/57

NBS MONOGRAPH 90

U. S. Cu'; .

L I i

Calibration of

Liquid-in-Glass Thermometers

U.S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

THE NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards is a principal focal point in the Federal Government for assuring

maximum application of the physical and engineering sciences to the advancement of technology in

industry and commerce. Its responsibilities include development and maintenance of the national

standards of measurement, and the provisions of means for making measurements consistent withthose standards; determination of physical constants and properties of materials; development of

methods for testing materials, mechanisms, and structures, and making such tests as may be nec-essary, particularly for government agencies; cooperation in the establishment of standard practices

for incorporation in codes and specifications; advisory service to government agencies on scientific

and technical problems; invention and development of devices to serve special needs of the Govern-ment; assistance to industry, business, and consumers in the development and acceptance of com-mercial standards and simplified trade practice recommendations; administration of programs in

cooperation with United States business groups and standards organizations for the developmentof international standards of practice; and maintenance of a clearinghouse for the collection anddissemination of scientific, technical, and engineering information. The scope of the Bureau'sactivities is suggested in the following listing of its four Institutes and their organizational units.

Institute for Basic Standards. Electricity. Metrology. Heat. Radiation Physics. Mechanics.Applied Mathematics. Atomic Physics. Physical Chemistry. Laboratory Astrophysics.* RadioStandards Laboratory: Radio Standards Physics; Radio Standards Engineering.** Office of Stand-ard Reference Data.

Institute for Materials Research. Analytical Chemistry. Polymers. Metallurgy. Inorganic

Materials. Reactor Radiations. Cryogenics.** Office of Standard Reference Materials.

Central Radio Propagation Laboratory.** Ionosphere Research and Propagation. Troposphere,and Space Telecommunications. Radio Systems. Upper Atmosphere and Space Physics.

Institute for Applied Technology. Textiles and Apparel Technology Center. Building Research.

Industrial Equipment. Information Technology. Performance Test Development. Instrumenta-tion. Transport Systems. Office of Technical Services. Office of Weights and Measures. Office

of Engineering Standards. Office of Industrial Services.

*NBS Group, Joint Institute for Laboratory Astrophysics at the University of Colorado.**Located at Boulder, Colorado.

UNITED STATES DEPARTMENT OF COMMERCE • Luther H. Hodges, Secretary

NATIONAL BUREAU OF STANDARDS • A. V. Astin, Director

Calibration of

Liquid-in-Glass Thermometers

James F. Swindells

National Bureau of Standards Monograph 90

Issued February 12, 1965

[Supersedes Circular 600]

For sale by the Superintendent of Documents, U.S. Government Printing Office

Washington, D.C., 20402 - Price 25 cents

Library of Congress Catalog Card Number : 64-62825

Foreword

The Kquid-in-glass thermometer is probably the most widely used tem-

perature measuring device in both science and industry. In spite of its fragile

nature, its relative simpUcity makes this type of thermometer singularly

attractive where reliable temperature measurements are required but where

the highest attainable accuracy is not necessary.

The hquid-in-glass thermometer is not an entirely foolproof instrument,

however. If the user is to reaUze the accuracy of which his thermometer is

capable, and to recognize its inherent Umitations as well, he must have, in

additon to its caUbration. some knowledge of the behavior to be expected of

such a thermometer. It is the purpose of this Monograph to emphasize the

important features of good practice in the design and use of Uquid-in-glass

thermometers, and to describe the techinques used by the National Bureau of

Standards in their calibration. This information is intended to be of value not

only to those who wish to submit thermometers to the Bureau for caUbration,

but also to manufacturers, to other standards laboratories, and to those whowish to caUbrate their own instruments.

A. V. AsTix, Director.

ContentsPage

Foreword iii

1. Introduction 1

2. Thermometer calibration services 1

2.1. Kinds of thermometers accepted for calibration 1

2.2. Reports of calibration 2

2.3. General instructions to applicants for tests 2

a. Initial arrangements 2

b. Shipping instructions 2

3. Definitions 5

4. Temperature scales and standards 6

5. Cahbration procedures 7

5.1. Equipment 7

a. Ice bath 7

b. Steam bath 7

c. Comparison liquid baths 7

5.2. Number and choice of test points 10

5.3. Determination of scale corrections 10

5.4. Corrections for emergent stem 11

a. Measurement of emergent-stem temperature ,11

b. Formula for total-immersion thermometers 12

c. Formula for partial-immersion thermometers 13

d. Formula for calorimeter thermometers 13

e. Formula for Beckmann thermometers 13

6. Common thermometers and factors affecting their use 14

6.1. Total-immersion thermometers 14

6.2. Partial-immersion thermometers 15

6.3. Low-temperature thermometers 15

6.4. Beckmann thermometers 16

6.5. Calorimeter thermometers 17

7. Thermometer design 17

7.1. Materials of construction 18

7.2. Scale design and workmanship 18

7.3. Scale dimensions 18

7.4. Reference point on scale 19

7.5. Marking of partial-immersion thermometers 19

8. Special notes 19

8.1. Glass changes 19

a. Temporary changes 20

b. Permanent changes 20

8.2. Pressure effects 21

8.3. Lag 21

8.4. Separated columns 22

9. References 23

iv

Calibration and Use of Liquid-in-Glass Thermometers

James F. Swindells

This Monograph, which supersedes Circular 600, contains information of generalinterest to both manufacturers and users of liquid-in-glass thermometers, as well as thosewho wish to calibrate thermometers or submit them to the National Bureau of Standardsfor calibration. Instructions are provided for applicants requesting calibration services,

and the techniques and equipment used in the calibration procedures are described.Important elements of thermometer design are discussed, and factors affecting the use ofcommon types of liquid-in-glass thermometers are included together with tables of tolerancesand reasonably attainable accuracies. The calculation of corrections for the temperature of

the emergent stem is given in detail for various types of thermometers and conditions of use.

1. Introduction

It is the responsibility of the National Bureau of

Standards to establish, maintain, and assumecustody of the Nation's standards of physicalmeasurement. One important activity underthis responsibility is the accurate reproduction of

the International Practical Temperatiu-e Scale as

a basis for the uniform measurement of tempera-ture throughout the scientific and industrial

activities of the United States. To this end the

Bureau accepts for calibration with reference to

this scale selected types of temperatiu-e-measuring

instruments [1] ^ for use as reference or workingstandards where precise-temperature measure-

ments are required. Less precise types of instru-

ments are not accepted, nor are the more routine

calibrations performed in cases where such workcan be done in qualified commercial testing

laboratories. This Monograph describes the

practices employed at the Bureau in the calibra-

tion of acceptable types of liquid-in-glass ther-

mometers. The information is intended for thosewho wish to submit thermometers for calibration

or who have occasion to use thermometerscalibrated at the Bureau.Important features of good practice in the use

of liquid-in-glass thermometers are emphasized to

assure realization of the accuracy of whichthermometers are capable, as well as to point outtheir inherent limitations.

In this Monograph, the material presented in

Circular 600 has been somewhat expanded andbrought up to date. The rearrangement of thematerial is intended to inform the reader immedi-ately of the Bureau's calibration services and howto make use of them, with the detailed description

of calibration methods and discussions of topics

in thermometry coming later.

2. Thermometer Calibration Services

The liquid-in-glass thermometer, discussed in

this Monograph, is one of many types of precise

instruments and standards for which calibration

services are offered by the NBS. A completelisting is found in NBS Miscellaneous Publication250.

;

As services are initiated or discontinued, or as

fees are changed, announcements will appear in

the Federal Register. Major changes in these will

be noted in the Standards and Calibration columnof the NBS Technical News Bulletin. TheBureau also plans to issue periodical listings of

such changes. To be placed on a mailing list to

receive these inserts as they are issued, a requestshould be addressed to The Ofl&ce of TechnicalInformation, National Bureau of Standards,Washington, D.C., 20234.

' Figures in brackets indicate the literature references at the end of this

Monograph.

2.1. Kinds of Thermometers Accepted for

Calibration

Liquid-in-glass thermometers include a widevariety of types, not all of which are accepted for

test. In general, considerations of design, intendeduse, and probable stability of the thermometerindications are the principal factors governingacceptability for test. Thermometers belonging

to the large and varied group which may beclassed as laboratory or "chemical" thermometersare regularly accepted. These may be of the

etched-stem or enclosed scale (Einschluss) type.

Other acceptable types include such special-

purpose thermometers as Beckmanns and calo-

rimeter thermometers. Thermometers of the

so-called industrial or mechanical types, withspecial mountings for their various intended uses,

can be accepted for test only when their construc-

tion permits testing with the equipment available.

1

Ordinary household or meteorological thermom-eters will not, in general, be accepted unless the

scale is graduated on the glass stem itself and the

thermometer can be readily detached from its

mounting for insertion in a testing bath.

Every thermometer submitted must be uniquelj''

identified by a serial number and must pass a

preliminary examination for details of construc-

tion before being finally accepted for test. Theexamination is made with optical aid (15 or 20 X)for fineness and uniformity of graduation, cleanness

of the mercury and capillary bore, and freedomfrom moisture, gas bubbles, and cracks in the

glass. Among other possible defects detected in

other ways, are omission of gas filling whereneeded, insufficient annealing and misnumberedgraduations. A complete listing of all possible

defects is not practicable. When serious defects

are found the thermometer is retiu-ned untested.

2.2. Reports of Calibration

A Report of Calibration issued by the Bureaufor a liquid-in-glass thermometer, in addition to

giving the results of the calibration, may be takenas an indication that the thermometer is free fromserious defects of design, material, or workman-ship, as discussed in section 7. Except in special

instances, a Report of Calibration is issued onlywhen the thermometer has been calibrated at a

sufficient number of points to provide reasonableassurance that the corrections obtained at the

temperatures of calibration can be applied, withinterpolation and extrapolation, throughout the

whole scale (see sec. 5.2).

In addition to the scale corrections listed withthe temperatures of calibration, the Reportcontains an estimate of the uncertainties associ-

ated with the corrections. The Report will also

show the following information: the manufac-turer's identification markings and numbers, the

agency or firm for which the calibration was made,the NBS test number and date of test, andexplanatory notes necessary to define the condi-

tions under which the results of test are applicable.

When necessary, the Report is accompanied by a

sheet showing how to calculate the correction for

emergent stem. If the thermometer is of the

metastatic (Beckmann) type, the Report will beaccompanied by a table of setting factors to enablethe user to apply the calibration results when the

thermometer is used with a setting other than thatfor which the corrections are given. Figure 1

shows the face of a sample Report and figure 2

shows the back of the same Report.It should be emphasized that the estimates of

error assigned to the scale corrections do notassure the user of this accuracy in a temperaturemeasurement. Care must be taken that the

thermometer bulb is at the temperature of the

medium whose temperature is to be measured.This involves considerations of heat transfer

from the medium to the bulb and heat conductionalong the thermom.eter stem. Any departurefrom the conditions under which the corrections

were obtained in calibration may significantlychange the values of the corrections. Conditionsof immersion are particularly important (seesec. 6), and even a change in the pressure to whichthe bulb is exposed may require an additionalcorrection (sec. 8.2).

Some of the reasons why a thermometer maybe denied a Report of Calibration are summarizedas follows:

(a) Defective design or workmanship.(b) Omission, where required, of ice point or

other reference point.

(c) Part of graduated scale not usable.(d) Defects in scale graduation or numbering.(e) Omission of required marking on partial-

immersion thermometers.(f) Unsuitable bulb glass or inadequate an-

nealing.

(g) Inadequate gas filling.

(h) Excessive scale error.

Details of good design and workmanship arediscussed in section 7.

2.3. General Instructions to Applicants forTests

Tests in accord with the policies of the NationalBureau of Standards, and of the types indicatedin the fee schedules as published in the "FederalRegister", will be undertaken. If need arises fora special test, not listed in the fee schedule butof a similar nature, the Biireau should be consulted.If the required measurements appear feasible, and,in the opinion of the Bureau, sufficiently impor-tant to justify the work, such tests will be under-taken for a special fee determined by the natureof the work. In aU requests the following pro-cedures and information are pertinent.

a. Initial Arrangements

A letter or purchase order, stating the tests

desired and referring to the appropriate section andsubsections of the fee schedule, should be sent to

the Bureau prior to any shipment. The purposeof this requirement is to determine whether or notthe Bureau will undertake the test and to insurecorrect procedure in reporting, shipping, andbilling. In the case of routine or periodic tests,

of a type made previously for the requester, this

letter njay be sent at the time shipment is made.In general, the purpose of the test and the mannerin which the results are to be used should be stated.

If the thermometer submitted has been previouslycalibrated by the Bureau, reference should bemade to the former test number. A test numberwill be assigned by the Bureau to each project,

and this test number must be referred to in all

subsequent communications.

b. Shipping Instructions

Shipping charges, both to and from the Bureau,must be assumed by the applicant. Return ship-

ments are made by the Bureau in accordance with

2

FORM NBS-186(T-l-«*l

U.S. Department of CommerceNATIONAL BUREAU OF STANDARDS

WASHINGTON. D.C. 20234

NATIONAL BUREAU OF STANDARDS

REPORT OF CALIBRATIONLIQUID-IN-GLASS THERMOMETER

Tested for: National Bureau of StandardsDivision 221, Section 01

Marked: Surety 198692

Range: -2 to +102 °C in 0.2°

ThermometerReading Correction

- 0.06 °C +0„06 °C

10.00 + .08

20.00 ^ .u30.00 + .10

i^O.OO + .04.

50.00 + .OA

60.00 + .04.

70.00 + .06

80.00 -1- .06

90.00 + .06

100.00 + .OA

If the correction is + the true temperature is higher than the indicated temperature; if the correction

is - the true temperature is lower than the indicated temperature. To use the corrections properly,

reference should be made to the notes marked by asterisks on the reverse of this sheet.

Estimated uncertainties ih the above corrections do not exceed 0,05° up to 102 °C , and

between and For a discussion of accuracies attainable with

such thermometers see National Bureau of Standards Circular 600, Calibration of Liquid-in-Glass

Thermometers.

Test No.Completed:

For the Director

311-30-64December 3, 1964.

KSL:dh

James F. Swindells, ChiefThermometry LaboratoryHeat Division USCOMM-DC >eB07-P93

Figure 1.

—

Facsimile of face of a Report of Calibration.

NOTES

*NOTE A.-The tabulated corrections apply for the

condition of total immersion of the bulb and liquid

column. If the thermometer is used at partial im-

mersion, apply an emergent stem correction as ex-

plained in the accompanying stem correctionsheet.

NOTE B.-The tabulated corrections apply for thecondition of total immersion of the bulb and liquid

column. Although this thermometer is not ordinarily

used in this way, no significant errors should beintroduced by neglecting the corrections for emer-gent stem.

NOTE C.-The thermometer was tested in a large,

closed-top, electrically heated, liquid bath at animmersion of The tem-perature of the room was about 25° C (77° F). If

the thermometer is used under conditions whichwould cause the average temperature of the emer-gent liquid column to differ markedly from that

prevailing in the test, appreciable differences in

the indications of the thermometer would result.

NOTE D.-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 behigher (or lower) by the same amount.

*NOTE E.-The tabulated corrections apply provided

the ice-point reading, taken after exposure for not

less than 3 days to a temperature of about 25° C(77° F) is -0.06 °C If the ice-point

reading is found to behigher(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 or less, for

each 10° 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.

NOTE F.-The tabulated corrections apply pro-vided the reading when the thermometer is im-mersed in steam at 100° C (212° F) is

If the reading is found to be higher

Special Note.-

(or lower) than stated, all other readings will behigher (or lower) by the same amount. The tem-

perature of steam is 100° C (212° F) only if the

pressure is 760 mm (29.921 inches). If the pres-

sure differs from 760 mm (29-921 inches) allowancemust be made for this. If the pressure is higher

(or lower) than 760 mm (29.921 inches) the tem-

perature will be higher (or lower) than 100° C(212° F) by approximately 0.037° C per mm dif-

ference (1.68° F per inch difference).

NOTE G.-The thermometer, before testing, washeated to the temperature of the highest test point.

The application of the tabular corrections to the

readings of the thermometer will give true tempera-

ture differences provided the thermometer is usedin its upright position and is heated previously

(within an hour before using) to the highest tem-

perature to be measured.

NOTE H.-The thermometer was tested for use in

differential measurements, such as the measure-

ment of temperature differences in a flow calori-

meter. The two thermometers used in a flow calori-

meter should be compared occasionally in stirred

water at some convenient temperature and if their

indications, after application of the tabular cor-

rections, are found to differ, an additional cor-

rection equal to the difference should be applied

to the indications of one of them.

NOTE I.- The tabulated corrections apply for a

"setting" of 20° C. Setting factors for use with

other settings are given on the accompanying sheet.

NOTE J. -The tabulated corrections apply for the

condition of immersion indicated provided the ice-

point reading, taken after heating to

for not less 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.

NOTE K.-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= /° and an assumedtemperature of ° for the emergent stem .

FORM NBS-I8S (7-l-SS) U8COMM-DC I S507-Pei

Figure 2.

—

Facsimile of back of a Report of Calibration.

its judgment of the best method of shipping unless

specific instructions are received. Such instruc-

tions should be supplied at the time that arrange-

ments are being made for the test. If a test

number has been assigned prior to the shipment,this number should appear on the shipping con-

tainer. If a test number has not been assigned

at this time, a purchase order, or letter shoidd besent under separate cover. In either case the

shipment should include a packing list.

AU possible care will be taken in handlingthermometers at the Bureau, but the risk of

damage either in shipment or in testing must beassumed by the applicant. The applicant shouldconsider the nature of the equipment he is shippingand pack it accordingly, with appropriate labeling.

Attention is called to the availability of securityexpress in shipping thermometers.

3. Definitions

The principal features of a solid-stem liquid-in-

glass thermometer are shown in figure 3. Not aUof the features shown would necessarily be incor-

porated in any one thermometer.Bulb: The liquid reservoir. The bulb of a

thermometer will contain a voliune equivalent to a

specific number of degrees of the scale dependingupon the coefficients of expansion of the thermo-metric liquid and bulb glass. For mercury in a

"normal" glass bulb the voliune is equivalent to

about 6200 °C, or 11, 200 °F. For organic thermo-metric hquids with higher coefficients of expansionthan mercury, the degree equivalents of the bulbvoliune are correspondingly lower.

Stem: The glass capillary tube through whichthe thermometric Hquid advances or retreats withchange in temperature.

Main Scale: The scale graduated in degrees or

multiples or submultiples of degrees.

Auxiliary Scale: A short scale including a refer-

ence temperature such as the ice point, to provide

a means for checking thermometer for change in

calibration with time. (See sec. 7.4.) This scale

is added when a suitable reference temperature is

not included in the range of the main scale.

Expansion Chamber: An enlargement at the topend of the capillary bore having a volume equiva-lent to not less than 20 mm of unchanged capillary.

Smaller chambers are not regarded as expansionchambers. The expansion chamber is providedto prevent the buildup of excessive pressures in

gas-filled thermometers as the liquid filling ad-vances toward the top of the scale.

Contraction Chamber: An enlargement of thecapillary bore which serves to reduce a long lengthof capillary or to prevent contraction of the liquid

column into the bulb. This chamber is introducedbelow the main scale or between the main scale

and an auxiliary scale.

Reference Point: Some reference temperature,within the range of the main scale or an auxiliary

scale, such as the ice point or steam point, at

which the thermometer may be checked periodic-

ally for changes in scale caUbration. (See sec. 7.4.)

Total Immersion Thermometer: A thermometerdesigned to indicate temperatures correctly whenused with the bulb and the entire liquid column in

the stem exposed to the temperature beingmeasured.

Partial Immersion Thermometer: A thermometerdesigned to indicate temperatures correctly when

^BULBCONTRACTIONCHAMBER

EXPANSION_CHAMBER

AUXILIARY_SCALE

IMMERSIONLINEJ MAI

SCALE

Figure 3.

—

Principal features of a solid-stem liquid-in-glass

thermometer.

used with the bulb and a specified part of the stemexposed to the temperature being measured. Theremaining part of the stem will be at the ambienttemperature, usually different from the tempera-ture being measured. Such thermometers aremarked with an immersion line to indicate theproper depth of immersion. The emergent stemrefers to the length of liquid column and stem atthe ambient temperature.

Complete Immersion Thermometer: A thermom-eter designed to indicate temperatures correctlywhen the whole thermometer, including the expan-sion chamber, is exposed to the temperature beingmeasured. In gas-filled thermometers the readingwill be different for complete, as compared to total

immersion as a result of the effect of temperatureon the gas pressure in the thermometer. (Seesec. 8.2). The difference in readings under thetwo conditions is particularly significant at hightemperatures.

Calibration Points are the temperatures at

which corrections to the thermometer scale are

determined.Accuracy: The accuracy of a measurement refers

to the closeness with which the result of themeasurement approaches the true value of thequantity being measured. In this Monographthe accuracy expected of a given thermometerrefers to the closeness of the observed indicationof the thermometer to the true temperature onthe International Practical Temperature Scale.

The accuracy attainable is principally limited bythe characteristics of the thermometer itself.

Instability of the thermometer glass, capillary

forces at the surface of the thermometric liquid,

non-uniformity of capillary bore, and inaccuracies

in scale graduation are among the importantfactors. With partial immersion thermometers,uncertainties in corrections for the emergent stemmay greatly limit the accuracy. Observer errors

are also involved, but with care these can usuallybe made relatively smaU.

5

Precision: The precision of measurement refers

to the degree of agreement amongst repeated

measurements of the same quantity. When a

thermometer is held at constant temperature andit is read repeatedly at the same scale reading,

one can be deceived in assuming that a correspond-ing accurac}'^ is being achieved. For example,capillary forces may be holding the liquid columnat the false level, or the bulb volume may havechanged since the time of calibration.

4. Temperature Scales and Standards

The calibration of a thermometer consists of

comparing its indications with known tempera-tures on a standard scale of temperature. Byinternational agreement, the Kelvin Scale is now-

accepted as the absolute Thermodynamic scale.

In 1954 the Tenth General Conference on Weightsand Measures defined the Kelvin Scale by meansof a single fixed point, the triple point of water, to

which was assigned the temperature 273.16 °K,exactly. Because of the difficulties encounteredin the practical realization of the Kelvin Scale,

however, a practical working scale, the Interna-

tional Temperature Scale, was first adopted in

1927 and later revised in 1948. In 1960 the

Eleventh General Conference changed the nameof the scale to International Practical TemperatureScale of 1948 (IPTS) and adopted a revised text

of the scale [2]. The Scale itself was not changed,however. The new text, therefore, does notchange the value of any temperature on the 1948scale by as much as the experimental error of

measurement. This Scale is intended to haveclose correspondence with the Kelvin Scale and to

provide scientific and industrial laboratories

throughout the world with a common basis for

stating temperatures. Cahbrations of thermom-eters at the Bureau, therefore, are made withreference to temperatures on the IPTS.

In the range of temperatures normally coveredby liquid-in-glass thermometry, the IPTS is

defined by four fixed points, the normal boiling

point of oxygen at — 182.97 °C, the triple point of

water at -|-0.01 °C, the normal boiling point of

water at 100 °C, and the normal boUing point of

sulfur at 444.6 °C. In place of the sulfur point,

however, the text of the Scale recommends the

use of the temperature of equilibrium betweensolid zinc and liquid zinc (zinc point) with the

value of 419.505 °C. Experience has shown the

zinc point to be more reproducible than the sulfur

point. Temperatures in the range —182.97 to

630.5 °C, at other than these fixed points, are

defined in terms of a standard platinum resistance

thermometer calibrated at the four fixed pointsand using a specified equation for interpolation.

Temperatures on the IPTS are expressed in

degrees Celsius (centigrade). Thermometersgraduated on the Fahrenheit Scale are calibratedwith reference to the IPTS using the conversionformula,

9temperature in °F = - (temperature in °C)-|-32.

When the highest accuracy is required in acalibration, the thermometer indications arecompared directly with temperatures obtainedwith a standard resistance thermometer. If lesser

accuracy is adequate, one of a series of mercury-in-glass standards is used, except below 0 °C andabove 300 °C, where the calibration is madedirectly with a resistance thermometer regardlessof the accuracy required. The series of mercury-in-glass thermometers which serve as standardsfor total-immersion comparisons is shown below.

Range Smallestgraduation

Auxiliaryscale

"C0 to 50

"C0.10.20.10.20.6

°C

0 to 100 -60 to 100.... atO

atOatO

100 to 200200 to 300

These standards are calibrated with referenceto the IPTS through comparisons with a standardresistance thermometer.

Partial-immersion standards, known as "like

standards", are maintained for the calibration of

accepted designs of partial-immersion thermom-eters. These standards are calibrated for stem-temperature conditions expected to prevail duringthe calibration of similar thermometers. Thisuse of like standards eliminates the need for manyof the precautions necessary when dissimilar

thermometers are compared. The procedure per-

mits the direct comparison of the indications of

similar thermometers as long as the bulbs are at

the same temperature and the stem temperaturesare essentially the same for all of the thermometersunder comparison.

For those who may want to use reproduciblefixed points in their own laboratories, the Bureausells triple-point-of-benzoic-acid cells, 122 °C(252 °F) ; and freezing point cells of phenol, 41 °C(106 °F), naphthalene, 80 °C (176 °F), and phthalicanhydride, 131 °C (268 °F). At higher tempera-tures freezing point standards of tin, 232 °C (450°F); lead, 327 °C (621 °F) ; and zinc, 419 °C (786°F) are available. (AU of the above temperaturesare approximate, but precise values are suppliedwith the standards.) Detailed information onthese cells and standards and their procurementis given in NBS Miscellaneous Publication 241.

6

5. Calibration Procedures

All liquid-in-glass thermometers are calibrated

in terms of the IPTS as defined by the standardplatinum resistance thermometer. The readings

may be compared directly with a standard resist-

ance thermometer, or indirectly using a mercury-in-glass standard. Ice and steam baths, together

with a series of stirred liquid baths, provide con-

trolled temperature media for the comparisons.

5.1. Equipment

a. Ice Bath

Through the use of an ice bath, the ice point

may be realized conveniently to better than 0.01

°C. A Dewar flask serves as a container for the

ice, the melting of the ice being retarded by the

insulating properties of the vessel. Ice shavedfrom clear cakes is mixed with distilled water to

form a slush. Enough water is used to afford

good contact with the thermometers, but not so

much as to float the ice. From time to time excess

water is syphoned from the bath. Care is takento prevent contamination of the ice and water. Asmall reading telescope with a magnification of 10

diameters aids in reading the thermometer indica-

tion and reduces parallax errors. Gently tapping

the thermometer just before reading may preventthe sticking of a falling meniscus. On the other

hand too vigorous a tap will occasionally cause the

mercury to reboimd to an erroneously high reading.

b. Steam Bath

The steam point may be realized in a steam-point apparatus either "by comparing the ther-

mometers with standards or by the determinationof the temperature of the steam from a measure-ment of the prevailing atmospheric pressure.

The steam bath, shown in figure 4, consists of a

double-walled steam jacket in which steam from a

boiler circulates. The thermometers are sus-

pended in such a manner as to insiire free circula-

tion of steam around them. Provision is made for

either reheving any excess pressure in the spacesiirrounding the thermometers, or for determiningthe excess by means of a smaU differential

manometer.When the steam bath is used as a fixed-point

apparatus a barometer is a necessary accessory

since the true temperature of the steam is depend-ent upon the prevailing atmospheric pressure.

The usual corrections are apphed to the barometerreading including any corrections necessary for the

value of local acceleration of gravity, for the

difference in height of the steam bath and the

barometer, and for any excess pressure aboveatmospheric in the steam jacket. The steamtemperature may then be fovmd from the pressure-

temperature values given in table 1. With a goodbarometer, acciirate to 0.1 mm Hg, this procediire

s capable of an accuracy of 0.002 to 0.003 deg Ci(0.004 to 0.005 deg F). The Fortin type barome-ter will usually serve for all but the most exactingmeasurements.The steam bath is also used as comparison bath,

in which case the temperature of the steam is deter-mined at the time of test by means of a previouslystandardized thermometer. This method is sim-pler than determining the steam temperature froma barometer reading, and may be preferable,

particularly when a resistance thermometer canbe used as the standard.

c. Comparison Liquid Baths

Stirred liquid baths of two designs are used atthe Bureau as comparators in which thermometersare calibrated in the range —40 to +500 °C.(-40 to +930 °F). This equipment permitsstirring adequate for uniform temperature distri-

bution, and provides controlled heat input for

temperature regulation.

A type suitable for use with media liquid atroom temperatiu"e is shown in figure 5. Thisbath is constructed with two tubes of different

diameters having connecting passages at the topand bottom. The heating coU, cooling coil for

circulating cold water for comparisons below room

Figure 4.

—

Schematic drawing of steam bath.

7

Table 1.

—

{Thermomelric) condensation temperature of steam [S]

(Astrisk (•) indicates change in integer]

Pressure in mm mercury (standard)

p 0 1 2 3 4 5 6 7 8 9

Temperature in degrees of International Scale

500 88. 678 0.730 0.782 0.834 0.886 0.938 0.990 •0. 042 •0.093 •0. 144fit ft 89. 196 . 247 . 298 . 350 . 401 . 452 . 502 . 553 .604 .655ROft 0. 705 . 756 . 806 . 856 . 907 . 957 •. 007 •. 057 *. 107 *. 157oou 90. 206 . 256 . 306 . 355 . 405 . 454 . 503 . 553 . 602 .651(Lift 0. 700 . 749 . 798 .846 .895 . 944 . 992 •. 041 *. 089 •. 138

550 91. 186 .234 .282 .330 .378 .426 .474 .521 .569 .617OOU 0. 664 . 712 . 759 . 806 . 854 . 901 . 948 . 995 •. 042 *. 089570 92. 136 . 182 . 229 . 276 . 322 . 369 . 415 . 462 . 508 . 554win 0. 600 . 646 . 692 . 738 . 784 . 830 . 876 . 922 . 967 '. 013690 93. 058 . 104 . 149 . 195 . 240 . 285 . 330 . 375 . 420 . 465

600 0. 5100 .5548 .5996 .6443 .6889 .7335 .7780 .8224 .8668 .9112610 . 9554 . 9996 *. 0438 *. 0879 *. 1319 *. 1759 *. 2198 *. 2636 '. 3074 '. 3511620 94. 3948 . 4384 . 4820 . 5255 . 5689 . 6123 . 6556 . 6989 . 7421 . 7852630 0. 8283 . 8713 . 9143 . 9572 *. 0001 *. 0429 •. 0857 '. 1284 *. 1710 *. 2136640 95. 2562 . 2987 . 3411 . 3834 . 4257 . 4680 . 5102 . 5523 . 5944 . 6366

650 yo. oioo . 7204 . 7623 . OlOV *. 0539oou 96. 0954 .1368 .1782 .2195 .2607 .3019 .3431 .3842 .4252 .4662670 0. 5072 . 5480 .5889 .6297 .6704 .7111 .7517 .7923 .8329 .8734680 .9138 . 9542 .9946 •.0349 *. 0751 M153 •. 1555 '. 1956 •.2356 •.2756

oyu 97. 3156 .3555 .3954 .4352 .4749 .5146 .6543 .5939 .6335 .6730

700 0. 7125 .7519 .7913 .8307 .8700 .9092 .9484 .9876 •. 0267 *. 0667710 98. 1048 . 1437 . 1827 .2216 .2604 .2992 .3379 .3766 .4153 .4539720 0. 4925 .5310 .5695 .6079 .6463 .6846 .7229 .7612 .7994 .8376730 .8757 .9138 .9519 .9899 •. 0278 •.0657 *. 1036 •. 1414 1792 •. 2110740 99. 2547 .2924 .3300 .3675 .4051 .4426 .4800 .5174 .5548 .6921

750 0. 6294 .6667 .7039 .7410 .7781 .8152 .8523 .8893 .9262 .9631

760 100. 0000 .036? .0736 .1104 .1471 .1838 .2204 .2570 .2936 .3301

770 0. 3666 .4030 .4394 .4758 .5121 .5484 .5846 .6208 . 6570 .6932780 .7293 .7653 .8013 .8373 .8733 .9092 .9450 .9808 •. 0166 •. 0524

790 101. 0881 .1238 .1594 .1950 .2306 .2661 .3016 .3371 .3725 .4079

temperature, and stirrer are located in the smaller

tube, the larger tube being left clear for immersionof the thermometers.The type shown in figure 6 is designed for use

at high temperatures with molten tin as the bathliquid. The bath is made with two coaxial tubesof which the inner tube is open at both ends. Thestirring propeller is mounted near the bottom of

the inner tube leaving the space above the pro-

peller free to receive thermometers which are in-

serted in reentrant tubes. Heat is supplied byheater coils wound on the outside tube. As is

also the case with the bath shown in figure 5, the

thermometers are shielded from direct radiation

from the hotter parts of the bath.

In each type of bath a 2- or 3-in. thickness

of insulation reduces heat loss and thus aids in

maintaining a uniform temperature distribution

throughout the bath liquid. Each bath is pro-

vided with an insulated cover carrying a ther-

mometer holder which can be rotated to bringsuccessive thermometers into the field of a ver-

tically adjustable reading telescope.

For calibrations in the range 5 to 99 °C (40 to

210 °F) water is used as the bath liquid. Onegrade of petroleum oil is used between 99 and200 °C (210 and 392 °F) and a second between200 and 315 °C (392 and 599 °F). The oils are

chosen with properties such that they are not too

viscous for adequate stirring at the lower temper-ature but at the same time have flash points which

THERMOMETERHOLDER

INSULATION

AIR SPACE

SPACE

BETWEENTUBES

BEARING

SUPPORT

Figure 5.

—

Stirred liquid bath.

STIR DRIVE

!,'il'u,:'i'< ''MS:

- INSULATION

-TESTING AREA

-AIR SPACE

-HEATING COIL

Figure 6.

—

Stirred high-temperature hath using liquidhaving freezing point above room temperature.

are not exceeded at the higher temperatures. Thetin bath is used from 315 °C up to about 540 °C(599 to 1004 °F).

Cahbrations from 0 to - 110 °C (32 to - 166 °F)are made in a cryostat similar lq essentials to thatdescribed by Scott and Brickwedde [4]. The cryo-stat, shown in fig\u"e 7, consists of an inner Dewarflask, D, which contains the bath hquid, sur-

rounded by liquid nitrogen in the outer Dewarflask, C. The rate of heat transfer between thebath hquid and the liquid nitrogen is controlledby varying the gas pressiue between the waUs of

the inner Dewar flask, which is connected to avacuum system through the side tube, M. Vigor-ous stirring of the bath liquid is maintained bythe propeller, I, which circulates liquid upwardsthrough the inside of the stuTer tube, P, and downthe outside. Excess refrigeration is compensatedby thermostatically controlled heat supplied by a

heater coU, J, wound outside the stirrer tube.

Figure 7.— Vertical section of cryostat.

For temperatures down to -75 °C (-103 °F)

the bath liquid used is the eutectic mixture of

carbon tetrachloride and chloroform (49.4 percent,

by weight, of CCI4, and 50 6 percent of CHCI3),which freezes at about -81 °C (-114 °F). Fortemperatures between —75 and —110 °C (—103and — 166 °F) a five-component mixture is usedcontaining 14.5 percent of chloroform, 25.3 per-

cent of methylene chloride, 33.4 percent of ethyl

757-©604

bromide, 10.4 percent of transdichloroethylene,

and 16.4 percent of trichloroethylene. This mix-ture freezes at about -150 °C (238 °F), butabsorbs moisture readily and becomes cloudy at

somewhat higher temperatures.

5.2. Number and Choice of Test Points

Usually corrections to a thermometer scale are

measured at uniformly spaced calibration points

covering the whole range of the main scale. Thelength of scale between calibration points shouldbe chosen with regard to the accuracy expected of

the thermometer in use. The points should notbe chosen unnecessarily close together, nor shouldthey be spaced so far apart as to destroy confidencein interpolated corrections at temperatures be-

tween the calibration points. For many yearsthe predecessors of this Monograph have containedthe statement: "In general, if the readings of athermometer are to be trusted to one or two-tenthsof the smallest scale division, the interval betweentest points should not exceed 100 divisions andusually need not be less than 40." Recent studies

of calibration data for over 50 thermometers pur-chased during the years 1930 through 1956 for useas laboratory standards showed that, while there

was considerable variation between individual

thermometers, the above statement was usuallyapplicable only to thermometers not graduatedabove about 200 °C. For the thermometers notgraduated above 200 °C, calibrations every 40 to

50 divisions were required for interpolation to oneor two-tenths of a division. In nearly aU cases,

interpolation between calibrations 100 divisions

apart could be relied upon only to one-half of adivision. For most of the thermometers gradu-ated above 200 °C, the data showed that interpola-

tions between calibrations 40 to 50 divisions apartwere reliable to only one-half division, and thatthe spacing had to be reduced to 20 to 25 divisions

if interpolation to one or two-tenths division wasto be expected. It was found also that an exami-nation of scale corrections obtained a given num-ber of divisions apart for a particular thermometerwas not sufficient to predict whether or not morecalibration points were required for reliable in-

terpolation. The above studies were made withonly a few of the many types of thermometerssubmitted to the Bureau for calibration, and,therefore, conclusions may not necessarily beapplicable to other types. Experience with aparticular type of thermometer seems to be themost reliable guide in the choice of calibration

points.

When a thermometer is to be calibrated withoutreference to any special use, the choice of calibra-

tion points should be left to the calibration labora-tory. In some cases the number and distribution

of test points can be decided only after a careful

inspection of the thermometer. If the thermome-ter is to be used for a special purpose, this fact

should be clearly stated before calibration. TheBureau will not make calibrations at more, orfewer, points than are necessary, although this

judgment may be influenced by considerations |l

given to special requests. In any case, no fewerthan two points are taken on the main scale. Atleast one reference point is included as a calibra- i

tion point when such a point (or points) is includedin the scale.

5.3. Determination of Scale Corrections

Through considerations of accuracy, Beckmannthermometers, calorimeter thermometers, andthermometers graduated in tenths of a degreeFahrenheit are calibrated using a platinum re-

sistance thermometer. A platinum thermometeris also used for all calibrations made below 0 °C(32 °F) or above 300 °C (572 °F). Other calibra-tions are generally made using mercury-in-glassstandards (listed in sec. 4) which have been

|

calibrated with a platinum thermometer.When comparing thermometers with liquid-in-

glass standards two standards are always used.In this way reading errors are more readily de-tected and cross checks of the standards are main-tained. The comparison procedures are describedin simplified form in the following hypotheticaltest of foiu" thermometers, Tl through T4.

Table 2 shows the observations taken in obtain-ing the corrections appficable to the thermometersat 20 °C. For simplification, aU of the entries in

the table reflect perfect thermometer performanceand no observer error.

Table 2.

—

Comparison of test thermometers with liquid-in-

glass standards

Ice-point readings of test thermometers

Observer A

SI Tl T2 T3 T4 S2

+0.02+.02+.02

-0.02-.02-.02

+0. 02+.02+.02

0.000. 00.00

Observer BMean ice points

Thermometer comparisons

Observer A reading left toright 19. 87 19.98 19. 96 20. 02 20. 03 19.89

Observer A reading right toleft 19.88 19.99 19. 97 20.03 20.04 19.89

Observer B reading left toright 19.88 19.99 19. 97 20.04 20. 05 19.90

Observer B reading right toleft 19. 89 20.00 19.98 20. 04 20. 05 19.90

Means 19.88 19. 99 19. 97 20.03 20.04 19. 895

Ice-point readings of standards

Observer A -0. 01-.01-.01

-0.08-.08-.08

Observer BMean ice points

Calculations of corrections

Correction to standards +0. 12

20.01

+0.04

20. Ols

Mean temperature, eachstandard _

Mean temperature of all read-ings 20. 01

+0.04Corrections to test thermom-

eters... +0. 02 -0.02 -0.03

The first observations are the ice points of thethermometers under test. These are entered in

the upper part of the table. The thermometersare then mounted in the comparison bath betweenthe two standards, and the power to the bath is so

10

adjusted that its temperature is slowly increasing

at a steady rate. The data shown in the table are

for a temperature rise of 0.001° between eachobservation. Two observers (A and B) are used,

first with one observer reading and the otherrecording, and next with the observers inter-

changed. Observer A reads in the order left to

right as the thermometers appear in the table andthen repeats the observations in the order right to

left. Observer B then immediately reads in the

same manner. The observations are spacedimiformly in time so that, with the bath tempera-ture increasing linearly with time, the mean of the

observations with any one thermometer will

correspond to the mean temperature of the com-parison bath during the observations of all of the

thermometers. Immediately after the comparisonobservations, ice points are taken of the twostandards. Using these ice point data, together

with the known scale corrections for the standards,

the temperatiu-es indicated by the standards are

calculated and an overall mean temperature for

the observations is obtained. This overall meantemperatiu-e is compared with the mean of the

observations for each thermometer to obtain a

correction to the scale of the thermometer at this

point. The thermometer comparisons are thenrepeated at the next higher test point and so onuntn corrections are obtained at a sufficient num-ber of points to cahbrate the complete scale, as

specified in section 5.2.

When a resistance thermometer standard is

used, the sequence of observations is the sameexcept that only one standard is used, the sameresistance thermometer being read foiu* times in

place of the separate observations of two hquid-in-glass standards.

Ice-point readings are not usually taken vtdth

each test point on the scale. For thermometersnot graduated above 300 °C or 600 °F, ice points

taken before the first test point on the scale andafter the last point will usually suffice. Withhigh-temperature thermometers, however, it is the

practice to take an ice point and then test immedi-ately at the highest test point on the scale. After

a rest period of 3 days at room temperature a

second ice point is taken. If a change in ice pointis found that is greater than the expected accuracyof the thermometer, the thermometer is deemedunsuitable for calibration and further tests are

unnecessary.

The corrections obtained in this manner applyas long as the ice point remains the same as that

observed during calibration. Subsequent changesin the ice point will be a result of small changes in

the glass which affect the volume of the thermom-eter bulb. The volume of the capillary stem also

changes, but the volume of mercury con-

tained in the stem is so smaU in comparison to

that in the biilb that changes in the stem volumecan usually be ignored. As a result, changes in

the ice-point reading will be duplicated by similar

changes in readings at each point along the scale.

Thus, when during use the correction at the ice

point is found to be higher (or lower) than thatobserved at the time of calibration, the otherreported corrections to the scale can confidentlybe taken to be higher (or lower) by the sameamount.

5.4. Corrections for Emergent Stem

The proper application of scale corrections asreported in NBS Reports presents no difficulties

in cases where thermometers are calibrated andiised under conditions of total immersion. In suchcases the temperature of the thermometer, includ-ing the stem up to the top of the mercury thread,is definitely specified and the corrections as givenapply when the thermometer is used at totalimmersion. Instances frequently occur, however,where some part of the mercury column is emer-gent from the region whose temperatiue is beingmeasured. In these cases the emergent part ofthe stem may be in an environment, not only inwhich the temperature is markedly different fromthat of the thermometer bidb, but in which pro-nounced temperature gradients may be present.If such a situation exists in the use of a thermom-eter which has been calibrated at total immersion,a correction may be calculated to account for thedifference in temperatm"e between the bulb andthe emergent stem. The calculation of this correc-tion requires a reliable estimate of the meantemperattu-e of the emergent stem, which, for thebest work, will be made from measurements. Butif the stem temperature measiu-ements are notrepeated each time the thermometer is used, theacciu"acy of the correction will depend upon theconstancy of the stem temperature over periodsof time. For example, if the emergent stem is

exposed to the air above a liquid bath, variationsin ambient temperature and air circulation cancause significant variations in the temperature of

the emergent stem.The same situation occiirs in the case of partial-

immersion thermometers. For this type of ther-

mometer, the reported scale corrections apply onlyfor the indicated depth of immersion and a par-ticular stem temperature. If the thermometer is

then used under conditions where the mean stemtemperature is different, the reported scale correc-

tions are not applicable, and a stem teniperaturecorrection is required.

The following paragraphs describe methodsfor determining stem temperatm-es and calculating

corrections. For a known or assumed condition,

the use of these formulas wiU indicate the impor-tance of the stem correction in relation to a desired

accuracy, and the corrections can then be appliedas necessary.

a. Measurement of Emergent-Stem Temperature

The mean temperatiu*e of the emergent stemmay be measured approximately by means of oneor more small auxiliary thermometers suspendednear the emergent stem, or more acciu"ately by

11

exposing a similar stem and capillary mercurycolumn beside the emergent stem and thus measur-ing its mean temperature [5, 6]. This is con-

veniently carried out with a faden thermometer("thread thermometer") in which the expansionof the mercury in a capillary tube (bulb) is measur-ed in a stiU finer capillary stem.The methods used at the NBS in calibration

work are based upon the use of faden thermometerswhenever possible. These thermometers havevery long bulbs (5 to 20 cm) with wall thicknesses

and bore sizes nearly the same as the stem of anordinary thermometer. If a faden thermometeris placed beside a thermometer to be observed, at

such a height that the top of the faden thermom-eter bulb is at the same level as the top of the

mercury column in the thermometer, the fadenthermometer reading will give approximately the

mean temperature of the adjacent portion of the

thermometer stem and mercury thread. Forexample, a faden thermometer with a 10-cm bulbwiU give the mean temperature of the adjacent 10

cm of the thermometer stem. This method of

using the faden thermometer is convenient for

correcting the readings of a total-immersionthermometer when being used at partial immersion.The use of a faden thermometer in this manner is

illustrated in figure 8(a) for the case where themercmy column in a total immersion thermometerextends a short distance above the surface of thebath to permit reading. In this case a correction

must be calculated for the emergent part of themercury column. If the stem temperature of apartial-immersion thermometer is to be measured,one or more faden thermometers are mounted so

as to indicate the mean stem temperature betweenthe immersion mark and the top of the mercurycolumn, as shown in figure 8(b). If faden ther-

mometers are not available, an estimate of thestem temperatm-e can be made with auxiliary

thermometers as in figure 8(c).

In calcvdating the correction for the emergentstem, it is convenient to express the length of

thermometer stem adjacent to the faden bulb in

terms of degrees on the thermometer scale. Thus,for a 10-cm faden thermometer, the number of

degrees corresponding to 10 cm must be found bymeasm-ement of a portion of the thermometerscale. This measm-ement should be made overthe portion of the graduated scale which wasadjacent to the faden bulb. This is particularly

important with high-temperature thermometerswhere the length of a degree is generally not thesame at aU parts of the scale.

b. Formula for Total-Immersion Thermometers

When a thermometer, which has been graduatedand calibrated for use at total immersion is actuallyused at partial immersion, the correction for theemergent stem may be calculated by the generalformula,

stem correction = jfiLTi (T—t),

7^.

FADENTHERMOMETER

l-'BULB7777

FADEN-THERMOMETERBULB

. LIQUID COLUMNOF THERMOMETER

IMMERSION LEVEL

(b) PARTIALIMMERSION

7777';

(c) PARTIALIMMERSION

AUXILIARYTHERMOMETERS

LIQUID COLUMNOF THERMOMETER

(a) TOTALIMMERSION

Figure 8.- -Schemes for measurement of emergent stemtemperature.

whereK= differential expansion coefficient of mercury

(or other thermometric liquid) in the par-ticular kind of glass which the thermom-eter is made (see table 3)

,

n = number of thermometer scale degrees adja-cent to the faden thermometer,

^ = average temperatiu-e of n degrees of thethermometer stem (faden thermometerreading)

,

7"= temperature of the thermometer bulb.The coefficient K is different for different kinds

of glass, and even for the same glass, it differs for

different temperature intervals, i.e., different val-

ues of (T—t). Since most of the change results

from the varying coefficient of the mercury, thechange in K with temperature for one glass mayreasonably be inferred from the change for anotherglass.

Calculation of the stem correction may beillustrated by the following example

:

A total-immersion thermometer reads 90° C in

a bath when immersed to the 80 °C graduationmark on the scale, and a 10-cm faden thermometer

Table 3.

—

Values of K for mercury-in-glass thermometers

Mfian temp. ^ +'°

2

KioT "normal" glass KfoT "borosilicate" glass

For Celsius thermometers

0° 0.000158 0. 000164100 .000158 .000164ISO .000158 .000165200 .000159 .0001672S0 . 000161 . 000170

300 .000164 .000174350 .000178400 .000183450 .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

12

placed alongside the thermometer is adjacent to

the scale between 60 and 90 °C. For this case

71 = 90 — 60 = 30. If the faden thermometer indi-

cates 80 °C, then the stem correction= 0.00016 X30(90-80) = +0.048, or + 0.05 °C. Note that

when the temperature of the emergent stem is

lower than the bath temperature, the sign of thecorrection is +

.

If a faden thermometer were not available in

the above example, the emergent-stem tempera-tiu'e could be estimated by suspending a smallauxiliary thermometer above the bath adjacent to

the main thermometer and with its bulb centered

at about the level of the 85° graduation. Thereading of the auxiliary thermometer will thenapproximate the mean temperature of the 10 deg C(80° to 90 °C) emergent from the bath. For this

condition n = 10. If the auxiliary thermometrereads 60 °C, the stem correction =0.00016X10(90-60) = +0.048 or +0.05 °C. This methodwill usually not be as reliable as the method usinga faden thermometer [6].

c. Formula for Partial-Immersion Thermometers

The scale corrections for partial-immersion ther-

mometers calibrated at the Bureau are reportedfor the conditions of immersion to the depth of the

immersion mark on the thermometer and, unless

otherwise requested, for the unspecified stemtemperatures resulting from the particular environ-

ments prevailing over the comparison baths in thecourse of the calibration. Frequently, however,thermometers are submitted for calibration with a

request for scale corrections which are applicable to aspecified mean temperature of the emergent stem.

In such cases the emergent stem temperatures are

measiired during the process of calibration. Thecalibration observations are then corrected as

necessary to account for any differences foundbetween the stem temperatures observed duringtest and the specified stem temperature for whichthe scale corrections are to apply. In this case,

the magnitude of the stem correction is propor-tional to the difference between the specified andobserved stem temperatures and may be calculatedfor Celsius mercurial thermometers by means of

the relation,

stem correction = 0.000 16w (Up— toba)

,

where

tgp = specified mean temperature of emergent stem(for which reported scale corrections

apply),

^oba = observed mean temperature of emergentstem,

n = number of scale degrees equivalent to thelength of emergent stem.

The above relation, of course, may also be usedto correct the indications of a partial-immersionthermometer when used under stem-temperature

conditions other than specified ones for which thescale corrections apply. In using the formula it

should be noted that n applies to the whole lengthof emergent stem, i.e., from the immersion markto the top of the mercury column. The un-graduated length between the immersion mark andthe first graduation on the scale must therefore beevaluated in terms of scale degrees and included in

the value of n.

For purposes of computing the emergent-stemcorrection, the value of K may be considered , asdepending on the average of T and t, that is

iT+t)/2. Values of as a function of iT+t)/2for two widely used thermometer glasses aregiven in table 3. If the kind of glass is not known,K may be taken as 0.00016 for Celsius mercurythermometers and 0.00009 for Fahrenheit ther-mometers.

d. Formula for Calorimeter Thermometers

The stem correction is often important whenthermometers are used for differential tempera-ture measurements, as in calorimetry. In this

case, provided the mean temperature of the stemremains constant, the correction may be computedfrom the following formula, involving the differ-

ence of the initial and final readings

:

stern correction

=

Kd(Ti+Ti—S—t),

where

iir= factor for relative expansion of glass

and mercury,Ti and T'2=the initial and final readings, respec-

tively,

d=T,-T„5'= scale reading to which the thermom-

eter is immersed,and ^=mean temperature of the emergent

stem.

This correction must be applied (added if +,subtracted if — ) to the difference of the readingsto give the true difference of temperature.Example: Suppose the thermometer was

immersed to its 20° mark; its initial reading, Ti,

was 25 °C; its final reading, T2, was 30 °C; andthe stem temperature was 20 °C. Then thecorrection is 0.00016X5 (25+ 30-20— 20)= +0.012 °C. The difference between andis 5°. The true difference between the initial andfinal temperatures was T2— 71+ correction=5.012°C.

e. Formula for Beckmann Thermometers

For a Beckmann theraiometer the correction

may be readily computed from the following

formula, differing only slightly from that for

calorimeter thermometers, provided the thermom-eter is immersed to near the zero on its scale andthat the temperature of the stem remains constant

:

stem correction=i^c?(5+ Ti + ^2— ^)

,

13

where

5'=setting of the thermometer (sec. 6.4), and theother symbols have the same meanings as

for calorimeter thermometers.

A Beckmann thermometer of the ordinary typeshould not be used with any part of the lowerportion of the stem exposed, as this part maycontain 5 to 10 times as much mercury per

centimeter as the graduated portion and, if

exposed, introduces a large and uncertain error.

If it is unavoidable, however, to use such a

thermometer with some of the lower portion of thestem emergent from the bath, the necessarycorrection may be computed from the above

formula, provided S in the formula is replaced byS+m, where m is the number of degrees thetemperature of the thermometer must be loweredto bring the nieniscus from the zero mark on its

scale to the point of immersion.If the thermometer is immersed to some point

other than its zero mark, as would ordinarily bethe case with thermometers having the zerograduation at the top of the scale, the differentialstem correction may be calculated from the aboveformula if S is replaced by S+m. The formula is

applicable whether the point of immersion is onthe scale or below it, provided the points at whichreadings are made are above the point to whichthe thermometer is immersed.

6. Common Thermometers and Factors Affecting Their Use

In this section common types of high-gradethermometers are mentioned with a discussion of

some of the factors affecting their use.

Tolerances allowed by the Bureau in issuing

Reports of Calibration are given in tables 4through 11 for individual types of thermometers.The values of these tolerances are the same as

those given in the first edition of Circular 600(1959). The accuracy bounds shown in the tables

may seem broad in some instances, but the definite

limitations of liquid-in-glass thermometry becomeapparent when all factors are considered. Forexample, if one keeps expanding the scale for moreprecise reading by reducing the capillary-borediameter, a practical limit is reached beyondwhich capillary forces, in combination with theelasticity of the thermometer bulb, will prevent asmooth advance or retreat of the mercury column.Particularly with a slowly falling temperature, themovement of the mercury meniscus may be foundto occur erratically in steps appreciably large in

comparison to the graduation interval. Large"meniscus jumps" are associated with less rigid

bulbs (relatively large diameters and/or thin walls)as well as small capillary-bore diameters. Ex-cessively elliptical or flattened bores are notrecommended. Thus increasing the length of adegree on the scale, for practical bulb sizes, im-proves thermometric performance to a certainpoint only, beyond which the precision of readingmay readily be mistaken for accuracy in tempera-ture measurement. A study of the effects of bulband capillary dimensions on thermometer per-formance, made by Hall and Leaver [7], providesvaluable guidelines for design purposes.

Other factors such as ice-point changes, unlessexactly accounted for, and differences in externalpressm-e may also account for inaccuracies muchgreater than the imprecision with which a scalehaving 0.1- or 0.2-deg graduations may be read.

6.L Total-Immersion Thermometers

Thermometers pointed and graduated by themanufacturer to read correct temperatures when

the bulb and entire liquid column in the stem areexposed to the temperature to be measured areknown as "total-immersion" thermometers.While these thermometers are designed for im-mersion of all the mercury, it is not necessary, andin some cases not desirable, that the portion of thestem above the meniscus be immersed. Theheating of this portion to high temperatures mightcause excessive gas pressures resulting in erroneousreadings if not permanent damage to the bulb.

In practice a short length of the mercury columnoften must be left emergent from the bath (or

region) so that the meniscus will be visible whenthe temperature is being measured. If a largeenough temperature difference exists between thebath and its surroundings, an appreciable temper-ature gradient may be found in the thermometerstem near the surface of the bath for which acorrection to the thermometer reading may berequired. The condition becomes more seriouswhen a thermometer designed and calibrated for

total immersion is intentionally used at partial

immersion, that is with a significant portion of theliquid column at a temperature different fromthat of the bath. The reading will be too low ortoo high depending upon whether the surroundingtemperature is lower or higher than that of thebath. For a total-immersion thermometer so

used, an emergent stem correction must be deter-

mined and applied in addition to the calibrationcorrections. The correction may be as large as20 Celsius degrees (36 Fahrenheit degrees) if thelength of emergent liquid column and the differ-

ence in temperature between the bath and thespace above it are large.

A method for determining this correction is

given in section 5.4.b.

The scale tolerances shown in tables 4 and 5 arechosen to be indicative of good manufacturingpractice. These tolerances are based on the fact

that in the manufacture of thermometers certain

small errors in pointing and graduation areinevitable, and also that the indications of ther-

mometers are subject to variations due to theinherent properties of the glass. The tolerances

14

Table 4. -Tolerances for Celsius total-immersion mercurythermometers

Temperature range in

degrees

Graduation Tolerance Accuracy Correc-

interval in in in degrees tions

degrees degrees stated to

Thermometer graduated under 150 °C

0 up to 150.

0 up to 150.

0 up to 100.

1. 0 or 0.

5

0.6 0.1 to 0.2 0.1

.2 .4 .02 to .05 .02

.1 .3 . 01 to . 03 .01

Thermometers graduated under 300 °C

0 up to 100Above 100 up to 300

0 up to 100.\bove 100 up to 200

} 1. 0 or 0. 5

}

f 0.5

\ 1.0

/ 0.4

I .6

0. 1 to 0. 2

.2 to .3

.02 to .05

.05 to .1

0.1.1.02.02

Thermometers graduated above 300 °C

0 up to 300Above 300 up to 500

0 up to 300Above 300 up to 500

} 2.0

} 1. 0 or 0. 5

/ 2.0

I 4.0

/ 2.0

I 4.0

0. 2 to 0. 5

. 6 to 1. 0

. 1 to 0. 5

.2 to .5

0.2.2. 1

. 1

Table 5.

—

Tolerances for Fahrenheit total-immersion

mercury thermometers

Temperature range indegrees

Graduationinterval indegrees

Tolerancein

degrees

Accuracyin degrees

Correc-tions

stated to

Thermometers graduated under 300 °F

32 up to 30032 up to 30032 up to 212

2.01.0 or 0.6.2 or .1

1.01.0

0.5

0. 2 to 0. 6

. 1 to .2

. 02 to . 06

0.2.1.02

Thermometers graduated under 600 °F

32 up to 212Above 212 up to 600 } 2 or 1

r 1.0

I 2.00. 2 to 0. 5

.5

0.2.2

Thermometers graduated above 600 °r

32 up to 600...Above 600 up to 95032 up to 600Above 600 up to 950

}

} 2orl

/ 4.0

I 7.0

/ 3.01 6.0

0. 6 to 1. 0

1. to 2.

0

0. 2 to 1.

0

. 6 to 1. 0

0.6.5.2

.2

must be sufl&ciently restrictive to insure to theuser a satisfactory high-grade thermometer but at

the same time must not cause undue manufactur-ing difficulties.

In addition to the above requirements, the error

in any temperature interval must not exceed 5 per-

cent of the nominal value of the interval. Theintent of this requirement is to eliminate ther-

mometers having large corrections of alternatingsigns, which would lead to uncertainties in theinterpolation of scale corrections between calibra-

tion points.

Tables 4 and 5 also give suitable values for thesubdivisions and the accuracy which may be ex-

pected. The word "accuracy" used in these tablesrefers to the best values attainable in the use of

the thermometer when all corrections are applied.The final columns state the decimal figures towhich the corrections are given for thermometerscalibrated by the Bureau. They are stated tosomewhat higher precision than can be attained

with certainty in calibrating the thermometers.They are so-stated to avoid the possibility of anadditional uncertainty due to rounding off.

6.2. Partial-Immersion Thermometers

In many instances it is required to measuretemperatm-es under conditions where it is incon-venient or impossible to use a liquid-in-glass ther-

mometer at total immersion. For such usespartial-immersion thermometers are designed withscales graduated to indicate true temperatureswhen the thermometers are immersed to specified

depths. No stem temperature correction is nec-essary, therefore, when these thermometers are

used with the same depth of immersion andemergent-stem temperature for which they are

calibrated. Unless otherwise stated, each Reportof Calibration issued by the Bureau gives correc-

tions that apply for the temperatures prevailing

above the comparison baths. When such a ther-

mometer is to be used with a different stem tem-perature, the necessary emergent stem correction

must be calculated as shown in section 5.4.c.

The accuracy attained with this type of ther-

mometer wiU usually be significantly less than thatpossible with total-immersion thermometers. Thisis particularly the case when partial-immersionthermometers are used with stem temperaturesgreatly different than the temperature being meas-ured. An unsteady or irreproducible environmentsurrounding the emergent stem, together with theinherent difficulty of estimating or measuring theemergent-stem temperature with sufficient accu-racy, can contribute markedly to the uncertaintyof a given thermometer indication. For this rea-

son tables 6 and 7 show that accuracies expectedof partial-immersion thermometers are not so highas those for total-immersion thermometers nor are

the calibration corrections stated so precisely.

6.3. Low-Temperature Thermometers

The lowest temperature to which a mercury-fUled thermometer can be used is limited by the

freezing point of mercury at -38.9 °C (-38.0 °F).

This limit may be extended to considerably lowertemperatures by alloying thallium with the

mercury. The eutectic alloy of 8.5 percent of

thallium by weight has a freezing point of — 59 "C( — 74 °F) and is used successfully in thermometersfor temperatures down to about — 56 °C ( — 69 °F)

.

The freezing temperature of the alloy is critically

affected in the neighborhood of the eutectic bythe amount of thallium present. Small differences

in composition, resulting in either too much or

too little thallium, have the effect of markedlyraising the freezing point of the alloy. It is there-

fore difficult to achieve the lowest freezing tem-perature in practice. In addition, some ther-

mometers with this filling have been found to

behave erratically in the range of about two degrees

above the freezing point. Consequently, ther-

mometers of this type should not be used below-56 °C.

15

Table 6.

—

Tolerances for Celsius partial-immersionmercury thermometers

Temperature range in

degreesGraduationinterval indegrees •

Toler-ance indegrees

Accuracy i>

in degreesCorrec-tions

stated to

Thermometers not graduated above 150 °C

0 up to 100

0 up to 150

1. 0 or 0.

5

1. 0 or 0.

6

1.01.0

0. 1 to 0.

3

0. 1 to 0.

5

0.

1

0.

1

Thermometers not graduated above 300 °C

0 up to 100Above 100 up to 300

1.01.0

1.01.5

0. 1 to 0.

3

. 5 to 1.

0

0.1

.2

Thermometers graduated above 300 °C

0 up to 300Above 300 up to 500. }

- 0 or 1.

0

0. 5 to 1.

0

1. 0 to 2.

0

0.5.5

Table 7.

—

Tolerances for Fahrenheit partial-immersionmercury thermometers

Temperature range in Graduation Toler- Accuracy t Correc-degrees interval in ance in in degrees tions

degrees » degrees stated to

Thermometers not graduated above 300 °F

32 up to 21232 up to 300 - -

2. 0 or 1.

0

2. 0 or 1.

0

2.02.0

0. 2 to 0. 5

0. 2 to 1.

0

0.20.2

Thermometers not graduated above 600 °F

32 up to 212Above 212 up to 600

2. 0 or 1.

0

2. 0 or 1.

0

2.03.0

0. 2 to 0. 5

1. 0 to 2. 00.2.5

Thermometers graduated above 600 °F

32 up to 600Above 600 up to 950 } 5. 0 or 2.

0

r 5.0\ 10.0

1. 0 to 2.

0

2. 0 to 3. 0

1.01.0

» Partial-immersion thermometers are sometimes graduated in smallerintervals than shown in these tables, but this in no way improves the per-formance of the thermometers, and the listed tolerances and accuracies still

apply.b The accuracies shown are attainable only if emergent stem temperatures

are closely known and accounted for.

Other low-temperatiire thermometers are com-monly filled with organic liquids. While not con-sidered to be as reliable as merciiry-thallium-fiUedthermometers, they serve to extend the rangebelow — 56 °C. Some of these Hquids are used as

low as -200 °C (-328 °F).

Alcohol, toluene, and pentane have all beenused as fluids for low-temperature thermometers.All of these fluids, however, have limitations of

one kind or another. Other organic liquids, aloneor in mixtvires, have been found by some manufac-turers to show better characteristics for particularapplications.

All of these organic liquids have the disadvan-tage of wetting the bore of the thermometer tubingwhich may lead to significant error in the indica-tions of such thermometers if sufficient precautionsare not taken. Any liquid that wets the tube will

leave a film on the wall as the meniscus falls, thethickness of the film being dependent among otherthings on the viscosity of the liquid, the interfacial

action between the liquid and glass, and the rate at

which the thermometer is cooled. Where possiblethe rate of cooling should be slow with the bulbcooled first. In this way the viscosity of the filling

fluid in the thermometer bore is kept as low aspossible until the final temperature is reached, thusminimizing the amount of liquid left behind on thewall. Even so, sufficient time should be allowedfor drainage from the wall to be essentially com-pleted. Under adverse conditions it may takean hour or more before the effect of drainage ends.

In addition to good drainage characteristics, asatisfactory low-temperature fluid should be free

of water, dirt, or other foreign material whichwill separate out at temperatures for which thethermometer is graduated. Furthermore, low-temperature thermometers are frequently de-signed for use up to room temperature or above.In these cases the vapor pressure of the filling

Uquid becomes important. A low vapor pressureis necessary to prevent distillation of the Uquidat the higher temperatures. Any dye added toimprove the visibility of the thermometer Uquidshould be chosen for good color fastness withrespect to Ught cxposm-e or chemical action withthe thermometer liquid.

Tolerances applicable to low-temperature ther-

mometers are given in tables 8 and 9.

6.4. Beckmann Thermometers

A metastatic, or Beckmann thermometer is

usually of the enclosed-scale type, so constructedthat portions of the mercury may be removedfrom, or added to, the bulb permitting the samethermometer to be used for differential measure-ments in various temperature ranges. The scales

are kept short, usually to 5 or 6 deg C, althoughsome micro types have a scale of only 3 deg C.The "setting" of such a thermometer refers to thetemperatiire of the bulb when the reading is 0°

on the scale. When the setting is changed to

allow for use at a higher or lower temperature, the

quantity of mercury affected by a temperaturechange is different. It follows that two equalchanges in temperature at different settings cause

different indications on the scale. Therefore a

"setting factor" must always be used to convertreading differences into true temperature differ-

ences whenever the thermometer is used at anysetting different from the one at which its scale

was calibrated. These setting factors combinecorrections for the different changes in volume of

different quantities of mercury during equal tem-perature changes, and the difference between the

mercury-in-glass scale and the International

Practical Temperature Scale.

Table 10 lists setting factors calculated for

thermometers of Jena 16"" glass, or its Americanequivalent. Corning normal. The scale calibra-

tions for Beckmann thermometers as reported bythe Bureau are applicable to a setting of 20 °C, andthe factor is consequently 1 .0000 at this tempera-ture. For a setting of any other temperature the

observed temperature difference must be multi-

16

Table 8.

—

Tolerances for low-temperature total-immersionthermometers

Table 10.

—

Setting factors for Beckmann thermometers

Temperaturerange in

degrees

Type of Graduation Toler- Accuracythermometer interval in ance in in degrees

degrees degrees

Cor-rectionsstated to

Celsius thermometers

-35 to 0 Mercury 1 or 0. 5 0.5 0.1 too. 2 0.1

-35 to 0 do .2 .4 .02 to .05 .02-56 to 0 Mercury- .5 .5 .1 to .2 . 1

thallium.-56 to 0 do .2 .4 .02 to .05 .02-200 to 0 Organic 1.0 2.0 .2 to .5 . 1

liquid.

Fahrenheit thermometers

-35 to 32 Mercury 1 or 0. 5 1.0 0.1 to 0.2 0.1-35 to 32 do .2 0.5 .05 .02-69 to 32 Mercury- 1 or .5 1.0 .1 to .2 . 1

thallium.-69 to 32 do .2 0.5 .05 .02-328 to 32.... Organic 2 or 1. 0 3.0 .3 to .5 .2

liquid.

Table 9.

—

Tolerances for low-temperature partial-immersionthermometers

Temperature Type of Graduation Toler- Accuracy Cor-range in thermometer interval in ance in in degrees rectionsdegrees degrees degrees stated to

Celsius thermometers

-35 too Mercury 1. 0 or 0. 5 0.5 0. 2 to 0.

3

0.1-56 to 0 Merciu'y- 1.0 or .5 .5 .2 to .3 .1

thallium.-90 to 0 Organic 1.0 3.0 .4 to 1.0 .2

liquid.

Fahrenheit thermometers

-35 to 32 Mercury 1. 0 or 0. 5 1 0. 3 to 0. 5 0.1-69 to 32 Mercury- 1.0 or .5 1 . 3 to .5 . 1

thallium.-130 to 32.... Organic 2 or 1 5 . 8 to 2.

0

.5liquid.

plied by the appropriate factor from the table.

An example is given below the table.

In a common design of the Beckmann ther-

mometer the large bulb is joined to the fine

capillary, backed by the mUk-glass scale, by acapillary of much larger diameter. When such aninstrument is used at partial immersion this large

capillary is a source of some uncertainty, since the

temperature of this relatively large quantity of

mercury, enclosed in the glass case, cannot beactually measiu-ed. When an estimate can bemade of the temperatiu-e of the emergent stem,however, a correction may be calculated as de-

scribed in section 5.4. e.

Tolerance requirements for Beckmann ther-

mometers are given in table 11.

Under the heading "Accuracy of interval in

degrees" is given the estimated accuracy attain-

able in the measurement of any interval within

Setting Factor Setting Factor

°C "C0 0. 9934 55 1. 00965 .9952 60 1. 0107

10 .9969 65 1.011815 .9985 70 1. 012920 1. 0000 75 1. 013925 1. 0015 80 1. 014830 1. 0030 85 1. 015735 1. 0044 90 1. 016540 1. 0058 95 1. 017245 1. 0071 100 1. 017950 1. 0084

As an illustration, suppose the followingobservations were made;

Setting = 25''C. Lower reading =2. 058°

Stem tempera- Upper reading =5. 127°

ture=24°Lower Upper

Observed reading =2.058 5.127Correction from certificate = -|-0. 005 —0. 008

Corrected upper readingCorrected lower reading

5.1192. 063

Difierence = 3.056Difference multiplied by setting

factor (1.0015) = 3.061Emergent stem correction (see ac-

companying-stem correction sheet) =-|-. 004Corrected difference = 3. 065

Table 11. -Tolerances for Beckmann and calorimeterthermometers

Gradua- Allowable change Accuracy of Cor-Type of tion in- in correction in interval in rections

thermometer terval in degrees degrees stated todegrees

Beckmann 0.01 °c 0.01 over 0.5° 0. 002 to 0. 005 0.001Interval for

setting of 20 °C

Bomb calorimeter.. .01 °c 0.02 over 1.5° .005 to .01 .002interval

Do__ - .02 °C 0.02 over 1.5° .005 to .01 .002interval

Do .05 °F 0.04 over 2.5° .01 to .02 .005interval

Gas calorimeter .1 °r 0.16 over a 5° .02 to .05 .02interval

the limits of the scale.

No tolerances for scale error are given althoughit is desirable that the scale error be no greaterthan 0.02 °C over a 1.0 °C interval.

6.5. Calorimeter Thermometers

Calorimeter thermometers include a specialized

group of etched-stem mercury-in-glass thermom-eters which are used for acciurate differential

measurements. Since the accuracy of these ther-

mometers at any one temperature is of less impor-tance than the accuracy of the temperatureintervals, no reference point is required.

Table 11 gives the scale tolerances required of

some typical calorimeter thermometers. Notolerances for scale error are given although it is

desirable that the scale corrections be no larger

than about five graduation intervals.

7. Thermometer Design

To be eligible for calibration the thermometershall be of good design, material, and workmanshipand shall be permanently marked with a serial

number which will uniquely identify the ther-

mometer with its Report of Calibration. Noattempt is made to list specifically all possible

17

defects of design and workmanship, since somelatitude for juogment must be reserved for indi-

\ddual cases as they arise. Certain importantrequirements of general applicability can besingled out, however, and these are describedbelow.

7.1. Materials of Construction

While the cleanliness of the thermometer bulb,

bore, and liquid filling have a pronoimced effect

upon the performance of a finished thermometer,of equal importance is the proper choice of the glass

from which the thermometer is manufactured.Particularly, the thermometer bulb must be madeof glass suitable for use in the temperature rangefor which the thermometer is graduated. In addi-tion, the thermometer must be adequately an-nealed so that continued use will not greatly

change its indications. This is especially impor-tant for a thermometer graduated above 300 °C or

600 °F. The quality of the thermometer glass

and the adequacy of the annealing process may bejudged in part by the stability of reference-point

readings (such as ice points).

A method of test for bulb stability is describedin The American Society for Testing and Mate-rials' Method E77.

Table 12 lists some types of glasses commonlyused in the manufacture of thermometer bulbswith reasonable upper temperature limits of their

use. These estimates by Thompson [8] are basedupon the work of Liberatore and Whitcomb [9],

whose results show that significant changes in

bulb volume may occur if the bulb is heated for

long periods of time at a temperature higher than130 °C (234 °F) below the strain point of theglass. Thermometers may be used intermittently,

however, up to within 70 °C (126 °F) of the strampoint of the bulb glass. The strain point of a glass

is defined as that temperature at which the glass

has a viscosity of 10^*'^ poises [10].

It should be noted that the use of glass with ahigh strain point, such as that of borosilicate glass

or higher, result in better thermometer perform-ance and stability even in thermometers used at

temperatures much lower than the exposure limits

given in table 12.

Table 12.

—

Temperature exposure limits for variousthermometer glasses^

Exposure limitsStrainpoint

Continuous Intermittent

°C "C °F "C °FCorning normal 7560 500 370 700 b430* b805*

Kimble R 6 490 360 680 420 790Jena 16 III 495 365 690 425 796Corning borosilicate 8800 529 400 750 460 860Jena borosilicate 2954 548 420 790 480 900Corning 1720 668 540 1006 600 1110Jena Supremax 2955 665 535 995 595 1100

• From reference 18).

>> '405 °C or 760 '"F if Cori'.ing Standard Thermometer 0041 glass is usedfor the stem.

All high-temperature thermometers should befilled with a dry inert gas under sufficient pressureto prevent separation of the mercury at anytemperature for which the scale is graduated.Total-immersion thermometers graduated above150 °C or 300 °F must be gas fSled to minimizethe distillation of mercury from the top of thecolumn. Gas filling for lower temperatures is

optional, but is strongly recommended.

7.2. Scale Design and Workmanship

Thermometers of the soUd-stem type shall havethe graduation marks etched directly on the stemand so located as to be opposite the enamel back.In thermometers of the enclosed-scale type, thegraduated scale must be securely fastened toprevent relative displacement between scale andand capillary (for example, by fusing the scale tothe enclosing tube) or, if this is not done, a markshould be placed on the outer tube to locate thescale and indicate at any time whether the scaleis in its original position. The graduation marksshall be clear cut, straight, of uniform width, andin a plane perpendicular to the axis of thethermometer.

The scale shall be graduated either in 1.0-,

0.5-, 0.2-, or 0.1-deg intervals, or in decimalmultiples of such intervals. The divisions shall

be numbered in such a way that the identification

of any graduation is not unnecessarily^ difficult.

Thermometers with scales graduated in 0.25-degintervals, or in 0.25-deg intervals further sub-divided, are sometimes difficult to read and their

elimination is desirable. Thermometers graduatedin 0.1- or 0.2-deg intervals, or decimal multiplesof these, should have every fifth mark longer thanthe intermediate ones and should be numbered at

every tenth mark. Thermometers graduated in

0.5-deg intervals, or in decimal multiples of 0.5

deg, require three lengths of graduation marksconsisting of alternating short and intermediatemarks, with every tenth mark distinctly longerthe others, and numbering at every 10th or 20thmark.

The scale must not be extended to temperaturesfor which the particular thermometer glass is

unsuited. For example, a thermometer of boro-silicate glass graduated to 500 °C (932 "F) wouldbe ruined in a short time if used at that tempera-ture.

7.3. Scale Dimensions

Coarse graduation marks do not represent gooddesign. Optimum line width, however, dependsin some measure upon the use for which a particu-

lar thermometer is intended. If the thermometerindications' are to be observed precisely, for exam-ple to 0.1 division, the width of the graduation

marks in the extreme case should not be more than

0.2 of the interval between center hues of the

graduations. In cases where the thermometer

18

must be read quickly or in poor light, and less

precision is expected, somewhat wider lines maybe acceptable.

In addition, the graduation marks must not betoo closely spaced. The closest permissible spac-

ing depends upon the fineness and clearness of

the marks. In no case should the distance betweencenter lines of adjacent graduation marks on anetched-stem thermometer be less than 0.4 mm.The minimum permissible interval between grad-

uation marks for an enclosed-scale thermometeris 0.3 mm if the lines are ruled on a mUk-glassscale; for other scales the minimum is 0.4 mm.The minimum in no case represents good design,

and well-designed thermometers will have gradua-tion intervals considerably larger than the specified

minimum.In order that a thermometer scale be usable

over its entire range, graduation marks must not

be placed too close to any enlargement in the

capillary. Insufficient immersion of the mercm-yin the main biilb or a capillary enlargement,graduation marks placed over parts of the capillary

that have been changed by manufacturing opera-

tions, or graduations so close to the top of the

thermometer that excessive gas pressure results

when the mercury is raised to this level, may lead

to appreciable errors. The following distances

between graduations and the bulb and betweengraduations and enlargements in the bore are

considered as minimum hmits commensurate withgood thermometer design:

(a) A IS-nun length of unchanged capillary

between the bulb and the lowest graduation, if the

graduation is not above 100 °C (212 °F); a 30-mmlength if the graduation is above 100 °C (212 °F).

(b) A 5-mm length of unchanged capillary

between an enlargement and the graduation nextbelow, except at the top of the thermometer.

(c) A 10-mm length of unchanged capillary

between an enlargement, other than the bulb, andthe graduation next above, if the graduation is

not above 100 °C (212 °F) ; a 30-mm length if thegraduation is above 100 °C (212 °F).

(d) A 10-mm length of unchanged capillary

above the highest graduation, if there is anexpansion chamber at the top of the thermometer;a 30-mm length if there is no expansion chamber.For the purposes of this requirement, "an ex-

pansion chamber" is interpreted as an enlargement

at the top end of the capillary bore which shall

have a capacity equivalent to not less than 20 mmof unchanged capUlary.

7.4. Reference Point on Scale

Thermometers graduated above 150 °C or 300°F, or precision thermometers expected to be usedwith an accuracy better than 0.1 °C or 0.2 °F,

when calibrated for the measurement of actualtemperatures rather than temperature diflferences,

must have a reference point at which the thermom-eter can be conveniently retested from time totime. From these reference-point tests, the effects

of changes in bulb volume on the thermometerindications may be followed throughout the life of

the thermometer and the proper correctionsapplied at any time. If no suitable reference pointsuch as the ice or steam point is included in therange of the main scale, a short auxiliary scale

including a fixed point shall be provided. Toavoid making the thermometer unduly long, acontraction chamber may be introduced betweenthe auxiliary scale and the main scale. The gradu-ations on an auxiliary scale must extend for a shortinterval both above and below the reference point.

Similarly, when the main scale ends near a tem-perature to be used as a reference point, thegraduations must be continued for a short interval

above or below the reference point as the case

may be.

Any auxiliary scale must have graduationsidentical to those of the main scale, both di-

mensionally and in terms of temperature.Reference points are not needed on thermom-

eters intended for differential measurements(such as calorimeter thermometers) nor onthermometers not graduated above 150 °C or

300 °F if these are not to be calibrated to anaccuracy better than 0.1 °C or 0.2 °F.

7.5. Marking of Partial-ImmersionThermometers

Partial-immersion thermometers will not becalibrated unless plainly marked "partial im-mersion", or its equivalent (for example, "76-mmimmersion"), and unless a conspicuous line is

engraved on the stem to indicate the depth to

which the thermometer is to be immersed. Thismark must not be less than 13 mm above the topof the bulb. Special partial-immersion thermom-eters adapted to instruments which fix definitely

the manner for use (for example, viscometers andflash-point testers in which the therrnometer is

held in a ferrule or other mounting fitting the

instrument) need not be marked, although it is

always desirable that the thermometers be marked"partial-immersion"

.

8. Special Notes

The following brief notes on the characteristic

behavior of mercury-in-glass thermometers are

added to aid the user in understanding the be-havior of such thermometers and in a better utili-

zation of the information contained in the Reportsof Calibration.

8.1. Glass Changes

The changes which occur in thermometer bulbglass on heating to a temperature, high but still

within its intended range of use, and subsequent

cooling to ambient are an involved function of

19

time and temperature and will depend upon the

thermal history of the glass, both during manu-facture and previous use, the time of exposure to

the high temperature, and the rate of cooling.

Evidence from many investigations [9, 11, 12]

seems to show that when a glass is held indefi-

nitely at some fixed temperature, density (andv'olume) changes proceed more or less slowlytoward a preferred density corresponding to a

quasi equilibrium condition characteristic of theparticular kind of glass and the temperature.Since these changes involve molecular rearrange-

ments, they proceed more rapidly at high tem-peratures where the viscosity of the glass is lowerand the molecular mobUity consequently higher.

Thus a close approach to quasi equilibrium maybe reached in the order of hom's at annealing

temperatures, while infinite time may be required

at much lower temperatures. As a consequence,when a glass is cooled in the order of minutesfrom some high temperature, equilibrium is notreached at lower temperatures on the way down,and an equilibrium density more nearly corre-

sponding 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 its entire lifetime, a

thermometer may retain a "memory" of its ther-

mal history at the higher temperatures experi-

enced diu-ing manufacture. The techniques of

good manufacture, therefore, are designed to pro-

duce in the thermometer glass a state which will

result in maximum stability at the temperatiu-e

of use. The achievement of perfect stability for

all conditions of use, however, is not possible in

thermometer manufacture so that changes in ice

point readings with time and use are observed.

The changes observed in scale readings at the ice

point reflect changes of the same magnitude andsign at all points on the scale since they are the

result of changes in bulb volume; changes in the

stem have very little effect.

The changes in bulb volume are of two kindsresulting naturally from the behavior of glass as

discussed above.

a. Temporary Changes

Upon heating to high temperature the bulb ex-

pands from its initial state and, after a short

period of time, appears to reach an equihbriumcondition corresponding to that particular hightemperature If the thermometer is then cooled

sufficiently slowly through critical temperatureregions, the glass will return to close to its initial

state, and the ice point reading will show nochange on this account. If, on the other hand,the thermometer is cooled rapidly as, for example,cooling naturally in stUl air, the bulb will retain

a portion of its expanded condition, and the ice

point reading will be lower than its reading before

the heating. This phenomenon is known as

"zero, or ice-point depression". Thermometerswhich have been heated to high temperatures

recover from this ice-point depression in an un-predictable way, and frequently there wiU be nosignificant recovery after a year's time at roomtemperature. The ice-point depression has areproducible value, however, for a thermometercooled in stiU air, so that the ice point, taken fromtime-to-time immediately (within about 1 hour)following cooling in this manner, may be usedreliably to show changes in thermometer bulbvolume with time and use.

On the other hand, thermometers used only upto about 100 °C win usually exhibit a relativelyrapid recovery from the ice-point depression, andthe original bulb volume wUl be recovered withinthe equivalent of 0.01 or 0.02 deg C in about3 days. This phenomenon has an importantbearing on the precision attainable with mercurythermometers and most be taken into considera-tion in precision thermometry, especially in theinterval 0 to 100 deg C. Thus, if a thermometer is

used to measure a given temperature, it will readlower than it otherwise would if it has a shorttime previously been exposed to a higher tempera-ture. With the better grades of thermometricglasses the error resulting from this hysteresis wiUnot exceed (in the interval 0 to 100 deg) 0.01 of adegree for each 10-deg difference between thetemperatiu-e being measured and the higher tem-perature to which the thermometer has recentlybeen exposed and with the best glasses only a fewthousandths of a degree for each 10-deg difference.

The errors due to this hysteresis become somewhaterratic at temperatures much above 100 °C. Forthe reasons briefly set forth above it is customary,in precision thermometry, to apply a scale correc-tion based upon an ice point reading taken imme-diately after the temperatiu"e measurement.

b. Permanent Changes

A second type of change in thermometerglasses, known as the "secular change," results in

a non-recoverable decrease in bulb volume whichmay progress with time even at room temperatiu-e,

but which is markedly accelerated at high tem-peratmes. This type of change is evidenced byan increase in the ice point reading. At low to

moderate temperatures there may be a gradualchange which will continue for years. Withbetter grades of thermometer glasses the change wiUnot exceed 0.1 °C in many years, provided thethermQmeter has not been heated to temperaturesabove about 150 °C. In addition, permanentchanges in bulb volumes have sometimes beenobserved with thermometers which have beenrepeatedly cycled at low temperatures, for examplebetween -30 and -f25 °C [13]. At high tempera-tures the secular change usually progresses morerapidly at first, but, with continued heating,

tends toward lower rate of change with time. Therate of secular change wiU be dependent upon the

kind of glass used in the thermometer bulb andthe particular heat treatment given the ther-

mometer in manufacture. Thermometers manu-

20

factured according to good practices wUl evidence

only small secular changes, but thermometersmade of glass unsuitable for the use temperature,

or improperly annealed, may show changes as

large as 20 °C (36 °F), after continued heating at

high temperature [14].

In the use of high-temperature thermometerscare must be taken to avoid overheating. In only

a few minutes of heating at a temperatm-e higher

than the intended range of the thermometer, the

built up gas pressure above the liquid column maycause a permanent distortion of the bulb resulting

in lower thermometer indications.

8.2. Pressure Effects

Since glass exhibits elastic properties, the volumeof a thermometer bulb will change with change of

pressure, either internal or external. Therefore,

at the same temperature, the reading of a ther-

mometer in a horizontal position will be different

than its reading in a vertical position. Ther-mometer readings will change also with altitude

or when the external pressure is changed in someother way. Changes of about 0.1 °C (0.2 °F) peratmosphere have been found for many ther-

mometers with bulb diameters between 5 and7 mm. This value can be used with some con-fidence for estimating the probable effect of anexternal pressure change. The effect of change of

internal pressure is about 10 percent greater.

Formulas for both external and internal pressure

coefficients have been derived by Guillaume [15].

If the external pressure coefficient ^ is definedas the change in scale reading in degrees resulting

from a change of 1 mm Hg in external pressure,

Guillaume found the relation,

where i?e ^^d i?, are external and internal radii

of the bulb, and ^ is a constant containing elastic

properties of the glass and a conversion factor for

expressing the volume change in terms of change of

thermometer reading in degrees. For Celsius ther-

mometers, Guillaume found a value of 5.2X10~®degrees C/mm Hg for k, but Hall and Lever [7], byexperiment, found a value about 25 percent lowerfor their thermometers.

In cases where an accurate correction is neces-sary, (3e should be determined experimentally. Asimple apparatus for the determination is shown in

figure 9.

The internal pressure coefficient /3j is more diffi-

cult to determine accmrately but may be calculatedfrom by means of the relation,

^,=/3,+l.5xlo-^

for thermometers in Celsius degrees, or

^4=^e+2.7X10-5

for Fahrenheit thermometers.

Figure 9.

—

Apparatus for measurement of the externalpressure coefficient.

8.3. Lag

Practically all theoretical treatments of thequestion of thermometer lag are based on theassumption that Newton's law of cooling (i.e.,

that the rate of change in the reading of thethermometer is proportional to the difference be-tween thermometer temperature and bath tem-perature) holds for the thermometer. It is animmediate consequence of this law that when athermometer is immersed in any medium it doesnot take up the temperature immediately, butapproaches it asymptotically. A certain timemust elapse before the thermometer reading agreeswith the temperature of the medium to 0.1 deg,still longer to 0.01 deg, the temperature remainingconstant. If the temperature is varying, the ther-mometer always indicates, not the true temperature,but what the temperature of the medium was at someprevious time. The thermometer readings are thussaid to "lag" behind the temperature by an amountwhich may or may not be negligible, dependingupon the rapidity of temperature variation and thephysical characteristics of the thermometer. Amore complete treatment of this subject has beengiven by Harper [16].

For a thermometer immersed in a bath, thetemperatiu"e of which is changing uniformly, thelag may be defined as the interval in secondsbetween the time when the bath reaches a giventemperature and the time when the thermometerindicates that temperature. This lag X is depend-ent upon the dimensions and material of thethermometer bulb, the medium in which it is

immersed, and the rate at which this medium is

stirred. For instance, the lag when in the still air

of a room would be perhaps 50 times that of thesame thermometer when immersed in a well-stirred

water bath.Since the value of X for mercurial thermometers

is not large, being from 2 to 10 sec on a well-stirred

water bath, it is not generally necessary to correct

for it. For example, if two thermometers, onehaving a lag of 3 and another of 8 sec, are read

simultaneously in a bath whose temperature is

rising at the rate of 0.001 degree in 5 sec, the

21

1 1 1 1 r

0.10 -

TIME, sec

Figure 10.

—

The approach to temperature in a stirred waterbath for three thermometers with typical lag constants.

former will read 0.001 degree higher than thelatter, due to the lag. In the intercomparison of

thermometers the rate of temperature rise maynearly always be kept so small that this lag

correction is negligible.

If a thermometer at a given initial temperatureis plunged into a bath at a different temperature,the lag, X, is the time required for the original

difference in temperature between thermometerand bath to be reduced to 1/e (that is 1/2.7) of

itself. In a length of time 4 X the difference will

have become about 1.5 percent and in a length of

time 7 X about 0.1 percent of the original difference.

Determinations of X for solid stem laboratorythermometers representative of American manu-facture have yielded values of about 2 to 3

seconds in a weU-stirred water bath. Figure 10shows the approach of thermometer readings to

the water bath temperature for 3 selected ther-

mometers having different values of X. Forexample, if the thermometer for which X=2.2sec is initially at 25 °C and then is immersed in abath at 75 °C, the thermometer reading will bewithin 0.05 °C (0.1 percent of 50 °C) of the bathtemperature in 15 sec and within 0.01 °C in 19sec. The curve for X=3.1 was obtained for anAmerican Society for Testing and Materials(ASTM) specification 56C calorimeter thermome-ter with a bulb diameter (outside) of 7.9 mm andbulb length of 44 mm. The value of X=2.2 was

found for an ASTM 7C thermometer having bulbdimensions of 5.4 by 12 mm. The third curve,for X=1.7, was obtained for a bulb with dimensionsof 5.4 by 34 mm. It is probable that most solidstem thermometers of American manufacture will

have values of X lying within the range covered bythe 3 curves shown.

According to Harper [16] the value of X for agiven thermometer in a well stirred oil bath willbe about twice its value for a water bath.When a thermometer is used to measure changes

of temperature, as in calorimetry, it has beenshown Dy White [17] that the lag enters into theobservations in such a way as to be eliminatedfrom the results in applying the usual radiationcorrections. Therefore the lag need not beconsidered, provided only that the initial and final

readings are made when the temperature is varyinguniformly. This is not strictly true, however, in

the case of some Beckmann thermometers thathave no true value of X, as has been explained inthe paper referred to above.

8.4. Separated ColumnsMany inquiries are received concerning sepa-

rated mercury columns, particularly after ship-ment. Since no means of avoiding such occur-rences has yet been found, some directions for

joining the mercury may be helpful. The mercurymay separate somewhat more readily in ther-

mometers which are not pressure-fiUed, but it

can be more easily joined smce there is little gasto separate the liquid. The process of joiningbroken columns consists of one or a series of manipu-lations which may be effective, and these are

briefly described here.

(a) The bulb of the thermometer may be cooledin a solution of common salt, ice, and water (or

other cooling agent) to bring the mercury downinto the bulb. Moderate tapping of the bulb on apaper pad or equally firm object or the application

of centrifugal force usually serves to unite themerciu^y in the bulb. If the salt solution doesnot provide sufficient cooling, carbon dioxide

snow (dry ice) may be used. Since the tempera-ture of dry ice is about —78 °C (-108 °F) andmercury freezes at about —40 °C (—40 °F) it will

cause the mercury to soUdify. Care must betaken to warm the top of the bulb first so that

pressiores in the bulb due to the expandingmercury may be relieved.

(b) If there is a contraction chamber above the

bulb or an expansion chamber at the top of the

thermometer the mercury can sometines beunited by warming the bulb until the columnreaches the separated portions in either enlarge-

ment. Great care is necessary to avoid filling

the expansion chamber completely with mercury,which might produce pressures large enough to

burst the bulb. Joining the mercury is morereadily accomplished if the quantity in either

cavity has first been shattered into droplets bytapping the thermometer laterally against the

hand.

22

(c) As a last resort, especially for thermometershaving no expansion chambers, small separated

portions of the column can sometimes be dispersed

by warming into droplets tiny enough to leave

space for the gas to by-pass, and then droplets

can then be collected by a rising mercury column.The procedure for thermometers in which or-

ganic liquids are used is similar. Liquids in the

stem can more readily be vaporized and may thenbe drained down the bore. The latter process is

aided by cooling the bulb. All of these manipula-tions require patience, and experience is helpful,but they will yield results if care is used. Aconvenient method of ascertaining that all theliquid has been joined is a check of the ice point,or some other point on the scale.

9. References

[1] Federal Register, Title 15, Chapter II, Part 203(copies available from NBS on request)

.

[2] H. F. Stimson, The International Practical Tempera-ture Scale of 1948, J. Res. NBS 65A, 1939 (1961).

[3] N. S. Osborne and C. H. Meyers, A formula antables for the pressure of saturated water vapor in

the range 0 to 374 C, J. Res. NBS 13, 1 (1934)RP691.

[4] R. B. Scott and F. G. Brickwedde, A precision cryo-stat with automatic temperature regulation, BSJ. Res. 6, 401 (1931) RP284.

[5] E. Buckingham, The correction for emergent stem of

the mercurial thermometer, Bui. BS 8, 239 (1912)S170.

[6] L. H. Pemberton, Further consideration of emergentcolumn correction in mercury thermometry, J. Sci.

Instr. 41, 234 (1964).

[7] J. A. Hall and V. M. Leaver, The design of mercurythermometers for calorimetry, J. Sci. Instr. 36,183 (1959).

[8] R. D. Thompson, Recent developments in liquid-in-

glass thermometry. Temperature, Its Measurementand Control in Science and Industry 3, Part 1

(Reinhold Pubhshing Corp., New York, 1962)

p. 201.

[9] L. C. Liberatore and H. J. Whitcomb, Density changesin thermometer glasses, J. Am. Ceram. Soc. 35, 67(1952).

[10] American Society for Testing and Materials Designa-tion C 162-56, Standard Definitions of Terms Re-lating to Glass and Glass Products.

[11] H. R. Lillie and W. W. Shaver, Method of temperingglass, U.S. Patent No. 2,148,630 (Feb. 28, 1939).

[12] L. C. Liberatore, Method of stabilizing the moleculararrangement of glass thermometers, U.S. PatentNo. 2,610,445 (Sept. 16, 1952).

[13] W. I. Martin and S. S. Grossman, Calibration driftwith thermometers repeatedly cooled to —30 C,ASTM Bui. No. 231, 62 (July 1958).

[14] E. L. Ruh and G. E. Conklin, Thermal stability inASTM thermometers, ASTM Bui. No. 233, 35(Oct. 1958).

[15] C. E. Guillaume, Traits Practique de la Thermom-6trie, Gauthier-Villars et Fils, Paris (1889) p. 99.

[16] D. R. Harper 3d, Thermometric lag, Bui. BS 8, 659(1912) S185.

[17] W. P. White, Lag effects and other errors in calor-imetry, Phys. Rev. 31, 562 (1910).

23

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