which extends outside of the bath medium. When distillation is complete and no mercury remains at the top of the thermometer, the

thermometer bulb is then placed in the bath and heated, causing the

droplets, which are now on the thermometer scale, to be collected by the

rising mercury column.

The procedure for thermometers containing organic liquids is similar.

Separated liquid in the stem can be vaporized and permitted to drain down

the capillary. Another method consists of gently tapping the stem above

the separation against the palm of the hand, forcing the organic liquid to

break away from the wall of the capillary and flow down the bore to join

the main column.

Rough handling during shipping can also cause gas bubbles to form in the

bulb, a defect that also can be detected during the visual examination.

These gas bubbles will expand at a greater rate than the mercury that

should be in these spaces; therefore, they must be removed. This is done

by a procedure known as "washing" the bulb with a large gas bubble.

Instructions for washing are as follows: Bring all of the mercury into the

bulb as outlined in section (a) . Hold the thermometer in a horizontal

position and gently tap it against the hand to form a large gas bubble in

the bulb. Force the bubble to travel around the wall of the bulb by

rotating the thermometer and tapping it against the palm of the hand. When

the large gas bubble has come in contact with the entire inner surface of

the bulb, rotate the bubble to the top and reunite the mercury as described

above

29
The third reason for examining each thermometer under a microscope is to

Look for foreign material in the capillary and defects in the thermometer.

The foreign materials most often found are glass chips or oxides of

mercury. These objects can hold gas or mercury and cause the reading of

the thermometer to vary when the thermometer is repeatedly inserted into a regulated constant- temperature bath. The capillary of the thermometer must

be clean and free of any foreign material, and it must also appear to have

a uniform diameter. If any variation in the diameter of the capillary can

be seen under the microscope, the thermometer is not acceptable for

calibration. The distance between each scale graduation must be uniform

and the scale must be placed on the thermometer according to NBS

specifications (see Section 2.5). The thermometer must be numbered

correctly, be free of cracks in the glass, and have a serial number. If

any of the above conditions are not met in a thermometer that has been

submitted for calibration, it will be ineligible for test.

5.2 Number and Choice of Calibration Points

A thermometer submitted for test should be calibrated at several points, over at least 80% of the main scale, and at the reference point (if there

is one on the thermometer)

A thermometer is usually calibrated at points spaced uniformly over the

entire range of the main scale. The number of calibration points chosen

depends on the range of scale, graduation interval, and accuracy desired.

The interval between the calibration points should not be unnecessarily

small, nor should it be so large as to destroy confidence in interpolated

corrections for temperature values between the calibration points.

For thermometers not graduated above approximately 200 °C, it is generally

accepted that the interval between these points should not exceed 100 scale

divisions, if the corrected temperature values between the calibration

points are to have an expected uncertainty of approximately one -half of one scale division. If uncertainties of one or two-tenths of a scale division

are desired, it will be necessary to reduce the calibration interval to

every 40 or 50 scale divisions. If a thermometer is graduated above

200 °C, a 40 to 50 scale division calibration interval is required to

produce corrected temperature values with expected uncertainties of

approximately one-half of a scale division, and a 20 to 25 scale division

calibration interval is necessary for expected uncertainties to be

approximately one or two- tenths of a scale division.

The above results were derived from analysis of data taken on more than 50

NBS owned thermometers purchased from 1930 through 1956 for use as laboratory standards. The data indicated that there was considerable

variation among individual thermometers and that scale corrections obtained

over a given interval for a particular thermometer were not sufficient to

predict whether or not more calibration points were required. The above

studies represent only a few of the many types of thermometers submitted to

NBS for calibration and may not necessarily be applicable to other types.

Experience with a particular type of thermometer seems to be the most

reliable guide in the choice of its calibration points.

30
If a thermometer is submitted to NBS for calibration and the calibration

points are not specified on the purchase order, it will be tested at a reference point and at intervals of approximately every 100 scale divisions. If it is an ASTM thermometer, it will be calibrated at the

temperatures suggested in ASTM designation E-l, Standard Specification for

ASTM Thermometers [9]. A calibration should never consist of fewer than

two points on the main scale, and should always be tested at a reference

point, whether on the main scale or on an auxiliary scale.

5.3 Types of Thermometers and How They are Calibrated

Thermometers usually are calibrated according to their types. A particular

thermometer will only be calibrated differently if the customer

specifically requests it. A discussion is presented in this section on the

calibration of several types of thermometers.

5.3.1 Total -immersion Thermometers

Total- immersion thermometers are pointed and graduated by the manufacturer

to indicate correct temperatures when the bulb and the portion of the stem

containing the thermometric liquid are subjected to the temperature being

measured. While these thermometers are designed for immersion of all the

mercury, it is not desirable to immerse the portion of the stem above the

meniscus. The heating of this portion to high temperatures could cause excessive gas pressures resulting in erroneous readings and could possibly

cause permanent damage to the bulb. Distillation of the mercury could also occur

In practice, a short length of mercury column, approximately 6 to 12 mm,

often must be left emergent from the bath or medium being measured so that

the meniscus is visible. If the temperature difference between the bath

medium and its surroundings is large, an appreciable temperature gradient

may exist around the thermometer stem near the surface of the bath. This

condition becomes more serious when a total- immersion thermometer is

intentionally used at partial immersion, perhaps because it is too long for

the calibration bath and cannot be immersed to the proper depth. If either

situation exists, an emergent-stem correction, as explained in Section 6.3,

will be necessary. The correction may be as large as 20 Celsius degrees if

the length of the emergent liquid column and the difference in temperature

between the bath and the space above it are large

If the thermometer has a contraction chamber, it must be immersed well

below the surface of the bath medium. The contraction chamber contains a large amount of mercury and this mercury must be at the same temperature as the mercury in the bulb for the thermometer to give a correct reading. If

there is a large temperature gradient near the surface of the bath, as is

the case in the oil and tin baths, the contraction chamber must be placed

below this gradient, even if this means changing the calibration point.

31
These thermometers are calibrated starting at the lowest temperature

requested and proceeding in sequence to the highest point. At each

calibration point the thermometer must be immersed deeper into the

calibration bath to maintain the proper immersion.

5.3.2 Partial- immersion Thermometers

In many instances the use of a total- immersion liquid- in-glass thermometer

for temperature measurements is inconvenient or impossible. Partialimmersion thermometers are designed with scales graduated to indicate

correct temperatures when the thermometers are immersed to specified

depths. Partial- immersion thermometers must have an immersion line or the

immersion depth engraved or printed on the back. These thermometers are immersed only to the immersion line or specified depth. The portion of the

stem that contains mercury above the immersion line is known as the

emergent stem. It tends to reach ambient temperature or the temperature

prevailing above the calibration bath. Unless otherwise stated, each

Report of Calibration issued by NBS gives corrections which are applicable

for temperatures prevailing above the comparison baths. No stemtemperature correction is necessary when these thermometers are used under

conditions similar to those existing during calibration. However, if

conditions differ, especially the temperature of the emergent stem, the

necessary emergent-stem correction must be calculated as shown in Section

6.3. An unsteady or irreproducible environment surrounding the emergent

stem, together with the inherent difficulty of estimating or measuring the

emergent- stem temperature with sufficient accuracy, can contribute markedly

to the uncertainty of a given thermometer indication. If the emergent stem

is to have a specified stem temperature, as is the case with all ASTM

partial- immersion thermometers, a stem- temperature correction must be made

as described in Section 6.3. For these reasons, tolerances and

uncertainties expected of partial- immersion thermometers are not as stringent as those for total- immersion thermometers.

Calibration points are taken in the same sequence as for total- immersion

thermometers and the same precaution must be followed concerning the proper

immersion of the bulb and contraction chamber.

5.3.3 ASTM Thermometers

Over 120 different thermometer specifications are listed in ASTM

Designation E-l, Standard Specification for ASTM Thermometers [9]. The

thermometers were designed to be used in specific equipment and test

methods and are identified by having the acronym "ASTM" and a number

written on the back. Specification E-l lists the calibration points, stem

temperatures for ASTM partial- immersion thermometers, and any special

procedure that must be followed. An ASTM thermometer should be tested in

accordance with the procedure outline in E-l [9], and E-77, Verification

and Calibration of Liquid- in-Glass Thermometers [4]

32
5.3.4 Calorimetric Thermometers

In some cases it is only necessary to accurately measure a temperature

difference rather than the absolute temperature. Calorimetric thermometers

were designed for this purpose. Since the accuracy of these thermometers at

any one temperature is of less importance than the accuracy of the temperature intervals, no reference point is required. They are usually 600 mm

long, cover a short range of temperature (typically 6 to 16 degrees) , and

are graduated in intervals of 0.01, 0.02, or 0.05 degree. The thermometers

are calibrated at total immersion, usually every 50 to 100 scale divisions

(one or one-half degree intervals), and starting at the lowest point.

Because of the very small capillary diameter, they must be tapped lightly

at each reading to eliminate a possible error due to a sticking mercury

column, and they must be heated to the maximum calibration point before

testing. Heating to the top point initially causes the bulb to expand to

the maximum volume and eliminates the error that will occur because of the

gradual expansion of the bulb as the thermometer is heated. In order to

register accurate temperature differences, the bulb must be expanded before

calibration and use. The thermometer should be calibrated within 2 to 3 hours after it has been heated.

5.3.5 Beckmann Thermometers

A Beckmann thermometer is an enclosed-scale type and is constructed in a manner that permits mercury to be removed from, or added to, the bulb,

making it possible to use the same thermometer for differential temperature

measurements in various temperature ranges [10]. The scale usually

consists of 5 to 6 Celsius degrees (some micro types have a scale

containing only 3 Celsius degrees) and graduated in intervals of 0.01 °C.

The "setting" of a Beckmann thermometer refers to the temperature of the

bulb when the reading on the scale is 0° . When the setting is changed,

enabling the thermometer to be used at a higher or lower temperature range,

the quantity of mercury affected by a temperature change is not the same. Therefore, two equal changes in temperature at different settings cause different indications on the scale, and a "setting factor" must always be

used to convert reading differences into actual temperature differences

whenever the thermometer is used at any setting other than the one at which

the scale was calibrated. These setting factors combine corrections for

the different quantities of mercury during equal temperature changes, and

the difference between the mercury- in-glass scale and the International

Practical Temperature Scale of 1968. Table 3 lists setting factors

calculated for thermometers of Jena 16 111 glass or, its American

equivalent, Corning normal. The scale calibrations for Beckmann

thermometers as reported by NBS are applicable for a setting of 20 °C.

Consequently, the setting factor is 1.0000 at this temperature. For a setting other than 20 °C, the observed temperature difference must be

multiplied by the appropriate setting factor as shown in the example given

below the table.

33
TABLE 3

SETTING FACTORS FOR BECKMANN THERMOMETERS

For any scale length up to 15°

Setting Factor Setting Factor

0°C 0.9935 55°C 1.0092

5 0.9951 60 1.0102

10 0.9967 65 1 .0112

15 0.9984 70 1 .0121

20 1 .0000 75 1.0129

25 1 .0014 80 1.0137

30 1.0029 85 1.0146

35 1.0042 90 1.0154

40 1.0056 95 1 .0162

45 1.0070 100 1 .0170

50 1.0082

As an illustration, suppose the following observations were made:

Setting = 25°C Lower reading = 2.058°

Upper reading = 5.127°

Observed reading = 2.058 5.127

Correction from report = + . 005 - . 008

Corrected upper reading - 5.119

Corrected lower reading = 2 . 063

Difference = 3.056

Difference multiplied by setting factor 1.0014 = 3.060

Corrected difference = 3.060

For most Beckmann thermometers, the large bulb is joined to a fine

capillary (which is backed by a milk-glass scale) by a capillary of much

larger diameter. This large capillary is a source of some uncertainty when

the thermometer is used at partial immersion and this portion is not

entirely immersed. For appropriate emergent-stem corrections refer to

Section 6.3.8.

The Beckmann thermometer is a calorimetric thermometer and must be heated

to the highest test point, calibrated at total immersion, tapped gently

before reading, and calibrated at intervals of every 0.5 degree. Unlike

most thermometers calibrated at NBS , the Beckmann thermometer is calibrated

starting at the highest calibration point, usually the 6 degree point, and

proceeding to the 0 degree point on the scale.

34
5.3.6 Clinical Standard Thermometers

Clinical standard thermometers are used by the manufacturers of fever

thermometers, which are used for measuring body temperatures. In the

United States they are marked in degrees Fahrenheit with a range of

approximately +90 to +112 °F. They are provided with an auxiliary scale

at 32 °F and are graduated in intervals of 0.1 °F. The calibration points

are usually 32, 98, 102, and 106 °F and they are heated to 108 °F before

calibrating to initially expand the bulbs. Since they are heated to 108 °F

before calibrating, the ice points are taken after test. They are generally tested at total immersion and at partial immersion, immersed to

approximately the 92 °F mark.

5.3.7 Kinematic Viscosity Thermometers

When measuring the viscosity of liquids, it is imperative to accurately

measure one specific temperature. Kinematic viscosity thermometers are designed for this purpose and have a short 3 to 5 degree range with an auxiliary scale for an ice point. These thermometers are calibrated at two

points on the main scale. Ice points are measured afterwards.

5.3.8 Low- temperature Thermometers

The use of mercury- in-glass thermometers for low temperature measurements

is limited by the freezing point of mercury, which is -38.9 °C. This limit

may be extended to lower temperatures by forming an eutectic alloy

consisting of mercury and 8.5 percent by weight of thallium. The freezing

point of this alloy is approximately -59 °C. However, small differences in

the quantity of thallium present have the effect of markedly raising the

freezing point of the alloy. It has also been found that some thermometers

containing this liquid have behaved erratically in the range of -59 to

-57 °C. Consequently, thermometers using a mercury- thallium alloy as the

liquid should not be used below -56 °C.

Temperature measurements from -56 °C to approximately -200 °C can be made

by using thermometers containing organic liquids. Alcohol, toluene,

pentane , or other organic liquids, alone or in mixtures, have been used as fluids for low temperature thermometers. All of these fluids have

limitations, and thermometers containing organic liquids are not considered

to be as reliable as thermometers containing mercury or mercury- thallium

alloy.

Organic liquids have the disadvantage of wetting a surface and leaving a film on the wall of the capillary when the liquid column recedes. This may

lead to significant errors in the temperature indications if sufficient

precautions are not taken. The thickness of the film on the capillary wall

will depend, mainly on the viscosity of the liquid, the interfacial action

between the liquid and glass, and the rate at which the thermometer is

cooled. Whenever possible the rate of cooling should be slow with the bulb

cooled first, enabling the viscosity of the organic fluid in the capillary

to be kept as low as possible until the final temperature is reached. This

35
minimizes the amount of liquid left on the capillary wall. Sufficient time

should always be allowed to assure complete drainage. Under adverse

conditions this may take an hour or more.

In addition to good drainage characteristics, a satisfactory low

temperature fluid should not contain water, dirt, or other foreign material

which will separate from the liquid. Because low- temperature thermometers

are frequently designed for use above room temperature, the vapor pressure

of the liquid must be low to prevent distillation at these higher temperatures. Any dye, added to the fluid for improved visibility, should be

chosen for good color fastness with respect to light exposure or chemical

action with the organic liquid.

5.4 Stem- temperature Measurement

When a thermometer is calibrated and used under conditions of total

immersion, no difficulty is encountered when the scale corrections are applied as given on the report. The temperature of the thermometer bulb

and the portion of the stem containing the mercury is definitely defined as being at the temperature of the bath medium.

Occasionally it becomes necessary to use a total- immersion thermometer with

a portion of the stem emergent from the bath medium, which is different

from the calibration conditions of total immersion. The temperature of the

environment above the bath, or apparatus containing the thermometer, may

differ markedly from the temperature of the thermometer bulb. It is also

possible to have pronounced temperature gradients along the length of

exposed mercury column. A correction can be calculated to account for the

difference in temperature between the bulb and the emergent stem. A

reliable estimate of the mean temperature of the emergent stem is required

and should actually be measured. The determination of the stem temperature

should be repeated each time the thermometer is used in this way, or the

accuracy of the correction will depend upon the constancy of the environmental temperature over a period of time. Significant variations in the

temperature of the emergent stem may occur due to air circulation and

variations in ambient temperature, even though the location of the

thermometer does not change.

The same situation occurs in the case of partial- immersion thermometers.

The reported scale corrections apply only for the indicated depth of

immersion and a particular stem temperature. If the thermometer is used

under conditions other than specified, the reported scale corrections are

no longer applicable, and a stem- temperature correction is required.

A faden thermometer gives the most accurate measurement of the emergentstem temperature [11,12]. These thermometers have long bulbs measuring

between 5 and 20 cm, with wall thicknesses and bore sizes nearly the same

as the stem of an ordinary thermometer. The bulb length is selected to

approximate that of the emergent stem whose temperature is to be measured.

The stem of the faden thermometer has a finer capillary than the bulb and

is usually graduated in intervals of 2, 5, or 10 Celsius degrees. The

reading of the faden thermometer will indicate the mean temperature value

36
of the area surrounding the bulb, which is aiso the mean temperature value

of the adjacent portion of the thermometer stem. Stem- temperature

measurements taken at NBS are based upon the use of faden thermometers

whenever possible (see figure 19(b)).

An auxiliary thermometer can be used if a faden thermometer is not

available. It should be approximately 150 mm long with a scale of 0 to

100 °C, graduated in intervals of 1°, and with a conventional bulb of about

10 to 15 mm long (see figure 19(a)). Auxiliary thermometers are used most

often in conjunction with faden thermometers to measure the emergent- stem

temperature of partial- immersion thermometers. Figure 16 shows schemes for

measurement of emergent-stem temperatures.

FADEN THERMOMETER

•BULB

FADEN •THERMOMETER

BULB

LIQUID COLUMN

OF THERMOMETER

IMMERSION LEVEL

7*

AUXILIARY THERMOMETERS

.LIQUID COLUMN

OF THERMOMETER

777 777777

(c) PARTIAL IMMERSION

7777777.

n J.

7777 7777 777.

(b) PARTIAL IMMERSION

S

(a) TOTAL IMMERSION

LIQUID COLUMN

OF THERMOMETER

Fig. 16. Schemes for measurement of emergent-stem temperatures.

5.5 Checking the Standard Platinum Resistance Thermometer at the Triple

Point of Water

Every day the standard platinum resistance thermometer is used, its

resistance is determined at the triple point of water to check whether it

is still in calibration and to obtain the resistance at the 0 °C point for

the purpose of calculating the temperature of the bath medium (see Section

6.1). This is done by placing the standard platinum resistance thermometer

in a properly prepared triple point of water cell [13]. The reentrant well

of the triple point of water cell is first filled with ice water. A small

37
piece of foam is placed at the bottom of the reentrant well, enabling the

standard platinum resistance thermometer to have something soft on which to

rest. An aluminum bushing, which is approximately 50 mm long, is placed

inside of the reentrant well on the foam and is made to fit snugly around

the portion of the standard platinum resistance thermometer containing the

platinum coil. Before inserting the thermometer in the cell, it should be

checked to see that the ice mantle is moving freely around the reentrant

well. If not, a warming rod is inserted for a short interval to melt the

ice around the well. After inserting the standard platinum resistance

thermometer, it is covered with a black cloth to eliminate any error in the

resistance reading caused by ambient room radiation, especially from

ceiling lights. The standard platinum resistance thermometer is allowed to

remain in the triple point of water cell for a minimum of 15 minutes to

equilibrate with the current on. The AC bridge is balanced and the

resistance at the triple point of water is recorded.

The resistance value on the standard platinum resistance thermometer is

compared with previous resistance values at the triple point of water. If

the value has changed by an amount equal to or exceeding 0.001 °C, then the

standard platinum resistance thermometer is sent to the platinum resistance

thermometer calibration laboratory for recalibration.

It is desirable to determine the resistance at 0 °C under the conditions at

which the thermometer is used to measure temperatures. Changes in the

thermometer can occur faster at higher temperatures and, therefore, as a laboratory practice, if the standard platinum resistance thermometer is

going to be used below 150 °C, the triple point of water is taken at the

beginning of the day. If the standard platinum resistance thermometer is

going to be used above 150 °C, the triple point of water is taken at the

end of the day, after being out of the bath medium for at least 15 minutes.

5.6 Use of Ice Bath

A fresh ice bath is made each time it is needed. (An ice bath from a previous day is discarded.) As ice melts throughout the day, water is

siphoned off and new ice added. When it is determined that the ice is not

floating and that there is no excess water at the surface of the ice, then

the bath is ready for use.

For proper calibration at 0 °C, each liquid- in-glass thermometer should be

inserted to a specified depth (the immersion depth) into the ice bath.

Total- immersion thermometers should be inserted into the ice bath until the

0 °C mark on the thermometer scale is within one scale division of the top

of the bath. For partial- immersion thermometers, the depth is indicated

either by an additional line scribed on the glass (immersion line) or by

a number given on the back of the thermometer. In order to prepare the

bath to accept the thermometer, an area of ice at the center of the bath

is loosened with an object such as a clean glass rod and at a depth

approximately equal to the immersion depth.

The thermometer to be calibrated at the ice point is cleaned with cool

distilled water. (Never rinse with warm water, since it may expand the

38
bulb.) The thermometer is gently placed through the holder and into the

region of loosened ice. If the thermometer touches a firm surface before

it is immersed to the immersion line or 0 °C mark, the thermometer should

be removed and the ice loosened further down into the bath to enable the

thermometer to be immersed to the proper depth. If the thermometer does

not rest on a firm foundation and the immersion line or 0 °C mark passes

below the surface of the bath, it must be repacked and an area of ice

loosened to a more shallow depth.

After the thermometer is properly immersed and is being held perpendicular

to the observer's telescope, ice is firmly packed around the thermometer.

It is important to keep the ice clean while using the ice bath. The

operator's hands should also be kept clean or plastic gloves should be used

for this purpose. When the thermometer is resting on a solid section of

ice in the bath and cannot be immersed further, when it is perpendicular

to the telescope, when ice is firmly packed to the immersion line or one scale division below the 0 °C mark, and when any excess water is siphoned

from the ice bath, then the thermometer is ready to be read as shown in

Figure 17.

Fig. 17. Thermometer properly placed in the ice point bath.

The thermometer should remain in the ice bath for approximately one or two

minutes, or until the readings no longer change. (Thermometers using

organic fluid instead of mercury as the liquid will require approximately

39
15 minutes, because the organic fluid tends to cling to the wall of the

capillary.) When stability is reached (the meniscus stops moving), the

operator gently taps the thermometer to free a possible sticking mercury

meniscus and records the ice-point reading.

5.7 Placement of Thermometers in Calibration Baths

The thermometers to be calibrated are placed in the calibration bath in a circular arrangement with the standard platinum resistance thermometer in

the middle of the group within the circle. This placement is shown in

Figure 18. Total- immersion thermometers are immersed with the meniscus of

the mercury column approximately 6 to 12 mm from the surface of the bath

medium, and partial- immersion thermometers are immersed to the immersion

line or to the specified depth. The check standard thermometer, which is

placed in the bath to monitor the system as discussed in Section 8, is

placed at the end of the batch. It is essential that the bulb and

contraction chamber of each thermometer being calibrated be below the

unknown temperature region near the top of the calibration bath (see

section 4.2).

Fig. 18. Placement of thermometers in holder of a calibration bath.

40
5.8 Placement of Faden and Auxiliary Thermometers for Measurement of Stem

Temperatures

Faden or auxiliary thermometers, or their combinations, are used to measure

the mean emergent-stem temperature from the immersion line to the top of

the mercury column (meniscus) of the partial-immersion thermometer.

Figure 19(a) shows an ASTM 33C thermometer, which is being calibrated at

40 °C. The correction should reflect an emergent-stem temperature of 30 °C as specified by ASTM E-l, Standard Specification of ASTM Thermometers [9].

The length of the emergent-mercury column is 314 mm. In this example

two auxiliary thermometers are used to measure the temperature of the

emergent-mercury column. The centers of the auxiliary thermometer bulbs

are placed adjacent to the stem at distances of 105 mm and 209 mm from the

immersion line. The indication of the bottom auxiliary thermometer gives

the average temperature of the lower portion of the emergent stem of the

thermometer under test and the top auxiliary thermometer gives the average

temperature of the upper portion of the emergent stem. The average

temperature of the emergent stem is the average temperature of the two

auxiliary thermometers.

A combination of faden thermometers can also be used to measure the

emergent-stem temperature as shown in Figure 19(b). Two faden

thermometers, of 200 mm and 114 mm bulb lengths, are placed adjacent to the

emergent-mercury column. The bottom of the 200 mm faden thermometer bulb

is placed in a horizontal plane with the immersion line. The bottom of the

114 mm faden thermometer bulb is placed with the bottom on its bulb in a horizontal plane with the top of the 200 mm faden thermometer bulb.

Instead, a 200 mm and a 100 mm faden thermometer could be used along with

an auxiliary thermometer to measure the emergent- stem temperature of the

remaining top 14 mm portion.

Figure 20(a) shows an ASTM 34C thermometer with one auxiliary thermometer

being used to measure the emergent-stem temperature. The thermometer is

being calibrated at 45 °C and the correction should reflect a stem temperature of 37 °C as specified in ASTM E-l, Standard Specification for ASTM

Thermometers [9]. The emergent-stem temperature must be measured to

determine whether it is 37 °C and, if it is not, to correct for the

difference. There is a 120 mm length of emergent-mercury column from the

immersion line to the meniscus. The center of the auxiliary thermometer

bulb is placed at the 60 mm distance. The temperature indication of the

auxiliary thermometer, will be the average temperature of the emergentmercury column adjacent to it. If a faden thermometer is available, it

should be used instead of the auxiliary thermometer. This is shown in

Figure 20(b) . The faden thermometer bulb should be as long as the

emergent -mercury column plus or minus 8 or 9 mm. Since a 120 mm faden

thermometer is not available, either a 114 mm or a 129 mm faden thermometer

can be used. The bottom of the 114 mm faden thermometer bulb is placed in

a horizontal plane with the immersion line.

It is essential that the bulb and the contraction chamber of liquid- inglass thermometers be below the unknown temperature region. In the

41
n

A I

209 mm

'A I

78 D*gr««s

15 Dagraas

i

Fig. 19(a). Measuring the emergent- stem temperature of an ASTM

33C thermometer using two auxiliary thermometers.

42
I

Fig. 19(b). Measuring the emergent-stem temperature of an ASTM

33C thermometer using two faden thermometers.

43
A t

/K

20 Degree*

A I

A

1 5 Degrees

Fig. 20(a) . Measuring the emergent-stem temperature of an ASTM

34C thermometer using one auxiliary thermometer.

44
Fig. 20(b). Measuring the emergent-stem temperature of an ASTM

34C thermometer using one faden thermometer.

45
cryostat and water bath, the top of the bulb or the top of the contraction

chamber must be immersed a minimum of 25 mm. In the oil baths the bottom

of the bulb must be immersed a minimum of 76 mm and the top of the

contraction chamber immersed a minimum of 50 mm. In the tin bath the

bottom of the bulb must be immersed 130 mm and the top of the contraction

chamber 76 mm. If it is not possible to calibrate at a temperature

requested because of this restriction, the calibration point must be

changed to one higher on the scale to permit adequate immersion of the bulb

and contraction chamber.

Occasionally it is necessary to immerse a partial- immersion thermometer

more than the specified depth. An example of this is the ASTM 11C

thermometer. It is made to be used at an immersion of 25 mm and has a scale from -6 to +400 °C. When calibrating this thermometer, it is

essential that the bulb not be in the unknown temperature region of the

bath medium. In this case it would be necessary to immerse the ASTM 11C

thermometer deeper into the bath medium until the bulb is in the known

temperature region.

For the ASTM 11C thermometer, it is necessary to measure the temperature of

the emergent stem and correct for any difference there might be between the

observed value and the value specified in ASTM E-l, Standard Specification

for ASTM Thermometers [9]. When the faden thermometer is placed adjacent

to the stem from the immersion line to the meniscus, the lower portion of

the faden thermometer will be in the bath medium also. The error introduced by immersing the ASTM thermometer too deep will be corrected

when the stem- temperature correction is calculated (see Section 6.3). The

bottom of the faden thermometer bulb must always be in a horizontal plane

with the immersion line of the partial- immersion thermometer no matter

where the immersion line may be. This example is shown in Figure 21(a).

If the partial- immersion thermometer is not an ASTM thermometer, a stemtemperature measurement would not be made. However, a correction must

still be made for the error in the thermometer reading due to a portion of

the stem above the immersion line being in the bath medium. This correc- tion is referred to as a too-deep immersion correction.

When the thermometer is placed in the bath, it is noted how deep the

immersion line is under the bath surface. This distance is measured in

mm. The center of an auxiliary thermometer bulb is placed above the

meniscus of the partial- immersion thermometer exactly one-half the distance

that the thermometer is placed too deep into the bath. For example, if a partial- immersion thermometer is placed in a bath with the immersion line

50 mm below the surface of the bath, the center of the bulb of an auxiliary

thermometer should be placed 25 mm above the meniscus. This scheme is

shown in Figure 21(b), using the ASTM 11C thermometer discussed above as an example. The location of the auxiliary thermometer must be changed for

each calibration point (as the meniscus rises) and the room temperature

must be recorded as part of the data.

When corrections are given for total-immersion thermometers, they are applicable for the portion of the stem containing the mercury being at the

46
Fig. 21(a). Measuring the emergent—stem temperature of an ASTM 11C

partial- immersion thermometer with the immersion line

below the surface of the bath medium.

47
1\

156 Degrees

X

28.2 Degrees

si/

I

Room Temperature

0

25 mm

I

50 mm

Fig. 21(b). Placement of auxiliary thermometers needed to obtain

data for a too-deep immersion correction.

48
same temperature as the bulb. Because of the 50 mm region of unknown

temperature near the top of the oil baths and a 76 mm region of unknown

temperature near the top of the tin bath, a faden thermometer must be

placed in the bath to determine the temperature of this unknown region and

to correct for the temperature difference. A 100 mm faden is used for this

measurement in the oil baths (for temperatures above 150 °C) and a 200 mm

faden is used in the tin bath. The top of the faden bulb is placed on a horizontal plane with the meniscus of the thermometer under test as shown

in Figure 22.

The gradients of the unknown region in the cryostat, water bath, and in the

range of 100 to 150 °C in the low temperature oil bath do not result in

corrections. Experimentation and calculations have indicated that the

stem- temperature error is not significant when a portion of the stem

containing mercury is in this region of these baths.

5.9 Regulating the Bath, Reading Sequence, and Recording Data

In most cases thermometers are calibrated at NBS from the lowest point to

the highest point as requested by the customer. If the highest point is

300 °C or above, an ice point is taken and the highest point is calibrated

first. Three days later the ice point is taken again and compared with the

first ice point. If they agree within the uncertainty of that particular

type of thermometer (see Tables 14-17) , then the thermometer calibration is

completed starting from the lowest point to the highest point. If the ice

points do not agree within the uncertainty value, the thermometer is found

ineligible for test because of improper annealing or improper thermometer

glass

The lowest calibration point on most liquid- in-glass thermometers

calibrated at NBS is the ice point (0 °C) . The ice-point readings are recorded for each thermometer in a set. The thermometers are placed in the

calibration bath and the temperature of the bath medium is regulated.

Maximum current is directed to the heater coils to bring the temperature of

the medium within plus or minus one scale division of the calibration

point. Regulation is maintained by adjusting current to the coils through

a rheostat enabling the bath temperature to rise at a rate of no more than

one scale division in 3 minutes.

Control in the cryostat is maintained through the use of two separate sets

of heating coils. One set is manually adjusted to cause the temperature of

the bath to decrease slowly. The current in the second set of heating

coils automatically turns on or off to control the temperature of the

medium in a narrow range

When the bath temperature regulation is maintained, the thermometers are read and data recorded in the following sequence: standard platinum

resistance thermometer, thermometers TO through TX, standard platinum

resistance thermometer, thermometers TX through TO, standard platinum

resistance thermometer. Whenever the standard platinum resistance

thermometer is read, it is placed in front of the telescope to help

minimize errors due to temperature gradients in the calibration bath. A

49
hi

-7K

50 mm

100 mm

V

Fig. 22. Measuring the temperature of the portion of a total- immersion

thermometer stem that is in the unknown temperature region of

the oil bath using a 100 mm faden thermometer.

50
current of 1 ma is used for the standard platinum resistance thermometer

and the amplification is adjusted so that the value in the seventh dial

(0.00001 fl) can be seen. The phase is adjusted to zero on the AC bridge

meter. The phase/signal selector switch is changed to signal and the

bridge dials are set to produce a null on the meter. The dial readings are recorded. Thermometers graduated in 0.01, 0.02, 0.05, or 0.1 degree are read to three decimal places; thermometers graduated in 0.2, 0.5, or 1.0

degree are read to two decimal places; and thermometers graduated in 2.0 or 5.0 degrees are read to one decimal place. One of the thermometers that is

calibrated, usually thermometer TX, is an NBS owned check standard, which

will be discussed in Section 8. Any faden or auxiliary thermometers used

for stem- temperature determinations are read and recorded after this

sequence. The room temperature is recorded if a too-deep immersion

correction is to be made. A sample data sheet for a routine batch

calibration is shown in Table 4. A sample data sheet incorporating all of

the stem- temperature corrections shown in the examples in Section 5.8 is

given in Table 5. Both examples show data taken by one operator.

If two calibration operators are available, one should record the observed

thermometer readings while the other reads the thermometers. The two

operators should switch positions and take a second set of readings. It is

preferable to have two observers, since this procedure will reduce operator

bias and reading errors.

After a set of data is obtained at a calibration point, it is inspected to see that it looks reasonable. The calibrator examines the data for reading

errors and to insure that the temperature of the calibration bath rose at

the rate stated above. It is not acceptable for the temperature of the

bath to decrease while data is being recorded.

6.0 Calculations

Once the data has been recorded in the format shown in Tables 4 and 5, and

after inspection indicates that there are no suspicious data points, the

corrections to the thermometers are computed as explained in the following

sections

6.1 Computation of Bath Temperature

The data given in Table 4 for a routine batch calibration is reproduced in

Table 6 with computations added. The thermometers in the example are all

total immersion, with a range of -2 to +102 °C, and graduated in intervals

of 0.2°.

The first step is to average the two resistance values determined for the

standard platinum resistance thermometer at the triple point of water taken

on the day the calibrations were performed. This average resistance value

at the triple point of water, R(TP) , is converted to the resistance value

at the ice point, R(0) , by multiplying it by a factor of 0.99996101, which

51
TABLE 4

SAMPLE DATA SHEET

ROUTINE BATCH CALIBRATION

READINGS

NBS TEST NUMBER CK. STD. BRIDGE SPRT

TO Tl T2 T3 5 445

25.46480

-0.10 -0.10 +0.03 -0.11 25.46480

19.92 19.94 19.93 19.71 27.48504

19.93 19.95 19.93 19.71 510

515

39.90 39.90 39.88 39.67 29.48379

39.92 39.91 39.88 39.67 390

402

59.86 59.93 59.89 59.67 31.48629

59.86 59.94 59.90 59.67 633

638

80.03 79.96 79.90 79.81 33.48653

80.04 79.96 79.90 79.81 659

664

99.88 99.86 99.86 99.74 35.44998

99.88 99.88 99.87 99.74 5005

5019

52
TABLE 5

SAMPLE DATA SHEET STEM-TEMPERATURE CORRECTIONS

READINGS

NBS TEST NUMBER

T1 T5 T6 T7 ASTM 33C ASTM 31C ASTM 11C

50 MM 50 MM 25 MM IMMERSION IMMERSION IMMERSION

CK. STDS.

T8 T9 BRIDGE SPRT5 115 FADEN AUXILIARY

0.13 +0.5 +0.132 0.18

39.96

39.97 39.921 39.936

39.96

39.97 39.921 39.936

11.86

11.87 11.80711.809

11.86

11.87 11.807 11.809

100.52

100.52

150.

150.1

150.1

150.1

100.10

100.10

118.82 118.82

118.83

118.83

25.16180

25.16180

29.50189

196

199

29.50189

196

199

29.98976

989

999

29.98976

989 999

35.17688

698

707

10.19077

096

106

10.19180

190 200

AUX1

18

AUX1 AUX2

31 26

200 MM

30.0

111 MM

25.0

AUX1 33

1 11 MM

33.3

103 MM

112.9

100 MM 110.0

100 MM

110.0

AUXI RT

32 21

199.50

199.50

199.56

199.56 15.08799

829

859

100 MM

187.0

53
TABLE 6

SAMPLE DATA SHEET

ROUTINE BATCH CALIBRATION COMPUTATIONS

NBS TEST NUMBER CK. STD. BRIDGE SPRT

TO Tl T2 T3 5 445

25.46480

-0.10 -0.10 +0.03 -0.11 25.46480

R(TP)=25.46480a +0.10 +0.10 -0.03 +0.11 f R(0)=25.46381b

19. 92 19. 94 19. 93 19. 71

19. 93 19. 95 19. 93 19. 71

+ 05 + . 03 + 04 + 26*

39 90 39 90 39 88 39 67

39 92 39 91 39 88 39 67

07 06 04 + 17

59 86 59 93 59 89 59 67

59 86 59 94 59 90 59 67

+ 01 07 03 + 20

80 03 79 96 79 90 79 81

80 04 79 96 79 90 79 81

.04 + 04 + 10 + 19

99 .88 99 86 99 .86 99 74

99 .88 99 .88 99 .87 99 74

.00 + .01 + .02 + .14

t=19.97 °Ce 27.48504

510

515

R(t)=27. 48510°

R(t)/R(0)=1.079379d

t=39.84 °C 29.48379

390

402

R(t)=29. 48390

R(t)/R(0)=l. 157875

t=59.87 °C 31.48629

633

638

R(t)=31 .48633

R(t)/R(0)=l. 236513

t=80.00 °C 33.48653

659

664

R(t)=33. 48659

R(t)/R(0)=l. 315066

t=99.88 °C 35.44998

5005

5019

R(t)=35. 45007

R(t)/R(0)=l. 392175

Footnotes

a average resistance at triple point of water

b resistance value at 0 °C

c average resistance value

d resistance ratio

e temperature of bath medium

f corrections given on Reports of Calibration for

thermometers tested at temperature e

54
was derived from information given in NBS Monograph 126, Platinum

Resistance Thermometry [13] and the article in Metrologia, The International Practical Temperature Scale of 1968 Amended Edition of 1975 [5].

Since the derivation of this factor is not explicitly outlined in either of

the above publications, it is explained below.

The triple point of water cell has an axial well for the thermometers and

the triple point temperature is obtained whenever the ice is in equilibrium

with a liquid-vapor surface. The equilibrium temperature t 6 8 between the

ice and liquid water at a depth h below the liquid-vapor surface is given

by:

t 68 = A + Bh

A = 0.01 °C

B = -7*10"* nf 1 °C

h - height of the water column in the triple point cell

from the middle of the SPRT coil to the water surface

(Note: * indicates multiplication throughout the text)

The value h varies from cell to cell. Since the hydrostatic head of water

from the middle of the SPRT coil to the water surface of the cell used for

the calibration given in Table 6 was 0.315 m, the value t 68 of the triple

point of water is calculated to be:

t68 = A+Bh

t68 = 0.01+(-7*10-4 )*(0.315)

t68 = +0.0097795

To convert t68 to t' the m(t') relation is used (c f

, equation 10 of

reference [5]). Then there is obtained:

t' = (0.0097795)*(1. 000450)

The value for the resistance at 0 °C, R(0) , is calculated from the resistance at the triple point of water according to the following formula:

R(t)/R(0) = l+At'+Bt' 2

Since t' 2 is very small, the last term is dropped. The value A is determined from the formula:

A = aCl+S/100)

The a and 6 values are given with the report of calibration for each

standard platinum resistance thermometer. For the resistance thermometer

used in Table 6 the value of a was 0.003926378 and S was 1.496448. The

value A is calculated to be:

55
A = A = A =

a(l+6/100)

(0. 003926378)* [1+(1. 496448/100)]

0.0039851342

Knowing the value for A and the value t' at the triple point of water, the

factor used to convert the R(TP) value to the R(0) value can be determined

as shown below:

R(TP)/R(0) = 1+At'

R(0) = R(TP)*[(1/(1+At')]

R(0) = R(TP)*[l/(l+(0. 0039851342)*(0. 0097839))

R(0) = (25. 46480)*(0. 99996101)

R(0) = 25.46381

After the value R(0) is determined, the calculation of the bath

temperatures can be made. The first step is to find the average of the

three resistance readings at each temperature. This value is called R(t)

Since the tables computed for the standard platinum resistance thermometers

are based on a ratio of the resistance at a stated temperature to the

resistance at the ice point (the ratio of R(t)/R(0)), the value R(t) at

each calibration point must be divided by R(0) . The computation of the

value R(t)/R(0) for the first temperature in Table 6 is given below:

R(t) = 27.48510

R(0) = 25.46381

R(t)/R(0) = 1.079379

It is then determined where in the platinum resistance thermometer table

this ratio falls. A portion of the table for the standard platinum resistance thermometer used in the example is given in Table 7 . The computed

value for R(t)/R(0) of 1.079379 is between 19 and 20 °C. The temperature

of the calibration bath medium is, therefore, 19 and some decimal value.

To obtain the decimal portion of the temperature, the R(t)/R(0) value at

19 °C is subtracted from the R(t)/R(0) value in the example and the

difference is multiplied by the inverse difference, which is the inverse

(reciprocal) of the difference between successive values of R(t)/R(0)

given on the line at 20 °C. This procedure is shown below:

The table value for R(t)/R(0) at 19 °C for PRT 445 is 1.075531

The table value for R(t)/R(0) at 20 °C for PRT 445 is 1.079494

The value 1.079379 falls between these two ratios.

The temperature of the calibration bath will be 19. XX.

From R(t)/R(0) subtract R(t)/R(0) at 19 °C and multiply by the inverse

difference given for the nominal temperature of 20 °C.

56
TABLE 7

ONE PAGE OF A STANDARD PLATINUM

RESISTANCE THERMOMETER TABLE

October 17, 1978, IPTS-68 Table

Temp. Resi ^fcmrp J.11VC1 °C Ratio Diff

o 1-L • 000000 WWW 250 78

1 1 003986 250^86

2 1 007971 250 94

3 l! 011955 251 ! 01

4 l' 015938 251 ! 09

5 l! 019919 251 ' 17

6 1 023900 251 24

7 1 027878 251^32

8 1 031856 251 40

9 1 035833 251 ! 48

10 1 039808 251 55

11 1 043782 251 ! 63

12 1 047755 251 71 13 l! 051727 251.79

14 1 055697 251 86

15 l! 059666 251.94

16 1 063634 252 02

17 1.067601 252.09

18 1 071567 252 17

19 1. 075531 252.25

20 1 079494 252 33

21 1.083456 252.40

22 1 087417 252 48

23 1 091376 252 56

24 1 095334 252 64

25 1 099291 252.71

26 1 103247 252.79

27 1 . 107202 252.87

28 1.111155 252 95

29 1 115107 253.02

30 1 119058 253 10

31 1.123008 253 . 18

32 1 126957 253 26

33 1.130904 253.34

34 1.134850 253.41

35 1.138795 253.49

36 1.142739 253.57

37 1.146681 253.65

38 1.150622 253.72

39 1.154562 253.80

40 1.158501 253.88

41 1.162439 253.96

42 1.166375 254.04

43 1.170311 254.11

44 1.174245 254.19

45 1.178178 254.27

46 1.182109 254.35

47 1.186040 254.43

48 1.189969 254.50

49 1 . 193897 254.58

50 1.197824 254.66

for Resistance Thermometer 445

INfcio .Lis L-dl R_-t: XI LVcLiDC °c U 1 1 1 .

50 1 1 Q7894

51«yx X1 . 901 749 /

t-+.y Z__>H- . / 52 1 905674 954 «9

53 1 909597 954 89

54 1 911519 9SZl Q7

55 1 91 7/1/1

Q

X « Z_X / 1 TVy 9SS OS

56 X1 . 991159 Z.Z. J )~J y 57 1 995978 955 Z-J J . 91Z.X 58 1X 999195 z. z. y 1 y _y 955 99

59 1.233111 955 16

60 1x . 917096 Z..J / Vy/_U 955 LL

61 1 . 240939 255 52

62 1 ! 244852 255 60

63 1 ! 248763 255^68

64 1 ! 252673 955 75

65 l' 256582 255.83

66 1 960489 955 £. . 91y x 67 1 264396 255 . 99

68 1 968301 956 07

69 1 . 272205 256.15

70 L 276108 256^22

71 1x > 280009 t-uwvy 256 '. 30

72 1 983910 256 38

73 1 287809 256*46

74 1 . 291707 256 54

75 1 ! 295604 256^62

76 1

'. 299499 256 70

77 303394 256^78

78 1 307287 256 85

79 1.311179 256^93

80 1 31 5070 957 Z__^ / . 01v/X 81 X1 . 318960 X*J J\J\J 257.09

82 1 322848 957 Z__/ / . 17X / 83 1

' 326736 257 25

84 1.330622 257.33

85 1.334507 257.41

86 1.338390 257.48

87 1.342273 257.56

88 1.346154 257.64

89 1.350034 257.72

90 1.353913 257.80

91 1.357791 257.88

92 1.361668 257.96

93 1.365543 258.04

94 1.369417 258.12

95 1.373290 258.20

96 1.377162 258.27

97 1.381033 258.35

98 1 . 384902 258.43

99 1.388771 258.51

100 1 . 392638 258.59

57
R(t)/R(0) = 1.079379

R(t)/R(0) at 19 °C = 1.075531

Difference = 0.003848

Decimal Value = Difference*Inverse Difference

Decimal value = (0 . 003848)*(252 . 33)

Decimal value =0.97

The calculated temperature of the calibration bath at the first calibration

point is 19.97 °C.

This procedure is repeated at each calibration point to determine the

temperature of the calibration bath medium.

6.2 Determining Corrections of Thermometers Being Calibrated

After the correct temperature of the calibration bath medium is calculated

at each calibration point, corrections for thermometers TO, Tl , T2 , and

check standard, T3 , are determined.

The two readings of each thermometer being calibrated and the check

standard are averaged and compared with the computed temperature of the

bath medium. If the thermometer under test reads higher than the bath

temperature, the correction is negative; if the thermometer under test

reads lower than the bath temperature, the correction is positive.

Using the data taken for the thermometers in Table 6 at the first calibration point and the computed bath temperature of T=19.97 °C, we calculate

that their respective corrections are +0.05, +0.03, +0.04, and +0.26 °C at

20 °C. This procedure is followed for the other temperatures, thereby

generating the data for the Reports of Calibration for these three

thermometers

(The Report of Calibration for thermometer serial number TO is given as Figures 24 and 25 .

)

Readings at the ice point are taken on the thermometers that were calibrated not less than 72 hours after test. The second readings at the

ice point should agree with the initial ice-point readings within the

expected uncertainty of the thermometer. Thermometers with a range of 0 to

+100 °C and graduated in 0.2° have an expected uncertainty of 0.05° at the

calibration points. The ice point readings should agree within this

limit. If the two ice point readings are not in agreement, indicating that

the bulb has not recovered from expanding after heating (due probably to

improper annealing) , then the thermometer must be completely recalibrated.

The data are analyzed to see if the results are reasonable. A very useful

technique for analysis is to plot the calibration data. An example for a total -immersion thermometer graduated in 0.2 °C divisions is shown in

Figure 23. The corrections at 80 °C and 100 °C are suspect for two

reasons: 1) the magnitude of the difference between two adjacent

corrections is approximately one scale division, and 2) the sign of the

correction changes. A deviation curve as shown in Figure 23 is possible

58
.20

I

Uncertainty

.10 c

o

o

a>

i—

l_oO

.00

1 Scale

Division

0 20 40 60 80 100

Temperature °C

Fig. 23. Thermometer correction versus temperature.

for liquid- in-glass thermometers. If these data were taken by two

observers, the probability for reading error is small and recalibration in

this case is not necessary. If, on the other hand, the data were obtained

by one observer, the thermometer should be recalibrated at 80 °C and

100 °c.

The plot may indicate another effect. If the trend of the curve is

downward as the temperature is increased, the thermometer probably has gas

in the bulb. The gas must be removed (see Section 5.1) and the thermometer

retested.

6.3 Stem-Temperature Corrections

If the thermometer being calibrated is a total- immersion thermometer used

at partial immersion, with a portion of the emergent stem containing the

liquid above the bath or in the unknown temperature region, or a partial

immersion thermometer requiring a correction that reflects a specified

emergent-stem temperature, it will be necessary to correct for the

variation in the stem temperature.

The following formula, or some variation of it, will be used to determine

stem- temperature corrections.

Stem- temperature correction = kn(tobs - t sp )

k = differential expansion coefficient of mercury (or other

thermometric liquid) in the particular kind of glass of which

the thermometer is made

59
n = number of scale degrees equivalent to the length of emergent

stem (including the evaluated region above the immersion line)

tobs = observed mean temperature of the emergent stem (Faden or auxiliary thermometer reading)

t sp = specified mean temperature of the emergent stem (for which

reported scale corrections apply)

All stem- temperature corrections require that four values be determined.

The first value is the differential expansion coefficient of mercury (or

other thermometric liquid) in the particular kind of glass from which the

thermometer is made (k) . The coefficient k varies for different kinds of

glass, or for different temperature intervals, i.e, different values of

(tj^-t). For purposes of computing the emergent-stem correction, the value

of k may be considered as depending on the average of t 1 and t. Values of

k as the function of (t x +t)/2 for two widely used thermometric glasses are given in Table 8. If the kind of glass is not known, it is permissible to use k=0 . 00016 for mercury thermometers graduated in degrees Celsius and

k=0. 00009 for mercury thermometers graduated in degrees Fahrenheit.

The expansions of liquids such as alcohol, toluene, etc., vary quite

rapidly with the temperature causing k to vary considerably for different

temperature intervals. An approximate stem correction for such thermometers may be calculated by setting the value of k as equal to 0.001 for

Celsius thermometers or 0.0006 for Fahrenheit thermometers.

The second value needed for computing the stem- temperature correction is

the number of scale degrees equivalent to the length of emergent stem (n)

This is essentially the number of degrees that is in the incorrect

temperature environment. If it is a total- immersion thermometer with a portion of the stem above the bath, then the value n would be the number of

degrees from the degree mark at the surface of the bath medium to the

meniscus (the top of the mercury column). If the thermometer is a partial- immersion thermometer, the value n would be the number of degrees

from the immersion line to the meniscus. Since partial- immersion thermometers are not graduated to the immersion line, there is a portion of the

stem containing no scale divisions. It must be determined how many degrees

could be inscribed on this portion of stem and the number included in the

value n. One way of doing this is to measure the distance from the

immersion line to the lowest scale graduation, then move the ruler on the

thermometer scale and determine how many degrees this distance represents.

The third value needed is the observed average temperature of the emergent

stem (tobs ). This value is found by actually measuring the temperature

environment where the emergent stem is located. The preferred way of doing

this involves the use of faden thermometers. Because the availability of

faden thermometers is limited, the emergent-stem temperature can also be

measured using one or more auxiliary thermometers, which are usually not as reliable [12]. whether one, two, or even three faden or auxiliary thermometers are needed depends on the length of mercury column emergent from the

bath. Any combination of faden and/or auxiliary thermometers can be used

for this purpose.

60
TABLE 8

VALUES OF THE DIFFERENTIAL COEFFICIENT OF CUBICAL EXPANSION

OF MERCURY IN GLASS (k) FOR MERCURY- IN -GLASS THERMOMETERS

Table 8(a)

Mean Temperature k k

(ti + t) / 2 "Normal" Glass "Borosilicate" Glass

For Celsius Thermometers

0° 0.000158 0.000164

100 .000158 .000164

150 .000158 .000165

200 .000159 .000167

250 .000161 .000170

300 .000164 .000174

350 .000178

400 .000183

450 .000188

For Fahrenheit Thermometers

0° 0.000088 0.000091

200 .000088 .000091

300 .000088 .000092

400 .000089 .000093

500 .000090 .000095

600 .000092 .000097

700 .000100

800 .000103

Table 8(b)

Bath Temperature °C

Faden 150 200 250 300 350 400 450 500 550

Thermometer

Reading °C

100 000165 166 167 168 170 171 173 176

150 165 166 167 169 171 173 175 177

200 166 167 169 170 172 174 176 179

250 167 168 170 172 174 176 178 181

300 170 172 174 176 178 180 184

350 174 176 178 180 183 186

400 178 180 182 185 189 193

450 182 184 189 193 197

500 197 201

61
TABLE 9

NBS TEST NUMBER

T4 T5 T6 T7 ASTM 33C ASTM 34C ASTM11C

50 ran 50 ran 25 run IMMERSION IMMERSION IMMERSION

-K3.U3 +0.5 - .5.0

-0.43

SAMPLE DATA SHEET STEM-TEMPERATURE CORRECTIONS

COMPUTATIONS

CK. T8

STDS.T9

-0.5

+0.132 +0.1*

-0.132 -0.1*

BRIDGE SPRT

5 445

25.46480

25.46480

R(TP)=25. 46480

R(0) =25. 46381

FADEN AUXILIARY

AUX1 18

(19*18)/19=18

0.00016*34. 2*(18-18)=.0

39.96 39.97

+.06

-.02e

39.924

39.936

+.091

t=40.021 °C 29.50189

196

199 R(t)=29.50195

R(t)/R(0)=1. 158583

AUX1 AUX2

31 a 26b

(31 +26)/2=28.5c 0.000l6«93*(28.5-30)=-.02d

39.96 39.924 t=40.021 °C 29.50189 200 ran 114 rrm 39.97 39.936 196 30.0a 25.0b

+.06 199 +1.08 +.98

-.02e R(t)=29.50195 ~.2h -1 .Oh

R(t)/R(0)=1. 158583 30. 8* 24.9*

.04^ +.091 (200*30. 8)*(11 4*24. 9)/31 4=28.7° O.OOOl6*93*(28.7-30)=-.02d

44.86

44.87

+ .02 -.02

44.807 44.809

.00 +.082

t=44.890 °C 29.98976

989 999

R(t) =29. 98988

Rt(t)/R(0)=1. 177745

AUX1 33

0 . 0001 6*35* ( 33-37 ) =-.02

44.86 44.807 t=44.890 °C 29.98976 114 ran 44.87 44.809 989 33-3

+.02 999 +.9 -.02 R(t)=29. 98988 -1.4

R(t)/R(0)=1. 177745 32.8

.00 +.082

(1 14*32. 8)/1 14=32.8 0.0O0l6*35*(32.8-37)=-.02

62
100.52 100.40 t=100.15 °C 35,47688

100.52 100.10 698

707 -.37 -.25 R(t)=35. 17698 R(t)/R(0)=1. 393231

150.1 148.82 t=148.39 °C 40.19077 103 rrm 100 nm

150.1 148.82 096 112.9 140.0

-1.7 -.43 106 +.6 0.0

+1.7e -.03 R(t)=40. 19093 -.9 +2.2 R(t)/R(0)=1 .578355 112.6 142.2

.0 f -.46

(103*112. 6)/103=112.

0.00016*184. 2*(112.6-54)=+1 .7

0.000165*100*0. 31*0 48-1 42)=(-). 03

150.1 148.83 t=l48.40 °C 40.19180 100 rim AUX1 RT

150.1 148.83 190 140.0 32J 24k -1.7 -.43 200 0.0

+1.7 -.03 R(t)=40. 19190 +2.2

R(t)/R(0)=1 .578393 142.2

.0 -.46

32-(24-23)=31 1 (50-(50/( 1 +0.0001 6*( 1 48-31 ))) )*1 .8=+1 .7m

0.0001 65*100*0. 31 *(148-142)=(-). 03

199.50 199.56 t=199.27 °C 45.08799 100 rrm 199.50 199.56 829 187.0 -.23 -.29 859 0.0 -.20e -.05 R(t)=45.08829 +2.8 R(t)/R(0)=1 .770681 189.8

0.000167*100*1 .3*(199-190)=(-).2On

0. 000167*100*0. 31*(199-190)=(-) .05

Observed terrperature of the lower portion of the errergent stem

^Observed temperature of the upper portion of the emergent stem

cAverage temperature of the emergent stem

dealculation of stem-temperature correction

eEmergent stem-temperature correction

fAlgebraic addition of thermometer correction and stem-tenperature correction

Sice-point correction ^interpolated scale correction of faden thermometer

^•Corrected faden thermometer reading

J Temperature of environment above the mercury column

kRoom temperature

'Adjusted auxiliary thermometer reading "Calculation of too-deep iumersion correction "Calculation of faden correction

63
The fourth value is the specified average temperature of the emergent stem

(t sp ). This value is the temperature that the emergent stem should be. If

the thermometer is a total- immersion thermometer having a portion of the

stem out of the medium being measured or in an unknown temperature region,

the specified temperature of that portion of the stem will be the

temperature of the thermometer bulb or medium in which the bulb is

located. If it is an ASTM partial-immersion thermometer, the specified

temperatures will be the values given in ASTM E-l, Standard Specification

For ASTM Thermometers [9].

The stem- temperature correction is added to or subtracted from the

thermometer correction. Examples are given in Table 9, which are the

computed results of Table 5, and are discussed in the following sections.

The temperature of the bath medium and thermometer corrections were determined as discussed in Sections 6.1 and 6.2.

6.3.1 Emergent Stem- temperature Correction Obtained using Two Auxiliary

Thermometers

Thermometer T5 is an ASTM 33C thermometer and at 40 °C the correction

should reflect an emergent stem temperature of 30 °C as specified in ASTM

E-l [9]. This example is shown in Figure 19(a). The length of the

emergent-mercury column is equal to 314 mm and the centers of the auxiliary

thermometer bulbs are placed adjacent to the stem 105 mm and 209 mm from

the immersion line. (Generally an auxiliary thermometer should be used

every 120 mm to 150 mm length of mercury column emergent from the bath.)

The indication on the auxiliary thermometer 1 gives the average temperature

of the lower portion of the emergent stem of T5 and auxiliary thermometer 2 the average temperature of the upper portion of the emergent stem of T5

The average temperature of the emergent stem is the average temperature of

the two auxiliary thermometers.

The average observed stem temperature (tobs ) is 28.5 °C [(31+26)/2], the

specified stem temperature (tsp ) is 30 °C, the coefficient of expansion of

mercury in normal glass for Celsius thermometers is 0.00016, and the number

of degrees emergent from the bath, including the evaluated portion from the

immersion line to the first graduation (n) , is 93 degrees.

Emergent stem- temperature correction = kn(tobs -tsp ) = 0.00016*(93)*(28.5-30)

= -0.02 °C

Notice that the values tobs and tsp are reversed in the above formula, as compared with the one given in NBS Monograph 150 [7], since the correction

is applied to a correction and not to the thermometer reading.

6.3.2 Emergent Stem- temperature Correction using Two Faden Thermometers

For this example the same ASTM 33C thermometer, serial number T5 , will be

discussed using the same thermometer readings and bath temperature. A

200 mm faden thermometer was used to measure the temperature of the lower

64
TABLE 10

FADEN THERMOMETER CORRECTIONS

Faden Thermometer Length

100 mm 103 mm 114 mm 200 mm

Ice-Point

Correction 0. 0 +0.6 +0.9 + 1.0

Scale Correction

Temperature

°C

0 0, 0 0.0 0.0 0.0

50 +0,.1 -1.0 -2.1 -0.3

100 +1..2 -1.0 -2.4 +0.2

150 +2..4 -0.6 -2.4 +2.0

200 +2,.9 -0.8 -2.8 +2.6

250 +3. 9 -1.1 -2.8 +3.0

300 +4,.1 -1.4 -3.0 +2.7

portion of the stem and a 114 mm faden thermometer was used to measure the

temperature of the upper portion as shown in Figure 19(b). Since the faden

thermometers had been calibrated, ice-point corrections and scale corrections at the indicated temperatures were applied. (Given in Table 10 are

the corrections for the faden thermometers used in these examples.)

To determine the temperature of the emergent stem (tobs ), the lengths of

the faden thermometers in millimeters are multiplied by the faden thermometer readings. The results are added and divided by the total length of

the emergent mercury column.

Emergent-stem temperature = [ (200)*(30. 8)+(114)*(24. 9) ]/314

= 28.7 °C.

Occasionally it may be necessary to use a faden thermometer that is longer

then the emergent mercury column. If this is the case, a second faden

thermometer of the appropriate length must be placed with the top of its

bulb on a horizontal plane with the top of the bulb of the longer faden

thermometer and the bottom of the bulb adjacent to the meniscus of the

thermometer being calibrated. The stem temperature is then determined by

subtracting the length of the upper faden thermometer multiplied by the

reading from the length of the lower faden thermometer multiplied by the

reading and dividing this value by the distance from the immersion line to

the meniscus of the thermometer being calibrated.

65
Calculating the stem- temperature correction after the temperature of the

emergent stem is determined is identical with the one discussed in Section

6.3.1. The calculation is given below:

Emergent Stem- temperature correction = kn(tobs -tsp ) = 0.00016*(93)*(28.7-30)

= -0.02 °C.

6.3.3 Emergent Stem- temperature Correction using One Auxiliary Thermometer

Thermometer T6 is an ASTM 34C thermometer. Since the length of the

emergent-mercury column is only 120 mm, placing the center of the bulb of

one auxiliary thermometer adjacent to thermometer T6 60 mm from the

immersion line is sufficient to measure the average temperature of the

emergent stem. This example is shown in Figure 20(a).

In the example the observed stem temperature (tobs ) is 33 °C, the specified

stem temperature (tsp ) is 37 °C, the coefficient of expansion of mercury in

glass (k) is 0.00016, and the number of degrees from the immersion line to

the mercury meniscus (n) is 35 degrees. The stem- temperature correction is

computed below:

Emergent stem- temperature correction = kn(tobs -tsp ) = 0.00016*(35)*(33-37) = -0.02 °C.

6.3.4 Emergent Stem- temperature Correction using One Faden Thermometer

The same example given in Section 6.3.3 and Figure 20(b) will be used to

discuss the stem- temperature correction for ASTM thermometer 34C using one faden thermometer to determine the temperature of the emergent-mercury

column (tobs ). The thermometer readings and bath temperature will be the same

Ice-point and scale corrections are applied to the faden thermometer

reading (See Table 10) and the result will be the temperature of the

emergent stem (tobs ). The other values are the same as given in Section

6.3.3. The emergent stem- temperature correction is given below:

Emergent stem- temperature correction - kn(tobs -tsp ) = 0.00016*(35)*(32.8-37)

= -0.02 °C.

If Fahrenheit thermometers are calibrated, the stem- temperature corrections

will be the same as shown in the above examples, except for the value of k.

The equivalent values of k for Fahrenheit thermometers are given in

Table 8.

66
6.3.5 Too-deep Immersion Correction

Sometimes it is necessary to immerse a partial- immersion thermometer with

the immersion line below the surface of the bath medium. This will be the case if the distance from the immersion line to the bottom of the thermometer bulb is less then 76 mm in the temperature range of 100 to 300 °C, or 130 mm in the range of 300 to 538 °C. Thermometer T7 of Table 9 and

Figure 21(b) will be used to discuss this correction referred to as a "too-deep immersion correction".

The placement of the auxiliary thermometer used to measure the temperature

of the environment, where a portion of the mercury column would be if the

thermometer was immersed to the immersion line, is shown in Figure 21(b)

and discussed in Section 5.8. In the example the auxiliary thermometer

(AUX) read 32 °C and the room temperature (RT) was 24 °C. The auxiliary

thermometer reading must be adjusted to represent a room temperature of

23 °C. The following formula is used:

Adjusted auxiliary thermometer reading (aux) = AUX-(RT-23)

In the example the adjusted auxiliary thermometer reading (aux) would be

31 °C [32-(24-23)]

The formula used to determine the too-deep immersion correction is a variation of the stem- temperature correction formula and is given below:

Too-deep immersion correction = {D- [D/(l+k(tb -aux) ) ] }B

D = distance from the immersion line to the surface of the bath medium

in millimeters (distance the thermometer is in too deep)

k = coefficient of expansion of mercury in glass

tb = temperature of bath medium

aux = adjusted auxiliary thermometer reading

B = number of degrees per millimeter at the calibration point on the

thermometer under test.

In the example the thermometer is immersed 50 mm too deep into the bath;

therefore, D is equal to 50. The coefficient of expansion of mercury in

glass (k) is 0.00016 and the bath temperature (tb

) to the nearest degree

was computed to be 148 °C. As shown above, the adjusted auxiliary

thermometer reading (aux) was calculated to be 31 °C. The value for B was found by placing a 1 cm plastic scale across the thermometer at the

calibration point and counting the number of degrees that are encompassed

by the 1 cm of scale length. This value is usually determined to the

nearest one- tenth of a scale division and was found to be 18 degrees per

cm. A decimal point shift will give the number of degrees per mm (1.8).

From these values the too-deep immersion correction can be determined as shown below:

Too-deep immersion correction = {D- [D/(l+k(tb -aux) ) ] }B = {50- [50/(1+0. 00016(148-31))] }1. 8 = +1.7 °C.

67
If the computed correction is positive, it is added to the thermometer

correction. If the computed correction is negative, it is subtracted from

the thermometer correction. The resulting correction is applicable when

this thermometer is used at an immersion of 25 mm.

If this correction is to be made on thermometers calibrated in the tin bath

(300 to 538 °C), the formula to be used is:

Too-deep immersion correction = {D- [D/(l+k(tb -aux-60) ) ] }B

A value of 35 is substituted for the 60 if the thermometer is inserted more

that 50 mm too deep into the tin bath medium.

In addition to the too-deep immersion correction computed above for

thermometers calibrated in the tin bath, a correction represented by the

formula given below must also be applied:

0.00016 * L * B * 35 = (-) correction

L = length from actual point of immersion to point of reading

(mercury meniscus) in millimeters

B = number of degrees per millimeter at the calibration point

on the thermometer under test

This correction will always be subtracted from the thermometer correction.

6.3.6 Faden Correction

A variation of the stem- temperature correction formula is used when a total -immersion thermometer is calibrated above 150 °C, and a portion of

the mercury column is in the region of unknown temperature near the surface

of the oil or tin bath. The correction is referred to as a "Faden

correction." Thermometer serial number T4 calibrated at 200 °C will be

used as an example.

A 100 mm faden thermometer is placed as discussed in Section 5.8 and shown

in Figure 22. The ice-point and scale corrections are applied to the faden

thermometer reading. The formula for this correction is given below:

Faden correction = kLB(tb

- tf )

k = coefficient of expansion of

L - length of faden thermometer

B = number of degrees per mm at

thermometer under test

tb = temperature of bath medium

tf = corrected faden thermometer

mercury in glass

bulb in mm

the calibration point on the

reading

Since this type of stem- temperature correction is used at high temperatures

and for thermometers made of borosilicate glass as well as normal glass,

the value for the coefficient of expansion of mercury in glass (k) is taken

from the appropriate column of Table 8. A variation of a portion of the

68
table is given in Table 8(b), where the value of k corresponding to the

bath temperature and faden thermometer reading can be easily determined.

The value LB is equivalent to n, as discussed in Sections 6.3.1 thru

6.3.4. This variation of the formula is used because a value for B is

easier to measure then a value for n degrees. This is done by placing a

1 cm scale along the thermometer as discussed in Section 6.3.5 and counting

the number of degrees in that 1 cm. This value is then divided by 10 to

determine the number of degrees in 1 mm. The multiplication of the value L

by B gives the value of n (number of degrees in the 100 mm length of

thermometer adjacent to the faden thermometer bulb).

In the example a 100 mm faden thermometer is used and the measured B at the

calibration temperature (200 °C) was 13 degrees per 1 cm, which is

1.3 degree for a 1 mm distance. The measured bath temperature was 199 °C

and the corrected faden reading was 190 °C. From this data the faden

correction was computed as shown below:

Faden correction = kLB(tb -tf ) = (0. 000167 )*(100)*(1 .3)^(199-190)

= 0.20 °C.

The correction will always be subtracted from the thermometer correction,

since the portion of the stem at the surface of the bath will always be

cooler then it should be.

6.3.7 Emergent Stem- temperature Correction for Calorimetric Thermometers

Calorimetric thermometers are calibrated at total immersion, but are sometimes used at partial immersion. If this is the case an emergent

stem- temperature correction must be made.

The correction may be computed from the following formula, which involves

the difference between the initial and final readings, provided the mean

temperature of the emergent stem remains constant.

Emergent stem- temperature correction = kd(

A +tf

- I - t)

k = coefficient of expansion of mercury in glass

d = tf -t± ti = initial thermometer reading

t f = final thermometer reading

I = scale reading to which the thermometer is immersed

t = mean temperature of the emergent stem

This correction must be applied (added if positive, subtracted if negative)

to the difference of the readings to give the actual temperature

difference

69
6.3.8 Emergent Stem- temperature Correction for Beckmann Thermometers

Beckmann thermometers are also calibrated at total immersion, but may be

used at partial immersion. The formula used to compute the emergent

stem- temperature correction is similar to the one used for calorimetric

thermometers. The formula given below is applicable provided the

thermometer is immersed near the zero degree indication on the scale and

the temperature of the stem remains constant.

Emergent stem- temperature correction = kd( S+tL +t f

- t)

k = coefficient expansion of mercury in glass

d - tf-tj

S = setting of the thermometer

t A = initial reading of thermometer

t f = final reading of thermometer

t = mean temperature of the emergent stem

A Beckmann thermometer should not be used with any part of the lower

portion of the stem exposed to ambient temperature. Since this part may

contain 5 to 10 times more mercury per centimeter than the graduated

portion, a large and uncertain error will be introduced if this section is

not in the bath medium. If it is unavoidable, and a Beckmann thermometer

must be used in this way, the necessary correction may be computed from the

above formula, provided S in the formula is replaced by S + m, where m is

the number of degrees the temperature of the thermometer must be lowered to

bring the meniscus from the zero mark on the scale to the point of

immersion.

If the thermometer is immersed to some point other than the zero mark, as would ordinarily be the case with thermometers having the zero graduation

at the top of the scale, the differential stem correction may be calculated

from the above formula if S is replaced by S + m. The formula is

applicable whether the point of immersion is on the scale are below it,

provided the points at which readings are made are above the point to which

the thermometer is immersed.

All the calculations shown in Sections 6.3.1 to 6.3.6 are on a computer

program stored in the main computer at NBS . Access to the program is

through the NBS network.

7.0 Documentation

7.1 Report of Calibration

After corrections are made to the thermometers and the data are considered

acceptable, a Report of Calibration is generated for each thermometer

submitted for calibration. Figures 24 and 25 show a sample Report of

Calibration that would be issued by NBS for thermometer serial number TO.

All reports will include the following:

70
U. S. DEPORTMENT OF COMMERCE

NOTIONAL BUREAU OF STANDARDS

NATIONAL MEASUREMENT LABORATORY

GAITHERSBURG,' MD. £0899

REPORT OF CALIBRATION

LIQUID-IN-GLASS THERMOMETER.

TESTED FOR: NATIONAL BUREAU OF STANDARDS

DIVISION 522

MARKED: SURETY TO

RANGE: -2 TO +102 DEGREES C IN 0.2 DEGREE

THERMOMETER CORRECTION

READING (IPTS-68)**

-. 10 C . 10 C

20. 00 . 05

40.00 -.07

60.00 .01

80. 00 -. 04

100.00 .00

**ALL TEMPERATURES IN THIS REPORT ARE BASED ON THE INTERNATIONAL

PRACTICAL TEMPERATURE SCALE OF 1968, IPTS-68. THIS TEMPERATURE SCALE

WAS ADOPTED BY THE INTERNATIONAL COMMITTEE OF WEIGHTS AND MEASURES AT

ITS MEETING IN OCTOBER, 1968, AND IS DESCRIBED IN "THE INTERNATIONAL

PRACTICAL TEMPERATURE SCALE OF 1968 AMENDED EDITION OF 1975,"

METROLOGIA 12, NO. 1, 7-17 (1976).

ESTIMATED UNCERTAINTIES IN THE ABOVE CORRECTIONS DO NOT EXCEED 0.05

DEGREE UP TO 102 DEGREES C . FOR A DISCUSSION OF ACCURACIES ATTAINABLE WITH SUCH THERMOMETERS SEE

NATIONAL BUREAU OF STANDARDS MONOGRAPH 150, LIQUID-IN-GLASS

THERMOMETRY.

IF NO SIGN IS GIVEN ON THE CORRECTION, THE TRUE TEMPERATURE IS HIGHER

THAN THE INDICATED TEMPERATURE; IF THE SIGN GIVEN IS NEGATIVE, THE TRUE

TEMPERATURE IS LOWER THAN THE INDICATED TEMPERATURE. TO USE THE CORRECTIONS PROPERLY, REFERENCE SHOULD BE MADE TO THE NOTES GIVEN BELOW.

THE TABULATED CORRECTIONS APPLY FOR THE CONDITION OF TOTAL IMMERSION OF

THE BULB AND LIQUID COLUMN. IF THE THERMOMETER IS USED AT PARTIAL IMMERSION, APPLY AN EMERGENT STEM CORRECTION AS EXPLAINED IN THE ACCOMPANYING

STEM CORRECTION SHEET.

TEST NUMBER 999999

COMPLETED 1-22-85

Fig. 24. Facsimile of page 1 of an NBS Report of Calibration

for thermometer, serial number TO.

71
PAGE £

THE TABULATED CORRECTIONS APPLY PROVIDED THE ICE-POINT READING, TAKEN

AFTER EXPOSURE FOR NOT FEWER THAN 3 DAYS TO A TEMPERATURE OF ABOUT 23

DEGREES C (73 DEGREES F), IS -0.10 C . IF THE ICE-POINT READING IS FOUND

TO BE HIGHER (OR LOWER) THAN STATED, ALL OTHER READINGS WILL BE HIGHER

(OR LOWER) BY THE SAME AMOUNT. IF THE THERMOMETER IS USED AT A GIVEN

TEMPERATURE SHORTLY AFTER BEING HEATED TO A HIGHER TEMPERATURE, AN ERROR

OF 0.01 DEGREE OP LESS, FOR EACH 10-DEGREE DIFFERENCE BETWEEN THE TWO

TEMPERATURES, MAY BE INTRODUCED. THE TABULATED CORRECTIONS APPLY IF THE

THERMOMETER IS USED IN ITS UPRIGHT POSITION; IF USED IN A HORIZONTAL

POSITION, THE INDICATIONS MAY BE A FEW HUNDREDTHS OF A DEGREE HIGHER.

FOR THE DIRECTOR,

NATIONAL MEASUREMENT LABORATORY

TEST NUMBER 999999

COMPLETED 1-2S-85 ROBERT J. SOULEN, JR.

CHIEF, TEMPERATURE AND PRESSURE DIVISION

CENTER FOR BASIC STANDARDS

Fig. 25. Facsimile of page 2 of an NBS Report of Calibration

for thermometer, serial number TO.

72
1) Company, agency, or establishment that submitted

the thermometer,

2) Manufacturer's trade name and serial number of the

thermometer

3) Range and graduation interval,

4) Calibration temperatures and corrections,

5) Temperature scale used (IPTS)

6) Estimated uncertainties,

7) Instructions for use of corrections,

8) NBS test number, and

9) Date of calibration.

One or more notes, specific to each thermometer, will also appear on the

Report of Calibration. The following list contains examples of notes most

commonly used.

ALL TOTAL- IMMERSION THERMOMETERS. The tabulated corrections apply for the

condition of total immersion of the bulb and liquid column. If the thermometer is used at partial immersion, apply an emergent stem correction as explained in the accompanying stem correction sheet. (See Figures 26 and

27.)

ALL PARTIAL- IMMERSION THERMOMETERS WITH NO STEM- TEMPERATURE CORRECTIONS.

The thermometer was tested in a large, closed- top, electrically heated,

liquid bath at an immersion of . The temperature of the room was about 23 °C (73 °F) . If the thermometer is used under conditions which

would cause the average temperature of the emergent liquid column to differ

markedly from that prevailing in the test, appreciable differences in the

indications of the thermometer would result.

PARTIAL- IMMERSION THERMOMETERS WITH THE SAME STEM TEMPERATURE AT EACH

CALIBRATION POINT. These corrections are applicable for immersion

and for an emergent stem temperature of .

PARTIAL- IMMERSION THERMOMETERS WITH DIFFERENT STEM TEMPERATURES AT EACH

CALIBRATION POINT. These corrections are applicable for immersion

and for temperatures of the emergent mercury column as given below:

Reading of thermometer

Temperature of emergent mercury .

RECALIBRATI ON NOTE USING ICE POINT. The tabulated corrections apply

provided the ice-point reading is . If the ice-point reading is

found to be higher (or lower) than stated, all other readings will be

higher (or lower) by the same amount.

RECALIBRATION NOTE USING ICE POINT FOR TOTAL- IMMERSION THERMOMETERS

GRADUATED UNDER 150 °C AND IN GRADUATION INTERVALS OF 0.2° OR LESS. The

tabulated corrections apply provided the ice-point reading taken after

exposure for not fewer than 3 days to a temperature of about 23 °C (73 °F)

is . If the ice-point reading is found to be higher (or lower) than

stated, all other readings will be higher (or lower) by the same amount.

If the thermometer is used at a given temperature shortly after being

73
CORRECTION FOR EMERGENT STEM

This stem correction sheet is designed to explain

the process of computing the corrections for emergent

stem, but has not been specifically adapted to the individual thermometer with which it is issued. If a total-immersion thermometer is actually used

with a part of the liquid column in the capillary

emergent from the bath, a stem correction must be

calculated and applied as explained below, making

use of the formulas given.

The general formula used in computing the correction for emergent stem is: Stem correction=fex«(*i — t), where fe=the differential expansion coefficient of mercury (or other liquid in the thermometer such as alcohol, toluene, pentane,

etc.) in the particular kind of glass of which the thermometer is made; (for

numerical values see below)

nrrnumber of degrees emergent from the bath;

ii=temperature of the bath; trrmean temperature of the emergent stem. Example 1.—Suppose the observed reading was

84.76° C and the thermometer was immersed to the

20° mark on the scale, so that 65° of the column projected into the air, and the mean temperature of the emergent column was found to be 38° C, then

EXPLANATORY NOTES ON THE

Some thermometers are pointed and graduated by the maker to read correct, or approximately correct, temperatures when the bulb and the entire liquid Index in the stem are exposed to the temperature to be measured, while other thermometers are so pointed and graduated that they will read correct, or approximately correct, temperatures when the bulb and only a short length of the stem of the thermometer are immersed in the bath, the temperature of which is to be measured. Thermometers of the former class are known as "total-immersion thermometers," and

those of the latter class as "partial-immersion thermometers."

Total-immersion thermometers are tested under the condition

of total immersion and the corrections resulting from such a test will serve to reduce the observed readings of the thermometer to true temperatures only if the thermometer is used as a total- immersion thermometer. If such a thermometer is actually used

as a partial-immersion thermometer, i.e., with a part of the mercury column emergent into the space above the bath, and

with the emergent stem therefore either colder (or warmer) than

the bulb, the thermometer will obviously read lower (or higher) than it would under the condition of total immersion. Hence, if a total-immersion thermometer is so used, a so-called stem

correction must be applied to the observed reading in addition

to the correction taken from the accompanying table of corrections. This stem correction is very large if the number of degrees

emergent and the difference of temperature between the bath and the space above it are large. It may amount to more than

20° C (36° F) for measurements made with a mercury

thermometer at 400° C (750° F).

The coefficient k is different for different kinds of glass and, even for the same kind of glass, it differs for different temperature intervals, i. e., different values of (t

x — t). Values for k

for two widely used thermometric glasses, for use in calculating stem corrections are tabulated as follows :

Fig. 26. Stem temperature expl

for total- immersion t

Stem correctjon=0.00016x65 (85°—38°) =+0.49° C. The true temperature is therefore the observed

reading, 84.76° C, + tabular correction as interpolated

from the report, + emergent stem correction (+0.49° C).

Example 2.—Suppose the observed reading was

780° F and the thermometer was immersed to the 200° mark on the scale, so that 580° of the column

projected into the air, and the mean temperature of the emergent column was found to be 170° F, then

Stem correction=0.00009x580(780°—170°) =+32° F

as a first approximation.

Since the result shows that the bath temperature was approximately 780° F-f32° F, a second approximation should be made, using ti=812° F instead of ti=780° F. This givesStem correction=0.00009x580(812°—170°) =+34° F. The true temperature is therefore the observed

reading, 780° F, + tabular correction as interpolated

from the report, + emergent stem correction (+34° F).

It will be noted that if the average temperature of the stem is below that of the bulb, the sign of the cor- rection will be +, while if the temperature of the stem is above that of the bulb, the sign of the correc- tion will be —

EMERGENT STEM CORRECTION

VALUES OF k FOR MERCURY-IN-GLASS THERMOMETERS

For Celsius thermometers For Fahrenheit thermometers Mean

temp.

t, + t

k

for "normal"

glass

k

for "borosilicate" glass

Mean

temp.

*, + (

k

for "normal"

glass

k

for "borosllicate" 2 2 glass 0° 0.000158 0.000164 0° 0.000088 0.000091 100 158 164 200 88 91 150 158 165 300 88 92 200 159 167 400 89 93 250 161 170 500 90 95 300 164 174 600 92 97 350 178 700 .000100 400

450

183

188

800 103

If the kind of glass of which the thermometer is made is known, the value of k to be used in computing the stem correc- tion may be taken from the above table. If the kind of glass is not known, use £ =0.00016 for Celsius or 0.00009 for Fahrenheit

thermometers. High-grade thermometers are now generally made

of "normal" or "borosilicate" glasses. If a thermometer is grad- uated only to about 450° C (850° F), it may be made of either

of the above glasses; if it is graduated to 500° C (932° F) and

is actually usable at that temperature, it is made of one of the

borosilicate glasses or a similar glass. The expansions of liquids such as alcohol, toluene, etc., vary

quite rapidly with the temperature, so that k varies considerably

for different temperature intervals. An approximate stem cor- rection for such thermometers may be calculated by taking k in the above equation = 0.001 for Celsius thermometers or 0.0006

for Fahrenheit thermometers. The value of t, the mean temperature of the emergent stem, Is the most difficult of the terms in the above formula to estimate.

It may be quite accurately measured by the use of special capil- lary thermometers. This is, however, very rarely done except in the testing laboratory, and then only when the stem correction must be determined with considerable precision (to 10 percent or

better). In general, the value of t may be determined to a suffi- cient approximation by judgment or preferably by suspending an

auxiliary thermometer close beside the emergent stem, with the bulb of the auxiliary thermometer somewhat nearer to the top

of the bath than to the liquid meniscus. ation sheet attached to reports

rmometers

74
DIFFERENTIAL CORRECTION FOR EMERGENT STEM

This sheet is designed to explain a convenient process

of computing the differential correction for emergent

stem but lias not been specifically adapted to the

individual thermometer with which it is issued.

If a calorimetric or differential or a metastatic (Beckmann) thermometer is actually used with a part of its stem emergent from the hath, a differential stem correction must he calculated and applied as explained below, making use of the formulas there

given.

Example 1. —Suppose the point. 1°. to which the thermometer was immersed was 16° C : it.s initial reading, T" u was 24.127° : its final reading, T"i, was

27.876° ; the mean temperature. i°, of the emergent

stem was 26° ; then—

Differential stem correction =0.00016 (2S- 24) (24° +

28° - 16° - 26

° ) = 4- 0.006°.

The result, 0.006°, should be added to the difference between T°* and T",, found after applying to each

the corrections tabulated on the Report of Calibration. Example 2. —Suppose a Beckmann thermometer was

immersed to the 0° mark on its scale; Its initial reading,

T°,. was 2.058°; its final reading, T

0

,, was 5.127°; the mean temperature, t°, of the emergent stem was 24° C ; and the setting, S°, was 25° C; then

Differential stem correction=0.00016(5-2) (25° +

2° +5° -24°) = +0.004°.

The result + 0.004°, should be added to the difference l>etween T° z and T°i, found after applying to each the

corrections tabulated on the Report of Calibration and

multiplying the difference by the setting factor (1.0014 for a setting of 25° )

EXPLANATORY NOTES ON THE EMERGENT STEM CORRECTION

Calorimetric and differential and metastatic (Beckmann)

thermometers are pointed and graduated by the makers to read correct or approximately correct temperature intervals when the bulb and the entire mercury index in the stem are exposed to the temperature to be measured, and such thermometers are standardized for the condition of "total immersion," and the corrections Riven in reports apply for the condition of total immersion.

In practically all cases, however, such thermometers are

actually used with only the bulb and a portion of the stem

immersed, the remainder of the stem projecting into the air above the bath. In such cases the accuracy attained can be increased by

applying the necessary corrections for the emergent stem. The emergent stem correction corresponding to any reading may be computed by means of the formula

Stem correction = fcXJi ( T" —t°) ; where fc=the differential expansion coefficient of mercury in glass ; = 0.00016 for Celsius thermometers ; = 0.00009 for Fahrenheit thermometers:

»i = number of degrees emergent from the bath : T° = temperature of the bath:

t° = mean temperature of the emergent stem.

However, in differential measurements the parts of the

Scale on which readings are made are, in general, emergent from the bath and it is usually permissible to assume that t° will be constant during the measurement. In this case, in- stead of calculating the stein corrections for the initial and

final readings, and applying them separately, the differential stem correction can be more conveniently computed by using

the appropriate formula of the two given below.

Differential emergent stem correction for ordinary thermometers. -The differential stem correction may be computed

from the following formula :

Differential stem correction = fcxrf(7'°i-f 7'°;— T°—t°) ; fr=0.00016 for Celsius thermometers ; = 0.00009 for Fahrenheit thermometers:

7'°i = the initial reading;

T°- = the final reading:

d = T°-— r, :

7° =scale reading to which the thermometer was immersed ; t°=mean temperature of the emergent stem.

It should be noted that this differential stem correction, as

well as the difference d°, may be either positive or negative, and the correction must be applied with due regard to these

signs. Differential emergent stem correction for metastatic (Iicckmann) thermometers.—The differential emergent stem

correction may be computed from the following formula, pro- vided the thermometer is immersed to its 0° mark : Differential stem correction =fcXrf(S°4- T°i+T°z—1°) ; where S° = the "setting" of the thermometer, and k. d, T°i. T°~ and t° have the meanings given in the preceding para- graph.

It should be noted that this differential stem correction, as well as the difference d, may be either positive or negative, and the correction must be applied with due regard to these signs. A Beckmann thermometer of the ordinary type should not

he used with any part of the lower portion of the stem exlM>sed. as this part may contain from 5 to 10 times as much

mercury per centimeter as the graduated portion, and if ex- posed introduces a large and uncertain error.

In case it is necessary to use such a thermometer with some

of the lower portion of the stem emergent from the bath, the necessary correction may be computed from the above

formula, provided S° in the formula is replaced by S

0 +"m°, where m is the number of degrees the temperature of the thermometer must be lowered to bring the meniscus from

the zero position on its scale to the point of immersion.

If the thermometer is immersed to some point other than its 0° mark, as would ordinarily be the case with thermometers

having the 0° graduation at the top of the scale, the differ- ential stem correction may also be computed from the above

formula, provided S° in the formula is replaced by S°+m°,

where m is the number of degrees the temperature of the thermometer must be lowered to bring the meniscus from the

zero position on its scale to the point of immersion. Provided

the points at which readings are made are above the point

to which the thermometer is immersed, the preceding state- ment is applicable whether the point to which the thermometer is immersed is on the scale or below it.

Fig. 27. Stem temperature explanation sheet attached to reports

for calorimetric thermometers calibrated at total

immersion.

75
heated to a higher temperature, an error or 0.01 °C or less, for each 10

degree difference between the two temperatures, may be introduced. The

tabulated corrections apply if the thermometer is used in its upright

position; if used in a horizontal position, the indications may be a few

hundredths of a degree higher.

STEAM POINT USED AS REFERENCE POINT. The tabulated corrections apply

provided the reading when the thermometer is immersed in steam at 100 °C

(212 °F) is . If the reading is found to be higher (or lower) than

stated, all other readings will be higher (or lower) by the same amount.

The temperature of steam is 100 °C (212 °F) only if the pressure is 760 mm

(29.921 inches). If the pressure differs from 760 mm (29.921 inches)

allowance must be made for this. If the pressure is higher (or lower) than

760 mm (29.921 inches) the temperature will be higher (or lower) than

100 °C (212 °F) by approximately 0.037 °C per mm difference (1.68 °F per

inch difference)

CALORIMETRIC THERMOMETERS HEATED TO TOP POINT BEFORE TESTING. The thermometer, before testing, was heated to the temperature of the highest test

point. The application of the tabular corrections to the readings of the

thermometer will give true temperature differences provided the thermometer

is used in its upright position and is heated previously (within an hour

before using) to the highest temperature to be measured.

SETTING FOR BECKMANN THERMOMETERS. The tabulated corrections apply for a "setting" of 20 °C. Setting factors for use with other settings are given

on the accompanying sheet. (See Figure 28).

ICE POINT TAKEN AFTER TEST, SUCH AS CLINICAL AND KINEMATIC VISCOSITY

THERMOMETERS. The tabulated corrections apply for the condition of

immersion indicated provided the ice-point reading, taken after heating to

for not fewer than 3 minutes, is . If the ice -point reading,

which should be taken within 5 minutes after removal of the thermometer

from the heated bath, is found to be higher (or lower) than stated all

other readings will be higher (or lower) by the same amount.

LOW TEMPERATURE PARTIAL- IMMERSION THERMOMETERS CALIBRATED AT TOTAL

IMMERSION WITH NO SPECIFIED EMERGENT STEM TEMPERATURE. At temperatures

below the ice point this thermometer was tested under conditions of total

immersion of the bulb and liquid column. The stated corrections were computed using a value of k= /degree and an assumed temperature of

for the emergent stem.

LOW TEMPERATURE PARTIAL- IMMERSION THERMOMETERS CALIBRATED AT TOTAL

IMMERSION WITH SPECIFIED EMERGENT STEM TEMPERATURES. At temperatures below

the ice point this thermometer was tested under conditions of total

immersion of the bulb and liquid column. The stated corrections were computed using a value of k= /degree .

76
This sheet gives a table of setting factors and an example to explain the processes

employed in calculations. The example, however, has not been specifically adapted to the

individual thermometer with which this sheet is issued.

The thermometer is said to have a given setting, for instance 20°C, if its scale reading is 0° when the temperature of the bulb is 20°C.

The following table, calculated for thermometers of Jena 16

111 glass, gives a series of

factors corresponding to different settings by which each observed temperature difference

must be multiplied after applying the corrections given on the preceding page. This factor is made unity for a setting of 20°C.

For any scale length up to 1 5°

Setting Factor Setting Factor

0°C 0.9935 55°C 1 .0092

5 0.9951 60 1.0102

10 0.9967 65 1.0112

15 0.9984 70 1.0121

20 1 .0000 75 1.0129

25 1.0014 80 1.0137

30 1.0029 85 1.0146

35 1 .0042 90 1.0154

40 1.0056 95 1.0162

45 1 .0070 100 1.0170

50 1.0082

As an illustration, suppose the following observations were made:

Setting .......= 25°C. Lower reading = 2.058

Stem temperature = 24° Upper reading = 5.127

Lower Upper

Observed reading = 2 .05 8 5.127

Correction from certificate = +.005 -.008

Corrected upper reading = 5.119

Correctediower reading = 2.063

Difference = 3.056

Setting factor 1.0014 corr. +.004

Emergent stem correction* = +.004

Corrected difference = 3.064

o

See accompanying stem correction sheet.

Fig. 28. Table of setting factors attached to reports for

Beckmann thermometers.

77
Other notes that are occasionally used and are self explanatory are given

below:

This thermometer complies with the accuracy requirement of the applicable

ASTM specification to the extent of the tests made.

This thermometer does not comply with the accuracy requirement of the

applicable ASTM specification.

Not tested at a sufficient number of points.

Not tested over the entire range of scale.

Not tested over the entire range of scale nor at a sufficient number of

points

Correction at exceeds the tolerance.

Corrections at and exceed the tolerance.

Graduated too close to the expansion chamber.

Graduated too close to the contraction chamber.

Graduated too close to the bulb.

No fixed point taken.

No fixed point.

If there is any other information concerning a specific thermometer that is

considered important for the user to know, a note should be written and

included on the report.

All Reports of Calibration are generated on the NBS computer.

8.0 Internal Quality Control

Obvious errors to be avoided in the calibration process are misreading the

thermometers or recording the standard platinum resistance thermometer

resistance values incorrectly. These errors can be reduced or eliminated

by either repeating the calibration point, or double checking the

information immediately after the calibration point has been recorded. The

operator should be sure that the last resistance value, which is still set on the bridge, is the number written in the data book and that the values

preceding it are reasonable. Look again at each thermometer that was

read. See if it was read on the correct side of the nominal temperature

(Was it 19.9 or 20.0?). Check that the two readings of each liquid-inglass thermometer are reasonable. See that the spread between the two

readings varies from nothing (or a very small value) for the last liquidin-glass thermometer in the set to a value somewhat equal to the spread of

78
the first and third platinum resistance thermometer values for the first

liquid- in-glass thermometer. Check any faden or auxiliary thermometer

readings for correctness.

8.1 Use of Check Standards

The above sources of error can be practically eliminated if care is taken

during the calibration process. Another source of error, which is

equipment failure during the day, is very difficult to detect.

At the beginning of the day the standard platinum resistance thermometer is

placed in a triple point of water cell to see if the thermometer is still

in calibration and that the bridge is performing properly. Any deviation

in the resistance value at the triple point of water is due to the platinum

resistance thermometer and/or the bridge and not the triple point of water

cell. Checking this point assures that the bridge and resistance thermometer are producing good results at the beginning of the day, but what

assurance is there that it will continue to perform properly during the

day?

As a check on the system, liquid- in-glass thermometers, called check

standards, belonging to NBS are incorporated into the calibration process.

These thermometers are calibrated, at each calibration point requested for

the other thermometers, as if they were submitted for test by an outside

company. The computed corrections on the check standards are compared with

the corrections obtained from previous calibrations. If they agree within

the uncertainty of each type of thermometer, it can be assumed that

the system was performing well and that the calibration of the other

thermometers will be acceptable.

8.2 Comparison of Corrections and Evaluation of Data on Check Standards

At NBS corrections obtained from repeated calibration of the check

standards are recorded in data books and compared with data taken at some previous time. A sample sheet of the data taken for thermometer serial

number 274762 is given in Table 11. This thermometer has a range of -1 to

+51 °C and is graduated in intervals of 0.1°. The expected uncertainty of

this thermometer (which will be calculated in Section 9) is 0.03 °C.

The control procedure for liquid- in-glass thermometer calibrations is

somewhat ad hoc because the data base of check standard values is sparse in

temperature regions where calibrations are rarely requested. All new

entries are compared with values taken at the same nominal temperature, or,

if necessary, with values taken within one or two degrees of the specified

temperature. If the new and old values agree within the uncertainty of the

thermometer, in this case 0.03 °C, then the calibration is considered

acceptable. Explanations for unacceptable calibrations include:

misreading of the thermometer; failure of the SPRT; and failure of the

bridge

In order for this procedure to work effectively, the old values must be

representative of the check standard; i.e., a sufficient history must exist

79
TABLE 11

RECORD OF CHECK STANDARD CORRECTIONS

Thermometer Serial Number 274762

DATE 3/26/76 3/29/76 4/1/76 4/6/76 4/21/76 5/17/76 5/25/76

BOOK F115 C193 C193 C193 G30 C194 F115

PAGE 182-83 169 173 174-75 192-93 2 188

Temp. Corrections (°C)

(°C)

0 +.130 +.130 +.130 +.129 +.129 +.125 +.130

12

34

56

7

89

10 +.150 + 153 +.149 +.157 +.148

1112

13

14

15 +.070

16 +.069

17

18

19 +.121

20 +.134 +.127 +.132 +.131

21 +.121 +.125 +.127

22 +.107

23

24 +.095 +.093

25 +.103

26 +.098

27 +.100 +.108

28 +.123

29

30 +.138 +.136 +.135 +.134 +.142

31 +.106 +.108

32 +.100

33 +.095

34 +.074

35

36

37

38

39

40 +.095 +.102 +.096 +.100

41

42

43

44

45

46

47

48

49

50 +.138 +.136 +.135 +.136

80
on the check standard to be able to tell whether it is the new or the old

value that is out-of control. Lack of agreement is always taken as an indication of a problem with the current calibration, and calibrations on all thermometers in the group are repeated.

9.0 Assessment of Uncertainties

9.1 Current Tolerance and Uncertainty Values

Shortly after the turn of the century, when the liquid- in-glass thermometer

calibration laboratory was established, tables listing tolerances and

uncertainties for liquid- in-glass thermometers were published. These

values can be found in NBS Monograph 150 [7]. These values varied for

different temperature ranges, graduation intervals, and types of

thermometers. Since there is a tremendous variety of liquid- in-glass

thermometers covering many temperature ranges and divided in different

graduation intervals, it would be impossible to evaluate all possible

combinations. Tolerance and uncertainty values for the most widely used

combinations are given in Tables 12 through 17 for both Celsius and

Fahrenheit thermometers. These combinations will be discussed in

Section 9.2.

The scale tolerances shown were chosen to be indicative of good manufacturing practice. When a thermometer is manufactured, small errors in

pointing (marks placed on a blank thermometer at various temperatures to be

used as guides for the placement of the graduation lines) and graduating

are inevitable. These graduation marks are also subject to variations due

to the inherent properties of the glass. The tolerances must be

sufficiently restrictive to insure a satisfactory high-grade thermometer,

and at the same time not cause undue manufacturing difficulties.

In addition to the scale tolerance limit, the error in any temperature

interval should not exceed 5 percent of the nominal value of the interval.

The purpose of this requirement is to eliminate thermometers having large

corrections of alternating signs, which lead to uncertainties in the

interpolation of scale corrections between the calibration points.

The word "uncertainty" used in these tables refers to the uncertainty of

the best values attainable in the use of thermometers when all corrections

are applied. The uncertainty bounds may seem broad in some instances, but

the definite limitations of liquid- in-glass thermometry become apparent

when all factors are considered. For example, if the scale is expanded by

reducing the diameter of the capillary, a practical limit is reached beyond

which capillary forces, in combination with the elasticity of the

thermometer bulb, will prevent a smooth advance or retreat of the mercury

column. The movement of the mercury meniscus may be erratic and occur in

steps appreciably large in comparison to the graduation interval. This is

particularly true when the temperature of the medium is decreasing. Less

rigid bulbs (relatively large diameters and/or thin walls) , as well as capillaries of small diameters, may cause large "meniscus jumps".

Excessively elliptical or flattened bores are not recommended for the same

81
TABLE 12

TOLERANCES AND UNCERTAINTIES FOR

LOW- TEMPERATURE TOTAL- IMMERSION

THERMOMETERS

Temperature Type of Graduation Toler- Uncertainty

range in thermometer interval in ance in in degrees

degrees degrees degrees

Celsius thermometers

-35 to 0 Mercury 1.0 or 0.5 0.5 0.1 to 0.2

-35 to 0 Mercury .2 .4 .02 to .05

-56 to 0 Mercury- .5 .5 .1 to .2

thallium

-56 to 0 Mercury- .2 .4 .02 to .05

thallium

-200 to 0 Organic 1.0 2.0 .2 to .5

liquid

Fahrenheit thermometers

-35 to 32 Mercury 1.0 or 0.5 1.0 0.1 to 0.2

-35 to 32 Mercury .2 .5 .05

-69 to 32 Mercury- 1.0 or .5 1.0 .1 to .2

thallium

-69 to 32 Mercury- .2 .5 .05

thallium

-328 to 32 Organic 2.0 or 1.0 3.0 .3 to .5

liquid

82
TABLE 13

TOLERANCES AND UNCERTAINTIES FOR

LOW-TEMPERATURE PARTIAL- IMMERSION

THERMOMETERS

Temperature

range in

degrees

Type of

thermometer

Graduation

interval in

degrees

Tolerance in

degrees

Uncertainty

in degrees

Celsius thermometers

-35 to 0

-56 to 0

-90 to 0

Mercury

Mercurythallium

Organic

liquid

1.0 or 0.5

1.0 or .5

1.0

0.5

.5

3.0

0.2 to 0.3

.2 to .3

.4 to 1.0

Fahrenheit thermometers

-35 to 32

-69 to 32

-130 to 32

Mercury

Mercurytha Ilium

Organic

liquid

1.0 or 0.5

1.0 or .5

2.0 or 1.0

1.0

1.0

5.0

0.3 to 0.5

.3 to .5

.8 to 2.0

83
TABLE 14

TOLERANCES AND UNCERTAINTIES FOR

CELSIUS TOTAL- IMMERSION

MERCURY THERMOMETERS

Temperature range in

degrees

Graduation

interval in

degrees

Tolerance

in

degrees

Uncertainty

in degrees

Thermometers graduated under 150 °C

0 up to 150

0 up to 150

0 up to 100

1.0 or 0.5

.2

. 1

0.5

.4

.3

0.1 to 0.2

.02 to .05

.01 to .03

Thermometers graduated under 300 °C

0 up to 100

Above 100 up to 300

0 up to 100

Above 100 up to 200

1.0 or 0.5

.2

0.5

1.0

.4

.5

0.1 to 0.2

.2 to .3

.02 to .05

.05 to .1

Thermometers graduated above 300 °C

0 up to 300

Above 300 up to 500

0 up to 300

Above 300 up to 500

2.0

1.0 or .5

2.0

4.0

2.0

4.0

0.2 to 0.5

.5 to 1.0

.1 to .5

.2 to .5

84
TABLE 15

TOLERANCES AND UNCERTAINTIES FOR

FAHRENHEIT TOTAL- IMMERSION

MERCURY THERMOMETERS

Temperature range in

degrees

Graduation

interval in

degrees

Tolerance

in

degrees

Uncertainty

in degrees

Thermometers graduated under 300 °F

32 up to 300

32 up to 300

32 up to 212

2.0

1.0 or .5

.2 or .1

1.0

1.0

.5

0.2 to 0.5

.1 to .2

.02 to .05

Thermometers graduated under 600 °F

32 up to 212

Above 212 up to 600

2.0 or 1.0

1.0

2.0

0.2 to 0.5

. 5

Thermometers graduated above 600 °F

32 up to 600

Above 600 up to 950

32 up to 600

Above 600 up to 950

5.0

2.0 or 1.0

4.0

7.0

3.0

6.0

0.5 to 1.0

1.0 to 2.0

.2 to 1.0

.5 to 1.0

85
TABLE 16

TOLERANCES AND UNCERTAINTIES FOR

CELSIUS PARTIAL- IMMERSION

MERCURY THERMOMETERS

Temperature range in

degrees

Graduation

interval in

degrees3

Tolerance

in

degrees

Uncertainty

in degrees13

Thermometers graduated under 150 °C

0 up to 100

0 up to 150

1.0 or 0.5

1.0 or .5

1.0

1.0

0.1 to 0.3

.1 to .5

Thermometers graduated under 300 °C

0 up to 100

Above 100 up to 300

1.0

1.0

1.5

0.1 to 0.3

.5 to 1.0

Thermometers graduated above 300 °C

0 up to 300

Above 300 up to 500

2.0 or 1.0

2.5

5.0

0.5 to 1.0

1.0 to 2.0

a Partial- immersion thermometers are sometimes graduated in smaller

intervals than shown in these tables , but this in no way improves the

performance of the thermometers, and the listed tolerances and

uncertainties still apply.

b The uncertainties shown are attainable only if emergent- stem temperatures

are closely known and accounted for.

86
TABLE 17

TOLERANCES AND UNCERTAINTIES FOR

FAHRENHEIT PARTIAL- IMMERSION

MERCURY THERMOMETERS

Temperature range in

degrees

Graduation

interval in

degrees3

Tolerance

in

degrees

Uncertainty

in degrees13

Thermometers graduated under 300 °F

32 up to 212

32 up to 300

2.0 or 1.0

2.0 or 1.0

2.0

2.0

0.2 to 0.5

.2 to 1.0

Thermometers graduated under 600 °F

32 up to 212

Above 212 up to 600

2.0 or 1.0

2.0

3.0

0.2 to 0.5

1.0 to 2.0

Thermometers graduated above 600 °F

32 up to 600

Above 600 up to 950

5.0 or 2.0

5.0

10.0

1.0 to 2.0

2.0 to 3.0

a Partial- immersion thermometers are sometimes graduated in smaller

intervals than shown in these tables, but this in no way improves the

performance of the thermometers, and the listed tolerances and

uncertainties still apply.

b The uncertainties shown are attainable only if emergent- stem temperatures

are closely known and accounted for.

87
reason. Therefore, increasing the length of a degree on the scale, for

practical bulb sizes, improves thermoraetric performance only to a certain

point. Beyond this point precision of reading may readily be mistaken for

accuracy in temperature measurement. A study of the effects of bulb and

capillary dimensions on thermometer performance, made by Hall and Leaver

[14], provides valuable guidelines for design purposes.

Other factors such as ice-point reading changes, unless exactly accounted

for, and differences in external pressure may also account for inaccuracies

much greater than the imprecision with which a scale having 0.1 or 0.2

degree graduations may be read.

In Table 18, Tolerances and Uncertainties for Beckmann and Calorimetric

Thermometers, the estimated accuracy attainable in the measurement of any

interval within the limits of the scale is given under the heading

"uncertainty of interval in degrees". No tolerances for scale error are given, although it is desirable that it be no larger than 0.02 °C over a 1.0 °C interval.

9.2 Evaluation of Uncertainties

In the past few years we at NBS have felt a need to determine realistic

uncertainty values for items calibrated at NBS. No one in the Temperature

and Pressure Division knows exactly how the published values were established for liquid- in-glass thermometers, or if the values are still

valid. The check standard measurements produce an enormous data base which

has been analyzed to determine the uncertainty of these types of

liquid- in-glass thermometers over various temperature ranges.

TABLE 18

UNCERTAINTIES FOR BECKMANN AND

CALORIMETRIC THERMOMETERS

Type of

thermometer

Graduation

interval

in degrees

Allowable change

in correction

in degrees

Uncertainty

of interval

in degrees

Beckmann 0.01 °C 0.01 over 0.

for setting

5° interval

of 20 °C

0.002 to 0.005

Bomb calorimetric .01 °C 0 02 over 1. 5° interval .005 to .01

Bomb calorimetric .02 °C 0 02 over 1. 5° interval .005 to .01

Bomb calorimetric .05 °F 0 04 over 2. 5° interval .01 to .02

Gas calorimetric .1 °F 0 15 over a 5° interval .02 to .05

88
Over the past sixteen years, fourteen liquid- in-glass thermometers,

representing the most accurate types in a given temperature range, have

been used as check standards. Two total- immersion thermometers of each

type were chosen for the standards. The thermometers are allowed to rest

at room temperature (23 °C) for three days before being calibrated,

allowing the volume of the bulb to recover from a previous thermal

cycling. Since no Celsius thermometers were available for the evaluation

of low temperature calibration points, thermometers graduated in degrees

Fahrenheit are used. All of the thermometers had an ice -point reading

either on the main scale or on an auxiliary scale. The range, graduation

interval, and resolution of the check standard thermometers are given in

Table 19.

TABLE 19

THERMOMETERS USED AS CHECK STANDARDS

Temperature Thermometer Resolution

Range Graduation

(°F) (°F) (°F)

-60 to -30 0.2 0.01

Temperature Thermometer Resolution

Range Graduation

(°C) (°C) (°C)

0 to 50

50 to 100

0 to 100

100 to 200

200 to 300

300 to 500

0.005

0.005

0.01

0.01

0.05

0.05

Because the customer is allowed to request calibration at any number of

points, every correction recorded for the check standards could not be

analyzed. Most calibrations occur at temperature intervals of every 10,

20, or 30 degrees; therefore, the data taken at these intervals were used

in the analysis. For each check standard, the correction versus

temperature is plotted as a function of time over a period of five to

twelve years. These plots are given in Figures 29(a) to 42(a2).

Several of the plots show the effect of a permanent change in bulb volume

with time and use. As the volume of a liquid- in-glass thermometer bulb

increases or decreases, the thermometer readings will decrease or increase,

respectively, throughout the whole range. This accounts for the uniform

shift of the correction versus temperature curves seen in some of the

examples. In order to analyze the data accurately, an adjustment must be

89
made for the bulb volume change. All of the data were normalized to a constant ice-point reading representing an approximate average of the

ice-point corrections. The data for selected points were again plotted and

the results are given in Figures 29(b) to 41(b).

The standard deviation as computed for each nominal bath temperature is a measure of both the instability of the thermometer and the random error in

realizing the bath temperature. Three times the pooled standard deviation

over the temperature range is taken as the limit to random error for the

calibration process in that range. The results are given in Table 20.

(Data for check standard, serial number 234456, were not included, because

too few data points were taken.) The column titled "Degrees of Freedom"

indicates one less then the number of measurements taken at the specified

temperature

It is also necessary to assess the systematic errors to establish the final

uncertainty for each thermometer. Systematic errors recognized for this

process are: the realization of the ice point; the uncertainty in the

calibration of the standard platinum resistance thermometer; and the

temperature gradients in the calibration baths. Any other sources of error

are considered negligible.

The uncertainty in the realization of the ice point was determined by

examining years of data accumulated from measuring the ice point on the

standard platinum resistance thermometer before a triple point of water

cell was used. The spread was found to be 0.005 °C.

The uncertainty in the calibration of the standard platinum resistance

thermometer is listed in Monograph 126, Platinum Resistance Thermometry,

[13] as ±0.0002 °C at the triple point of water, ±0.001 °C at the freezing

point of tin, and ±0.001 °C at the freezing point of zinc. From the

documentation on standard platinum resistance thermometers, the uncertainty

of the interpolated values between the fixed points is 0.001 °C to 450 °C

and increasing to 0.003 °C at 500 °C.

The gradients in the calibration baths were determined by simultaneous

measurements using three standard platinum resistance thermometers placed

at various depths and at different locations in the baths. These measurements were made at several regulated temperatures throughout the range of

each calibration bath. The values chosen for the systematic errors, due to

the bath gradients, both radially and horizontally, were the maximum

differences between the three standard platinum resistance thermometer

readings and shown in Table 21. The sum of the systematic errors are given

in Table 21.

The total uncertainty calculated for the liquid- in-glass thermometers is

given in Table 22. These values are the sum of the random error limit

(three standard deviation) and the systematic error.

90
0.00

YEAR

Fig. 29(a) Plot for thermometer, serial number T531432, at five

temperatures (1 at 32 °F, 2 at -30 °F, 3 at -40 °F, 4 at

-50 °F, and 5 at -60 °F) . The readings were not corrected for

ice-point shifts.

0.00

-0.05 -

-0. 10

-0. IS -

-0.20 -

-0.25 -

-0.30

YEAR Fig. 29(b). Plot for thermometer, serial number T531432, at five

temperatures (1 at 32 °F, 2 at -30 °F, 3 at -40 °F, 4 at

-50 °F, and 5 at -60 °F) . The readings were corrected for

ice-point shifts.

91
0.00

72 73 74 75 76 77 78 79 80 81

YEAR

Fig. 30(a). Plot for thermometer, serial number T531438, at tive

temperatures (1 at 32 °F, 2 at -30 °F, 3 at -40 °F, 4 at

-50 °F, and 5 at -60 °F) . The readings were not corrected for

ice-point shifts.

72 73 74 75 7G 77 78 79 80 81

YEAR Fig. 30(b). Plot for thermometer, serial number T531438, at five

temperatures (1 at 32 °F, 2 at -30 °F, 3 at -40 °F, 4 at

-50 °F, and 5 at -60 °F) . The readings were corrected for

ice-point shifts.

92
0. 18

0. 16

0. 14

S 0.12

0.10

0.08

0.06

YEAR

Fig. 31(a). Plot for thermometer, serial number 274762, at six

temperatures (1 at 0 °C, 2 at 10 °C, 3 at 20 °C, 4 at 30 °C, 5 at 40 °C, and 6 at 50 °C) . The readings were not corrected

for ice-point shifts.

0. M

0. 12

0. 10

0.08

0.06

YEAR Fig. 31(b). Plot for thermometer, serial number

temperatures (1 at 0 °C and 2 at 40 °C) . corrected for ice-point shifts.

274762, at two

The readings were

93
0.20

0. 18

0. 16

0.14

0.12-

0.10

72 74 76 78 80 82

YEAR

32(a)

u

LU

a.

<Yau

cc

UJILuEo

a.LUI

H

Plot for thermometer, serial number 275764, at six

temperatures (1 at 0 °C, 2 at 10 °C, 3 at 20 °C, 4 at 30 °C, 5 at 40 °C, and 6 at 50 °C) . The readings were not corrected

for ice-point shifts.

0. 15-

0. 14

0. 13-

0. 12

0. 1

YEAR 32(b). Plot for thermometer, serial number

temperatures (1 at 0 °C and 2 at 10 °C) . corrected for ice-point shifts.

274764, at two

The readings were

94
0 . 04

-0.04 |

I I I I

|

I I I I

|

I I I I

|

I I I I |I I I I 72 73 74 75 76 77

YEAR

Fig. 33(al). Plot for thermometer, serial number 4030424, at four

temperatures (1 at 0 °C, 2 at 50 °C, 3 at 60 °

, and 4 at

70 °C) . The readings were not corrected for ice-point shifts.

0. 1E5-T — 1

-O . 035 J | | I 1 |

| I I I | I I M |

I 1 I I

|

I 1 I I 72 73 74 75 76 77

YEAR Fig. 33(a2). Plot for thermometer, serial number 4030424, at three

temperatures (1 at 80 °C, 2 at 90 °C, and 3 at 100 °C) . The

readings were not corrected for ice-point shifts.

95
u

o

.1 00

.0 75

.0 50

.0 25

.0 00

7025

7G 77

33(b) Plot for thermometer, serial number 4030424, at three

temperatures (1 at 0 °C, 2 at 70 °C, and 3 at 100 °C) . The

readings were corrected for ice-point shifts.

0.01

0.00

-0.01

o

| -0.0E

-0.03

34(al). Plot for thermometer, serial number 4030425, at four

temperatures (1 at 0 °C, 2 at 50 °C, 3 at 60 °C, and 4 at

70 °C). The readings were not corrected for ice-point shifts.

96
0.08

0.06

0.04

0.02

0.00

-0.03

Fig. 34(a2)

YEAR

Plot for thermometer, serial number 4030425, at three

temperatures (1 at 80 °C, 2 at 90 °C, and 3 at 100 °C) . The

readings were not corrected for ice-point shifts.

.0 75

.0 50

.0 25

,000

-025-

-050

YEOR

Fig. 34(b). Plot for thermometer, serial number 4030425, at three

temperatures (1 at 0 °C, 2 at 60 °C, and 3 at 100 °C) . The

readings were corrected for ice-point shifts.

97
ijJ

0.2

0.1

0.0

0.1

-0.2

35(al)

u

LU

or

<rau

a.LU

hlll £o

£

LUX

Plot for thermometer, serial number 48425, at six temperatures

(1 at 0 °C, 2 at 10 °C, 3 at 20 °C, 4 at 30 °C, 5 at 40 °C,

and 6 at 50 °C) . The readings were not corrected for icepoint shifts.

0.10

0.05

-e.es

-e.ie

-e.is

-e.ae

YEAR 35(bl). Plot for thermometer, serial number 48425, at six temperatures

(1 at 0 °C, 2 at 10 °C, 3 at 20 °C, 4 at 30 °C, 5 at 40 °C,

and 6 at 50 °C) . The readings were corrected for ice-point

shifts

98
0. le

-0. 15—

J

1

1

1

1

1

1 1 76 78 80 82 84

35(a2). Plot for thermometer, serial number 48425, at five

temperatures (1 at 60 °C, 2 at 70 °C, 3 at 80 °C, 4 at 90 °C,

and 5 at 100 °C) . The readings were not corrected for icepoint shifts.

0.05-1 1

76 78 80 8E 84

YEAR 35(b2). Plot for thermometer, serial number 48425, at five

temperatures (1 at 60 °C, 2 at 70 °C, 3 at 80 °C, 4 at 90 °C,

and 5 at 100 °C) . The readings were corrected for ice-point

shifts

99
0.30

77 78 79 80 81 82 83 84

VEPR

36(al). Plot for thermometer, serial number 198694, at six

temperatures (1 at 0 °C, 2 at 10 °C, 3 at 20 °C, 4 at 30 °C, 5 at 40 °C, and 6 at 50 °C) . The readings were not corrected

for ice-point shifts.

77 78 79 80 81 82 83 84

YEPR 36(a2). Plot for thermometer, serial number 198694, at five

temperatures (1 at 60 °C, 2 at 70 °C, 3 at 80 °C, 4 at 90 °C,

and 5 at 100 °C) . The readings were not corrected for icepoint shifts.

100
0. 12

0. 10

0.08

YEAR

36(b). Plot for thermometer, serial number 198694, at three

temperatures (1 at 0 °C, 2 at 40 °C, and 3 at 90 °C) . The

readings were corrected for ice-point shifts.

-0.1

-0.5

37(al). Plot for thermometer, serial number, 382213, at six

temperatures (1 at 0 °C, 2 at 100 °C, 3 at 110 °C, 4 at

120 °C, 5 at 130 °C, and 6 at 140 °C) . The readings were not

corrected for ice-point shifts.

101
o

-0.35

-0.40

-0.45

-0.50

-0.55

-0.60

37(a2) Plot for thermometer, serial number 382213, at six

temperatures (1 at 150 °C, 2 at 160 °C, 3 at 170 °C, 4 at

180 °C, 5 at 190 °C, and 6 at 200 °C) . The readings were not

corrected for ice-point shifts.

-0. 1

-0.2-

-0.3

YEAR 37(b). Plot for thermometer, serial number 382213, at three

temperatures (1 at 0 °C, 2 at 120 °C, and 3 at 180 °C) . The

readings were corrected for ice-point shifts.

102
0.0

72 74 76 78 80 82 84

YEAR

38(al). Plot for thermometer, serial number 382215, at six

temperatures (1 at 0 °C, 2 at 100 °C, 3 at 110 °C, 4 at

120 °C, 5 at 130 °C, and 6 at 140 °C) . The readings were not

corrected for ice-point shifts.

-0.2

72 74 7G 78 80 82 84

YEAR 38(a2). Plot for thermometer, serial number 382215, at six

temperatures (1 at 150 °C, 2 at 160 °C, 3 at 170 °C, 4 at

180 °C, 5 at 190 °C, and 6 at 200 °C) . The readings were not

corrected for ice-point shifts.

103
-0.

-0.2

-0.3

-0.4

-0.5

Fig. 38(bl). Plot for thermometer, serial number 382215, at three

temperatures (1 at 0 °C, 2 at 100 °C, and 3 at 200 °C) . The

readings were corrected for ice-point shifts.

-0.20

-0.E5

-0.30

-0.35

-0.40

-0.45

-0.50

Fig. 38(b2). Plot for thermometer, serial number 382215, at six

temperatures (1 at 150 °C, 2 at 160 °C, 3 at 170 °C, 4 at

180 °C, 5 at 190 °C, and 6 at 200 °C) . The readings were corrected for ice-point shifts.

104
0.1

0.0

-0.1

-0.2

-0.3

Fig. 39(al)

Fig. 39(a2)

Plot for thermometer, serial number T1124411, at five

temperatures (1 at 0 °C, 2 at 200 °C, 3 at 210 °C, 4 at

220 °C, and 5 at 230 °C) . The readings were not corrected for

ice-point shifts.

0.30

0.25

0.20

0. 15

0.10

YEPR Plot for thermometer, serial number T1124411, at six

temperatures (1 at 250 °C, 2 at 260 °C, 3 at 270 °C, 4 at

280 °C, 5 at 290 °C, and 6 at 300 °C) . The readings were not

corrected for ice-point shifts.

105
0.25

0.20

0. 15

0. 10

0.05

YEAR

Fig. 39(b). Plot for thermometer, serial number T1124411, at two

temperatures (1 at 0 °C and 2 at 250 °C) . The readings were corrected for ice-point shifts.

or

tra

u

<r

HIh-£a

E

irujr

0.2

0. 1

0.0

-0.1

-0.2

-0.3

YEA3

Fig. 40(al). Plot for thermometer, serial number T1124412, at six

temperatures (1 at 0 °C, 2 at 200 °C, 3 at 210 °C, 4 at

220 °C, 5 at 230 °C, and 6 at 240 °C) . The readings were not

corrected for ice-point shifts.

106
0.35---

0.15

Fig. 40(a2). Plot for thermometer, serial number T1124412, at six

temperatures (1 at 250 °C, 2 at 260 °C, 3 at 270 °C, 4 at

280 °C, 5 at 290 °C, and 6 at 300 °C) . The readings were not

corrected for ice-point shifts.

0.25

0.20

0. 15

W 0. 10

0.05

0.00

YEAR Fig. 40(b). Plot for thermometer, serial number

temperatures (1 at 0 °C and 2 at 300 °C)

corrected for ice-point shifts.

Til 2441 2, at two

The readings were

107
1.0

-1.5

41 (al). Plot for thermometer, serial number 234453, at four

temperatures (1 at 0 °C, 2 at 300 °C, 3 at 310 °C, and 4 at

320 °C) . The readings were not corrected for ice-point

shifts

-0.75-

-1 .00

-1.25

g -1.50

1.75

-2.00

YEAR 41(a2). Plot thermometer, serial number 234453, at five temperatures

(1 at 340 °C, 2 at 350 °C, 3 at 370 °C, 4 at 380 °C, and 5 at

400 °C) . The readings wre not corrected for ice-point shifts.

108
0.5

41(b). Plot for thermometer, serial number

temperatures (1 at 0 °C and 2 at 350 °C) . corrected for ice-point shifts.

234453, at two

The readings were

42(al). Plot for thermometer,

temperatures (1 at 0 °C

330 °C, and 5 at 340 °C)

ice-point shifts.

YEAR serial number 234456, at five

2 at 310 °C, 3 at 320 °C, 4 at

The readings were not corrected for

109
-a.

74 76 78 80 83

TEAR

Fig. 42(a2). Plot for thermometer, serial number 234456, at five

temperatures (1 at 350 °C, 2 at 360 °C, 3 at 370 °C, 4 at

390 °C, and 5 at 400 °C) . The readings were not corrected for

ice-point shifts.

A comparison of the calculated values in Table 22 with the values listed in

Tables 12 and 14 are given in Table 23. In most cases the results are in

good agreement. The uncertainty in the range of 200 to 300 °C should

probably be changed to 0.2 °C, which would be closer to the calculated

value. This change will be considered. The calculated value for the low

temperature thermometer in the range of -60 to -30 °F is higher than listed

in Table 12. A change may be considered after more data is taken and

analyzed.

The statistical analysis verifies some of the values originally published

in Tables 12 and 14. Since no data was available for thermometers in the

similar temperature ranges but with larger graduation intervals,

statistical analysis was not possible. However, it has been noted that, in

most cases, the standard deviation of the check standard approximates the

resolution of the thermometer. Based on the above, the estimated

uncertainties for other types of thermometers listed in Tables 12 and 14 seem reasonable.

The only area where the uncertainties appear to be larger than calculated

is in the temperature range of -200 to 0 °C. Thermometers in this range

contain an organic liquid instead of mercury or a mercury alloy and the

published uncertainty presumably takes into account additional problems

associated with this type of thermometer. One such problem is that the

110
TABLE 20

LIMITS TO RANDOM ERROR COMPUTED FROM CHECK STANDARD MEASUREMENTS

Temperature

Range

(°F)

Bath

Temperature

(°F)

Check

Standard

Number

Limit to

Random Error

(3 Standard

Deviation)

Degrees of

Freedom

60 to -30 -30

-40

-50

-60

-30

-40

-50

-60

T531438

T531438

T531438

T531438

T531432

T531432

T531432

T531432

0.031

0.049

0.056

0.051

0.049

0.061

0.050

0.075

9 10

9

9

9

9

9

9

Pooled 0.054 73

Temperature

Range

(°C)

Bath

Temperature

CO

Check

Standard

Number

Limit to

Random Error

(3 Standard

Deviation)

Degrees of

Freedom

0 to 50 10

20

30

40

50

10

20

30

40

50

274762

274762

274762

274762

274762

274764

274764

274764

274764

274764

.014

.019

.017

.019

.019

.015

.016

.015

.015

.021

50

66

62

55

57

50

67

64

58

58

Pooled 017 587

50 to 100 60

70

80

90

100

50

60

70

80

90

100

4030424

4030424

4030424

4030424

4030424

4030425

4030425

4030425

4030425

4030425

4030425

020

015

020

022

029

018

.018

.017

.019

.020

.030

33

18

29

17

37

20

37

27

33

24

43

Pooled .023 300

111
Temperature

Range

(°C)

0 to 100

Bath

Temperature

Check

Standard

Limit to

Random Error

Degrees of

Freedom

100 to 200

( °C) Number (3 Standard

Deviation)

10 48425 .030 22

20 48425 .031 44

30 48425 .036 38

40 48425 .025 42

50 48425 .029 40

60 48425 .025 32

70 48425 .019 17

80 48425 .031 30

90 48425 .033 19

100 48425 .034 29

10 198694 .029 30

20 198694 .026 49

30 198694 .024 52

40 198694 .030 43

50 198694 .025 55

60 198694 .027 31

70 198694 .031 23

80 198694 .025 37

90 198694 .036 27

100 198694 .024 40

Poo led .028 700

100 382213 .047 35

110 382213 .036 9 120 382213 .057 23

130 382213 .058 8 140 382213 .068 19

150 382213 .073 21

160 382213 .049 18

170 382213 .081 12

180 382213 .087 26

190 382213 .091 6

200 382213 . 100 36

100 382215 .077 35

110 382215 .047 9

120 382215 . 087 26

130 382215 .045 16

140 382215 .089 28

150 382215 . 054 25

160 382215 .099 24

170 382215 .083 11

180 382215 .112 21

190 382215 .071 9

200 382215 .146 34

Pooled 084 451

112
Temperature

Range

CO

200 to 300

Bath

Temperature

CO

200

210

230

250

270

300

210

240

250

260

270

290

300

Check

Standard

Number

T112411

T112411

T112411

T112411

T112411

T112411

T112412

T112412

T112412

T112412

T112412

T112412

T112412

Limit to

Random Error

(3 Standard

Deviation)

.096

.156

.062

.068

.078

.072

.060

.030

.040

.084

.105

.108

.062

Degrees of

Freedom

2

32 13

4

14

2

2

9

54

2 13

Pooled 075 75

300 to 500 320

340

350

360

400

234453

234453

234453

234453

234453

.306

.203

.249

.306

.051

Pooled 240 19

TABLE 21

SYSTEMATIC ERRORS

Temperature Ice Point Platinum Bath Total

Range Resistance Gradient Systematic

(°C) Thermometer Error

100 to 0 0,,005 0,,001 0.01 0.016

0 to 50 0,,005 0.,001 0.005 0.011

50 to 100 0,,005 0.,001 0.,005 to 0, 01 0. Oil to 0..016

0 to 100 0..005 0..001 0,,005 to 0, 01 0..011 to 0 .016

100 to 200 0 ,005 0 .001 0.,01 to 0,,025 0..016 to 0 .031

200 to 300 0 .005 0 .001 0.05 0.056

300 to 500 0 ,005 0.001 to 0.003 0.,1 to 0..15 0..106 to 0 , 158

113
TABLE 22

CALCULATED UNCERTAINTIES FOR LIQUID- IN-GLASS THERMOMETERS

Temperature

Range

(°F)

-60 to -30

Thermometer

Graduation

(°F)

0.2

Limit to

Random Error

(3 a)

0.054

Total

Systematic

Error

0.029*

Calculated

Uncertainty

0.083

Temperature

Range

(°C)

0 to 50

50 to 100

0 to 100

100 to 200

200 to 300

300 to 500

Thermometer

Graduation

(°C)

0.1

0.1

1.0

Limit to

Random Error

(3 a)

0.017

0.023

0.028

0.084

0.075

0.240

Total

Systematic

Error

0.011

0.011 to 0.016

0.011 to 0.016

0.016 to 0.031

0.056

0.106 to 0.158

Calculated

Uncertainty

0.028

0.034 to 0.039

0.039 to 0.044

0.100 to 0.115

0. 131

0.346 to 0.398

^Fahrenheit equivalent of calculated value.

TABLE 23

COMPARISON OF PUBLISHED UNCERTAINTY VALUES

WITH CALCULATED UNCERTAINTY VALUES

Temperature Thermometer Published Values Calculated Values

Range Graduation of Uncertainty of Uncertainty

(°F) (°F)

-60 to -30 0.2 0.05 0.083

Temperature

Range

(°C)

Thermometer

Graduation

(°c)

Published Values

of Uncertainty

Calculated Values

of Uncertainty

0 to 50

50 to 100

0 to 100

100 to 200

200 to 300

300 to 500

0.1 0.01 to 0.03

0.01 to 0.03

0.02 to 0.05

0.05 to 0.1

0.2 to 0.3

0.2 to 0.5

0.028

0.034 to 0.039

0.039 to 0.044

0.100 to 0.115

0.131

0.346 to 0.398

114
fluid clings to the capillary wall as the liquid recedes into the bulb.

Because of this the thermometer should not be read immediately after

insertion into the medium. Up to one hour might be required before a reading can be recorded. Data will have to be taken on this type of

thermometer to verify the published uncertainty value or before a change in

this value is considered.

In Tables 12 and 15, uncertainties for Fahrenheit total- immersion thermometers are essentially the values given for Celsius thermometers having the same graduation interval in the various temperature ranges. In some cases,

where the thermometer graduation is much larger than the Celsius

equivalent, the uncertainty is approximately doubled (due to a decrease in

resolution) . Since one standard deviation seems to be an approximation of

the resolution of the thermometer, the uncertainties published for

Fahrenheit thermometers seem reasonable.

The uncertainties given in Table 18 are for temperature differences for

Beckmann and calorimetric thermometers. Systematic errors are not involved

in this uncertainty value, since they are eliminated when temperature

differences are obtained. Therefore, the resolution of the thermometer is

essentially the governing factor. Thermometers graduated in intervals of

0.01 or 0.02 degree can be read to the nearest 0.001 degree and thermometers graduated in intervals of 0.05 degree can be read to 0.005 degree.

Considering these numbers, the values given in Table 18 seem reasonable.

Data will be taken on this type of thermometer to verify these estimates.

No data is available for the uncertainty of partial-immersion thermometers. Several partial- immersion thermometers are currently being used

as check standards and data is being recorded for future statistical

analysis. Corrections are calculated both with and without emergent

stem- temperature corrections being applied. Until sufficient data is

available for analysis, the current published values given in Tables 13,

16, and 17 will be used.

10.0 Glass Changes and Recalibration of Thermometers

10.1 Glass Changes

The changes which occur in the glass of a liquid- in-glass thermometer bulb

after first heating to a high temperature within the acceptable exposure

limits of the glass and subsequent cooling to ambient temperatures, are a function of time and temperature. They will depend upon the thermal

history of the glass (both during manufacture and previous use) , the time

of exposure to the high temperature, and the rate of cooling. Evidence

from many investigations [2, 15, 16] seems to indicate that when a glass is

held indefinitely at some fixed temperature, density (and volume) changes

proceed toward a preferred density, corresponding to a quasi equilibrium

condition characteristic of the particular kind of glass and the temperature. Since these changes involve molecular rearrangements, they proceed

more rapidly at high temperatures where the viscosity of the glass is

lower, and the molecular mobility consequently higher. For this reason, a

115
close approach to quasi equilibrium may be reached in the order of hours at

annealing temperatures, while infinite time may be required at much lower

temperatures

If a glass that has been heated to a high temperature is allowed to cool

rapidly, it will be seen that equilibrium is not reached at the lower

temperatures during cooling, and an equilibrium density more nearly corres- ponding to the high temperature is "frozen" into the glass. This

characteristic behavior of glass has a lasting effect on the performance of

liquid- in-glass thermometers. For the entire lifetime of the thermometer,

it may retain a "memory" of the thermal history at the higher temperature.

The techniques of good manufacture are designed to produce in the thermometer glass a state which will result in maximum stability for the range of

temperature indicated on the scale. To achieve perfect stability for all

conditions of use is not possible in thermometer manufacture; therefore,

changes in the ice-point readings are observed periodically. The changes

observed at the ice point are reflected at all points on the scale by the same magnitude and sign, since they are the result of changes in the bulb

volume. The volume of the capillary also changes, but the volume of mercury

contained in the stem is so small, in comparison to the amount of mercury

in the bulb, that changes in the stem volume can usually be ignored.

Because of this behavior of glass, the changes in the bulb volume can be

either temporary or permanent.

10.1.1 Temporary Changes

Upon heating to a high temperature, the bulb of a thermometer will expand

from its initial state. After a short period of time, an equilibrium

condition corresponding to that particular high temperature will appear to

be reached. If the thermometer is cooled slowly through critical temperature regions, the glass will nearly return to its initial state, and the

ice-point reading will show no change. If, on the other hand, the thermometer is cooled rapidly (such as cooling naturally in still air) , the bulb

will retain a portion of its expanded condition, and the ice-point reading

will be lower than the reading taken before heating. This phenomenon is

known as "zero, or ice-point depression". Thermometers which have been

heated to high temperatures recover from this ice-point depression in an unpredictable way, and frequently there will be no significant recovery

after a period of one year at room temperature. Since the ice-point

depression has a reproducible value, ice-point readings may be used

reliably to show changes in the volume of the thermometer bulb with time

and use, provided the thermometer is allowed to cool in still air and the

ice point is taken within a reasonable period of time, not to exceed one hour, after being heated.

Thermometers below approximately 100 °C will usually exhibit a relatively

rapid recovery from the ice-point depression, and the original bulb volume

will recover within the equivalent of 0.01 or 0.02 °C in approximately

three days. This phenomenon has an important bearing on the precision

attainable with mercury thermometers, and must be taken into consideration,

especially in the range of 0 to 100 °C. If a thermometer is used to

116
measure a given temperature, it will indicate an erroneously low value if

it has, within a short period of time, previously been exposed to a higher

temperature. With the better grades of thermometric glasses the error resulting from this hysteresis will not exceed (in the interval of 0 to

100 °C) 0.01 of a degree for each 10-degree difference between the

temperature being measured and the higher temperature to which the

thermometer has recently been exposed. With the best glasses the error may

only be a few thousandths of a degree for each 10-degree difference. The errors due to this hysteresis become somewhat erratic at temperatures above

100 °C. For these reasons it is customary, in precision thermometry, to

apply a scale correction after the temperature measurement (See NBS

Monograph 150 [7], Section 5.2).

Where the range of temperature is small and the time between observations

is short (as in the use of calorimetric thermometers) , it is more satisfactory, each time the thermometer is used, to first heat to the highest

temperature to be measured, so that all the depression has taken place

before the observations are begun. The condition to be observed is that

the time required for observations is so short that no appreciable recovery

shall have taken place during this time. As this condition is fairly well

satisfied in calorimetric work, and as it is the only one for which consistent measurements of the same temperature interval can be made repeatedly,

calorimetric thermometers should be used in this way.

10.1.2 Permanent Changes

A "secular change" in thermometer glasses, which may progress with time,

results in a non-recoverable decrease in the bulb volume as indicated by an increase in the ice-point reading. At room temperature there may be a gradual change which will continue for years, but at high temperatures the

changes will be markedly accelerated. With better grades of thermometer

glasses the change will not exceed 0.1 °C over a period of many years,

provided the thermometer has not been heated to temperatures above approximately 150 °C. Initially, at high temperatures, the secular change usually

progresses more rapidly, but with continued heating and time it tends

toward a lower rate of change. The rate of secular change will depend upon

the kind of glass used in the thermometer bulb and the particular heat

treatment given the thermometer in manufacture. Thermometers manufactured

according to good practices will evidence only small secular changes.

However, thermometers made of glass unsuitable for the temperature range

indicated on the scale, or improperly annealed, may show changes as large

as 12 °C after heating for approximately 200 hours at high temperatures

[17]. Permanent changes in the bulb volume have also been observed when

thermometers have been repeatedly cycled at low temperatures (between -30

and +25 °C) [18] .

When using thermometers for high temperature measurements, one must use care to avoid overheating. After only a few minutes of heating the

thermometer at a temperature higher than its intended range, the increased

gas pressure above the liquid column may cause a permanent distortion of

the bulb resulting in lower thermometer indications.

117
10.2 Recalibration of Liquid- in-Glass Thermometers

The thermometer scale corrections quoted in the NBS Report of Calibration

apply as long as the ice -point reading remains the same as observed during

the calibration. As discussed above, subsequent changes in the ice-point

reading of the thermometer will result from small changes in the glass of

the thermometer bulb which affects its volume. As a result, changes in

the ice -point reading of the thermometer, taken after exposure of not fewer

than three days at a temperature of approximately 23 °C, will be reflected

by similar changes in readings at each point along the scale. Therefore,

when the correction at the ice point is found to be higher (or lower) than

that observed at the time of calibration, the other reported scale corrections will be higher (or lower) by the same amount. An example is given in

Table 24.

TABLE 24

RECALIBRATION OF LIQUID- IN-GLASS THERMOMETERS

Thermometer Correction from Correction Changed

Reading NBS Report of for Change in IceCalibration Point Reading

(°C) (°C) (°C)

+0.011

10.000

20.000

30.000

40.000

50.000

In Table 24, the thermometer readings are given in the first column and the

corrections that were determined at NBS are given in the second column.

The third column shows that the new ice-point correction was -0.019 °C,

indicating that the thermometer reading was +0.019 °C when the thermometer

was placed in an ice bath. This means that the thermometer bulb volume has

changed by an amount equal to 0.008° on the thermometer scale. Since the

thermometer now reads 0.008 of a degree higher at the ice point, it will be

reading 0.008 of a degree higher at all of the other calibration points

also. These values are given in the third column. These new corrections

should be used until a subsequent recalibration, by checking the ice point

again, is performed.

Once a thermometer has been calibrated, an ice-point check is all that is

necessary to obtain a current calibration, provided the thermometer has not

been abused, such as heating it beyond the highest temperature indicated on

the main scale. If the International Practical Temperature Scale changes, an additional correction for the difference between the two scales will be

provided by NBS. The difference between the two scales is added to the

-0.011

- .015

- .020 + .008

- .033

.000

-0.019

- .023

- .028

.000

- .041

- .008

118
current set of corrections for the thermometer (see NBS Monograph 150 [7],

Section 4). A liquid- in-glass thermometer will never have to be returned

to a calibration laboratory, such as NBS, for recalibration

11.0 Future

The demand for liquid-in-glass thermometer calibrations has been holding

steady at about 700 calibrations per year. A significant change in demand

is not anticipated, but the demand for other laboratory thermometers, such

as industrial resistance thermometers and thermistors, may increase.

Calibration services at present staffing levels can meet these new demands

if they amount to less than 50 per year. If the demand increases beyond

this point NBS may have to consider additional staff. No automation of

liquid- in-glass thermometers is contemplated, since the reading of these

thermometers by a computer would be difficult and costly to achieve.

12.0 Bibliography

[1] Thompson, R. D., Recent developments in liquid- in-glass thermometry,

Temperature, Its Measurement and Control in Science and Industry 3,

Part 1 (Reinhold Publishing Corp., New York, 1962) p 201.

[2] Liberatore, L. C, and Whitcomb, H. J., Density changes in

thermometer glasses, J. Am. Ceram. Soc . 35, 67 (1952).

[3] American Society for Testing and Materials, Designation C162,

Standard Definitions of Terms Relating to Glass and Glass Products,

Vol. 15.02.

[4] American Society for Testing and Materials, Designation E-77,

Verification and Calibration of Liquid- in-Glass Thermometers,

Vol. 14.03.

[5] The International Practical Temperature Scale of 1968 Amended Edition

of 1975, Metrologia 12, No. 1, 7-17 (1976).

[6] Cutkosky, R. D., An AC resistance thermometer bridge, J. Res. Nat.

Bur. Stand. (U.S.) 74C (Engr. and Instr.), Nos . 1 and 2, 15-18

(Jan. -June 1970)

[7] Wise, Jacquelyn A., Liquid-in-Glass Thermometry. Nat. Bur. Stand.

(U.S.) Monogr. 150; January 1976.

[8] Based on the data of Osborne, N. S., and Meyers, C. H., A formula and

tables for the pressure of saturated water vapor in the range 0 to

374 °C, J. Res. NBS 13, 1 (1934) RP691.

[9] American Society for Testing and Materials, Designation E-l, Standard

Specification for ASTM Thermometers, Vol. 14.03.

119
Ween, Sidney, "The Beckmann Differential Thermometer: Its Principles

of Construction and Application," Materials Research and Standards,

MTRSA, Vol. 12, No. 8, August 1972, p. 31.

Buckingham, E. , The correction for emergent stem of the mercurial

thermometer, Bui. BS 8, 239 (1912) S170.

Pemberton, L. H., Further consideration of emergent column correction

in mercury thermometry, J. Sci. Inst. 41, 234 (1964).

Riddle, John L. , Furukawa, George T., and Plumb, Harmon H., Platinum

Resistance Thermometry, Nat. Bur. Stand. (U.S.), Monogr. 126, April

1973, 126 pages.

Hall, J. A., and Leaver, V. M. , The design of mercury thermometers

for calorimetry, J. Sci. Instr. 36, 183 (1959).

Lillie, H. R. , and Shaver, W. W. , Method of tempering glass, U. S. Patent No. 2,148,630 (Feb. 28, 1939).

Liberatore , L. C, Method of stabilizing the molecular arrangement of

glass thermometers, U. S. Patent No. 2,610,445 (Sept. 16, 1952).

Ruh, E. L. , and Conklin, G. E. , Thermal stability in ASTM

thermometers, ASTM Bui. No. 233, 35 (Oct. 1958).

Martin, W. I., and Grossman, S. S., Calibration drift with thermometers repeatedly cooled to -30 °C, ASTM Bui. No. 231, 62 (July

1958) .

120
NBS-114A (REV. 2-8C) U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO.

NIST/SP-250/23

2. Performing Organ. Report No 3. Publ ication Date

September 1938

4. TITLE AND SUBTITLE

Liquid-In-Glass Thermometer Calibration Service

5. AUTHOR(S)

Jacquelyn Wise

6. PERFORMING ORGANIZATION (If joint or other than NBS. see instructions)

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY

(formerly NATIONAL BUREAU OF STANDARDS)

U.S. DEPARTMENT OF COMMERCE

GAITHERSBURG, MD 20899

7. Contract/Grant No.

8. Type of Report & Period Covered

Final

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. Stale, ZIP)

Same as item 6

10. SUPPLEMENTARY NOTES

Library of Congress Catalog Card Number: 88-600580

Document describes a computer program; SF-185, FlPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most si gnificant information. If document includes a significant

bibliography or literature survey, mention it here)

This document gives a description of the calibration of liquid-in-glass thermometers

at the National Bureau of Standards. The calibration equipment and procedures used

at NBS are discussed in detail. Calculations and stem-temperature corrections are shown and a discussion of the sources of error encountered in calibration and

estimates of uncertainties is presented.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

calibration; ice point; IPTS-68; liquid- in-glass thermometer; temperature;

uncertainty

13. AVAILABILITY

[A] Unlimited

| | For Official Distribution. Do Not Release to NTIS

r^M Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C.

20402.

fJQ Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF

PRINTED PAGES

128

15. Price

USCOMM-DC 6043-P80



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