/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 with

those 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 necessary, 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 Government; assistance to industry, business, and consumers in the development and acceptance of commercial standards and simplified trade practice recommendations; administration of programs in cooperation with United States business groups and standards organizations for the development

of international standards of practice; and maintenance of a clearinghouse for the collection and

dissemination of scientific, technical, and engineering information. The scope of the Bureau's

activities 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.* Radio

Standards Laboratory: Radio Standards Physics; Radio Standards Engineering.** Office of Standard 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. Instrumentation. 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 temperature 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 who

wish to caUbrate their own instruments.

A. V. AsTix, Director.
Contents

Page

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 general

interest to both manufacturers and users of liquid-in-glass thermometers, as well as those who wish to calibrate thermometers or submit them to the National Bureau of Standards

for 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 of common types of liquid-in-glass thermometers are included together with tables of tolerances and 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 assume

custody of the Nation's standards of physical

measurement. One important activity under

this responsibility is the accurate reproduction of the International Practical Temperatiu-e Scale as

a basis for the uniform measurement of temperature 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 working

standards where precise-temperature measure- ments are required. Less precise types of instruments are not accepted, nor are the more routine

calibrations performed in cases where such work

can be done in qualified commercial testing

laboratories. This Monograph describes the

practices employed at the Bureau in the calibration of acceptable types of liquid-in-glass thermometers. The information is intended for those

who wish to submit thermometers for calibration or who have occasion to use thermometers

calibrated 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 which

thermometers are capable, as well as to point out

their inherent limitations.

In this Monograph, the material presented in

Circular 600 has been somewhat expanded and

brought up to date. The rearrangement of the

material is intended to inform the reader immediately of the Bureau's calibration services and how

to 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 complete

listing is found in NBS Miscellaneous Publication

250.

; 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 column

of the NBS Technical News Bulletin. The

Bureau 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 request

should be addressed to The Ofl&ce of Technical

Information, 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 wide

variety of types, not all of which are accepted for

test. In general, considerations of design, intended

use, and probable stability of the thermometer

indications are the principal factors governing

acceptability for test. Thermometers belonging

to the large and varied group which may be

classed as laboratory or "chemical" thermometers

are regularly accepted. These may be of the

etched-stem or enclosed scale (Einschluss) type.

Other acceptable types include such specialpurpose thermometers as Beckmanns and calo- rimeter thermometers. Thermometers of the

so-called industrial or mechanical types, with

special mountings for their various intended uses, can be accepted for test only when their construction permits testing with the equipment available.

1
Ordinary household or meteorological thermometers 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 construction before being finally accepted for test. The

examination is made with optical aid (15 or 20 X)

for fineness and uniformity of graduation, cleanness

of the mercury and capillary bore, and freedom

from moisture, gas bubbles, and cracks in the

glass. Among other possible defects detected in

other ways, are omission of gas filling where

needed, insufficient annealing and misnumbered

graduations. 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 Bureau

for a liquid-in-glass thermometer, in addition to giving the results of the calibration, may be taken

as an indication that the thermometer is free from

serious defects of design, material, or workmanship, as discussed in section 7. Except in special

instances, a Report of Calibration is issued only

when the thermometer has been calibrated at a

sufficient number of points to provide reasonable assurance that the corrections obtained at the

temperatures of calibration can be applied, with

interpolation and extrapolation, throughout the

whole scale (see sec. 5.2).

In addition to the scale corrections listed with

the temperatures of calibration, the Report

contains an estimate of the uncertainties associated with the corrections. The Report will also show the following information: the manufacturer's identification markings and numbers, the

agency or firm for which the calibration was made,

the NBS test number and date of test, and

explanatory notes necessary to define the conditions 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 be

accompanied by a table of setting factors to enable

the user to apply the calibration results when the

thermometer is used with a setting other than that

for 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 not

assure the user of this accuracy in a temperature

measurement. 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 conduction

along the thermom.eter stem. Any departure

from the conditions under which the corrections

were obtained in calibration may significantly

change the values of the corrections. Conditions

of immersion are particularly important (see

sec. 6), and even a change in the pressure to which

the bulb is exposed may require an additional

correction (sec. 8.2).

Some of the reasons why a thermometer may

be denied a Report of Calibration are summarized

as 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 partialimmersion thermometers.

(f) Unsuitable bulb glass or inadequate annealing.

(g) Inadequate gas filling.

(h) Excessive scale error.

Details of good design and workmanship are discussed in section 7.

2.3. General Instructions to Applicants for

Tests

Tests in accord with the policies of the National

Bureau of Standards, and of the types indicated

in the fee schedules as published in the "Federal

Register", will be undertaken. If need arises for a special test, not listed in the fee schedule but

of a similar nature, the Biireau should be consulted.

If the required measurements appear feasible, and,

in the opinion of the Bureau, sufficiently important to justify the work, such tests will be undertaken for a special fee determined by the nature

of the work. In aU requests the following procedures and information are pertinent.

a. Initial Arrangements

A letter or purchase order, stating the tests desired and referring to the appropriate section and

subsections of the fee schedule, should be sent to the Bureau prior to any shipment. The purpose

of this requirement is to determine whether or not

the Bureau will undertake the test and to insure

correct procedure in reporting, shipping, and

billing. 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 manner

in which the results are to be used should be stated.

If the thermometer submitted has been previously

calibrated by the Bureau, reference should be

made to the former test number. A test number

will 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 shipments are made by the Bureau in accordance with

2
FORM NBS-186

(T-l-«*l

U.S. Department of Commerce

NATIONAL BUREAU OF STANDARDS

WASHINGTON. D.C. 20234

NATIONAL BUREAU OF STANDARDS

REPORT OF CALIBRATION

LIQUID-IN-GLASS THERMOMETER

Tested for: National Bureau of Standards

Division 221, Section 01

Marked: Surety 198692

Range: -2 to +102 °C in 0.2°

Thermometer

Reading Correction

- 0.06 °C +0„06 °C

10.00 + .08 20.00 ^ .u

30.00 + .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

311-30-64

December 3, 1964. KSL:dh

James F. Swindells, Chief

Thermometry Laboratory Heat 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 correction

sheet. NOTE B.-The tabulated corrections apply for the condition of total immersion of the bulb and liquid column. Although this thermometer is not ordinarily used in this way, no significant errors should be

introduced by neglecting the corrections for emergent stem. NOTE C.-The thermometer was tested in a large, closed-top, electrically heated, liquid bath at an immersion of The temperature of the room was about 25° C (77° F). If the thermometer is used under conditions which

would cause the average temperature of the emergent liquid column to differ markedly from that prevailing in the test, appreciable differences in the indications of the thermometer would result. 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 be

higher (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 be

higher (or lower) by the same amount. The temperature of steam is 100° C (212° F) only if the pressure is 760 mm (29.921 inches). If the pres- sure differs from 760 mm (29-921 inches) allowance must be made for this. If the pressure is higher

(or lower) than 760 mm (29.921 inches) the temperature will be higher (or lower) than 100° C

(212° F) by approximately 0.037° C per mm dif- ference (1.68° F per inch difference). NOTE G.-The thermometer, before testing, was

heated to the temperature of the highest test point.

The application of the tabular corrections to the readings of the thermometer will give true temperature differences provided the thermometer is used

in its upright position and is heated previously

(within an hour before using) to the highest temperature to be measured. NOTE H.-The thermometer was tested for use in differential measurements, such as the measurement 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 assumed

temperature 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 instructions should be supplied at the time that arrangements are being made for the test. If a test number has been assigned prior to the shipment,

this number should appear on the shipping container. If a test number has not been assigned

at this time, a purchase order, or letter shoidd be

sent under separate cover. In either case the

shipment should include a packing list. AU possible care will be taken in handling

thermometers at the Bureau, but the risk of damage either in shipment or in testing must be

assumed by the applicant. The applicant should

consider the nature of the equipment he is shipping

and pack it accordingly, with appropriate labeling.

Attention is called to the availability of security

express in shipping thermometers.

3. Definitions

The principal features of a solid-stem liquid-inglass thermometer are shown in figure 3. Not aU

of the features shown would necessarily be incorporated 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 depending

upon the coefficients of expansion of the thermometric 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 thermometric hquids with higher coefficients of expansion

than mercury, the degree equivalents of the bulb

voliune are correspondingly lower.

Stem: The glass capillary tube through which

the thermometric Hquid advances or retreats with

change 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 top

end of the capillary bore having a volume equivalent to not less than 20 mm of unchanged capillary.

Smaller chambers are not regarded as expansion

chambers. The expansion chamber is provided

to 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 the

capillary bore which serves to reduce a long length

of capillary or to prevent contraction of the liquid

column into the bulb. This chamber is introduced

below 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 periodically for changes in scale caUbration. (See sec. 7.4.) Total Immersion Thermometer: A thermometer

designed to indicate temperatures correctly when

used with the bulb and the entire liquid column in

the stem exposed to the temperature being

measured.

Partial Immersion Thermometer: A thermometer

designed to indicate temperatures correctly when

^BULB

CONTRACTION CHAMBER

EXPANSION_ CHAMBER

AUXILIARY_

SCALE

IMMERSION

LINE J MAI SCALE

Figure 3.

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

used with the bulb and a specified part of the stem

exposed to the temperature being measured. The

remaining part of the stem will be at the ambient

temperature, usually different from the temperature being measured. Such thermometers are marked with an immersion line to indicate the

proper depth of immersion. The emergent stem

refers to the length of liquid column and stem at the ambient temperature.

Complete Immersion Thermometer: A thermometer designed to indicate temperatures correctly

when the whole thermometer, including the expansion chamber, is exposed to the temperature being

measured. In gas-filled thermometers the reading

will be different for complete, as compared to total immersion as a result of the effect of temperature on the gas pressure in the thermometer. (See

sec. 8.2). The difference in readings under the

two conditions is particularly significant at high

temperatures.

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 the

measurement approaches the true value of the

quantity being measured. In this Monograph

the accuracy expected of a given thermometer

refers to the closeness of the observed indication

of the thermometer to the true temperature on

the International Practical Temperature Scale.

The accuracy attainable is principally limited by

the 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 important

factors. With partial immersion thermometers,

uncertainties in corrections for the emergent stem

may greatly limit the accuracy. Observer errors are also involved, but with care these can usually

be 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 and

it is read repeatedly at the same scale reading,

one can be deceived in assuming that a corresponding accurac}'^ is being achieved. For example,

capillary forces may be holding the liquid column

at the false level, or the bulb volume may have

changed since the time of calibration.

4. Temperature Scales and Standards

The calibration of a thermometer consists of comparing its indications with known temperatures on a standard scale of temperature. By

international agreement, the Kelvin Scale is now- accepted as the absolute Thermodynamic scale. In 1954 the Tenth General Conference on Weights

and Measures defined the Kelvin Scale by means

of a single fixed point, the triple point of water, to which was assigned the temperature 273.16 °K,

exactly. Because of the difficulties encountered

in the practical realization of the Kelvin Scale,

however, a practical working scale, the International Temperature Scale, was first adopted in

1927 and later revised in 1948. In 1960 the

Eleventh General Conference changed the name

of the scale to International Practical Temperature

Scale of 1948 (IPTS) and adopted a revised text

of the scale [2]. The Scale itself was not changed,

however. The new text, therefore, does not

change the value of any temperature on the 1948

scale by as much as the experimental error of

measurement. This Scale is intended to have

close correspondence with the Kelvin Scale and to provide scientific and industrial laboratories

throughout the world with a common basis for stating temperatures. Cahbrations of thermometers at the Bureau, therefore, are made with

reference to temperatures on the IPTS.

In the range of temperatures normally covered

by 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 between

solid 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 points

and using a specified equation for interpolation.

Temperatures on the IPTS are expressed in

degrees Celsius (centigrade). Thermometers

graduated on the Fahrenheit Scale are calibrated

with reference to the IPTS using the conversion

formula,

9

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

When the highest accuracy is required in a

calibration, the thermometer indications are compared directly with temperatures obtained

with a standard resistance thermometer. If lesser accuracy is adequate, one of a series of mercuryin-glass standards is used, except below 0 °C and

above 300 °C, where the calibration is made

directly with a resistance thermometer regardless

of the accuracy required. The series of mercuryin-glass thermometers which serve as standards

for total-immersion comparisons is shown below.

Range Smallest graduation

Auxiliary

scale

"C

0 to 50 "C

0.1 0.2

0.1 0.2

0.6

°C

0 to 100 -

60 to 100.... atO atO

atO

100 to 200

200 to 300

These standards are calibrated with reference

to the IPTS through comparisons with a standard

resistance thermometer.

Partial-immersion standards, known as "like

standards", are maintained for the calibration of accepted designs of partial-immersion thermometers. These standards are calibrated for stemtemperature conditions expected to prevail during

the calibration of similar thermometers. This

use of like standards eliminates the need for many

of 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 temperatures

are essentially the same for all of the thermometers

under comparison.

For those who may want to use reproducible

fixed points in their own laboratories, the Bureau

sells 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 phthalic

anhydride, 131 °C (268 °F). At higher temperatures 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 temperatures

are approximate, but precise values are supplied

with the standards.) Detailed information on

these cells and standards and their procurement

is 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 standard

platinum resistance thermometer. The readings

may be compared directly with a standard resist- ance thermometer, or indirectly using a mercuryin-glass standard. Ice and steam baths, together

with a series of stirred liquid baths, provide controlled 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 shaved

from 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 taken

to prevent contamination of the ice and water. A

small reading telescope with a magnification of 10

diameters aids in reading the thermometer indication and reduces parallax errors. Gently tapping

the thermometer just before reading may prevent

the 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 steampoint apparatus either "by comparing the thermometers with standards or by the determination

of 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 circulation of steam around them. Provision is made for either reheving any excess pressure in the space

siirrounding the thermometers, or for determining

the 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 dependent upon the prevailing atmospheric pressure. The usual corrections are apphed to the barometer

reading 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 above

atmospheric in the steam jacket. The steam

temperature may then be fovmd from the pressure- temperature values given in table 1. With a good

barometer, acciirate to 0.1 mm Hg, this procediire

s capable of an accuracy of 0.002 to 0.003 deg C

i(0.004 to 0.005 deg F). The Fortin type barometer will usually serve for all but the most exacting

measurements.

The steam bath is also used as comparison bath,

in which case the temperature of the steam is determined at the time of test by means of a previously

standardized thermometer. This method is simpler than determining the steam temperature from

a barometer reading, and may be preferable,

particularly when a resistance thermometer can

be used as the standard.

c. Comparison Liquid Baths

Stirred liquid baths of two designs are used at the Bureau as comparators in which thermometers

are calibrated in the range —40 to +500 °C.

(-40 to +930 °F). This equipment permits

stirring adequate for uniform temperature distri- bution, and provides controlled heat input for

temperature regulation.

A type suitable for use with media liquid at room temperatiu"e is shown in figure 5. This

bath is constructed with two tubes of different

diameters having connecting passages at the top

and 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. 144

fit ft 89. 196 . 247 . 298 . 350 . 401 . 452 . 502 . 553 .604 .655

ROft 0. 705 . 756 . 806 . 856 . 907 . 957 •. 007 •. 057 *. 107 *. 157 oou 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 .617

OOU 0. 664 . 712 . 759 . 806 . 854 . 901 . 948 . 995 •. 042 *. 089

570 92. 136 . 182 . 229 . 276 . 322 . 369 . 415 . 462 . 508 . 554

win 0. 600 . 646 . 692 . 738 . 784 . 830 . 876 . 922 . 967 '. 013

690 93. 058 . 104 . 149 . 195 . 240 . 285 . 330 . 375 . 420 . 465

600 0. 5100 .5548 .5996 .6443 .6889 .7335 .7780 .8224 .8668 .9112

610 . 9554 . 9996 *. 0438 *. 0879 *. 1319 *. 1759 *. 2198 *. 2636 '. 3074 '. 3511 620 94. 3948 . 4384 . 4820 . 5255 . 5689 . 6123 . 6556 . 6989 . 7421 . 7852 630 0. 8283 . 8713 . 9143 . 9572 *. 0001 *. 0429 •. 0857 '. 1284 *. 1710 *. 2136 640 95. 2562 . 2987 . 3411 . 3834 . 4257 . 4680 . 5102 . 5523 . 5944 . 6366

650 yo. oioo . 7204 . 7623 . OlOV *. 0539 oou 96. 0954 .1368 .1782 .2195 .2607 .3019 .3431 .3842 .4252 .4662

670 0. 5072 . 5480 .5889 .6297 .6704 .7111 .7517 .7923 .8329 .8734

680 .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 *. 0667

710 98. 1048 . 1437 . 1827 .2216 .2604 .2992 .3379 .3766 .4153 .4539 720 0. 4925 .5310 .5695 .6079 .6463 .6846 .7229 .7612 .7994 .8376

730 .8757 .9138 .9519 .9899 •. 0278 •.0657 *. 1036 •. 1414 1792 •. 2110

740 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 .6932

780 .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 immersion

of the thermometers.

The type shown in figure 6 is designed for use

at high temperatures with molten tin as the bath

liquid. The bath is made with two coaxial tubes

of which the inner tube is open at both ends. The

stirring propeller is mounted near the bottom of

the inner tube leaving the space above the propeller free to receive thermometers which are in- serted in reentrant tubes. Heat is supplied by

heater 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 thermometer holder which can be rotated to bring

successive thermometers into the field of a vertically adjustable reading telescope.

For calibrations in the range 5 to 99 °C (40 to 210 °F) water is used as the bath liquid. One

grade of petroleum oil is used between 99 and

200 °C (210 and 392 °F) and a second between

200 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 temperature but at the same time have flash points which

THERMOMETER

HOLDER

INSULATION

AIR SPACE

SPACE BETWEEN

TUBES

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 liquid

having freezing point above room temperature.

are not exceeded at the higher temperatures. The

tin 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 that

described by Scott and Brickwedde [4]. The cryostat, shown in fig\u"e 7, consists of an inner Dewar

flask, D, which contains the bath hquid, sur- rounded by liquid nitrogen in the outer Dewar

flask, C. The rate of heat transfer between the

bath hquid and the liquid nitrogen is controlled

by varying the gas pressiue between the waUs of the inner Dewar flask, which is connected to a vacuum system through the side tube, M. Vigor- ous stirring of the bath liquid is maintained by

the propeller, I, which circulates liquid upwards

through the inside of the stuTer tube, P, and down

the outside. Excess refrigeration is compensated

by 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). For

temperatures between —75 and —110 °C (—103

and — 166 °F) a five-component mixture is used

containing 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 mixture freezes at about -150 °C (238 °F), but

absorbs 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. The

length of scale between calibration points should

be chosen with regard to the accuracy expected of the thermometer in use. The points should not

be chosen unnecessarily close together, nor should

they be spaced so far apart as to destroy confidence

in interpolated corrections at temperatures between the calibration points. For many years

the predecessors of this Monograph have contained

the statement: "In general, if the readings of a thermometer are to be trusted to one or two-tenths

of the smallest scale division, the interval between

test points should not exceed 100 divisions and

usually need not be less than 40." Recent studies

of calibration data for over 50 thermometers purchased during the years 1930 through 1956 for use

as laboratory standards showed that, while there was considerable variation between individual

thermometers, the above statement was usually

applicable only to thermometers not graduated

above about 200 °C. For the thermometers not

graduated above 200 °C, calibrations every 40 to 50 divisions were required for interpolation to one

or two-tenths of a division. In nearly aU cases, interpolation between calibrations 100 divisions

apart could be relied upon only to one-half of a

division. For most of the thermometers graduated above 200 °C, the data showed that interpolations between calibrations 40 to 50 divisions apart were reliable to only one-half division, and that

the spacing had to be reduced to 20 to 25 divisions

if interpolation to one or two-tenths division was

to be expected. It was found also that an examination of scale corrections obtained a given number of divisions apart for a particular thermometer was not sufficient to predict whether or not more

calibration points were required for reliable in- terpolation. The above studies were made with

only a few of the many types of thermometers

submitted to the Bureau for calibration, and,

therefore, conclusions may not necessarily be

applicable to other types. Experience with a

particular type of thermometer seems to be the

most reliable guide in the choice of calibration

points.

When a thermometer is to be calibrated without

reference to any special use, the choice of calibration points should be left to the calibration laboratory. In some cases the number and distribution

of test points can be decided only after a careful

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

should be clearly stated before calibration. The

Bureau will not make calibrations at more, or fewer, points than are necessary, although this

judgment may be influenced by considerations |l given to special requests. In any case, no fewer

than two points are taken on the main scale. At

least one reference point is included as a calibra- i tion point when such a point (or points) is included

in the scale.

5.3. Determination of Scale Corrections

Through considerations of accuracy, Beckmann

thermometers, calorimeter thermometers, and

thermometers graduated in tenths of a degree

Fahrenheit are calibrated using a platinum re- sistance thermometer. A platinum thermometer

is also used for all calibrations made below 0 °C

(32 °F) or above 300 °C (572 °F). Other calibrations are generally made using mercury-in-glass

standards (listed in sec. 4) which have been | calibrated with a platinum thermometer.

When comparing thermometers with liquid-inglass standards two standards are always used.

In this way reading errors are more readily detected and cross checks of the standards are maintained. The comparison procedures are described

in simplified form in the following hypothetical

test of foiu" thermometers, Tl through T4.

Table 2 shows the observations taken in obtaining the corrections appficable to the thermometers

at 20 °C. For simplification, aU of the entries in

the table reflect perfect thermometer performance

and no observer error. Table 2.

Comparison of test thermometers with liquid-inglass 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

0.00

0. 00 .00 Observer B

Mean ice points

Thermometer comparisons

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

left 19.88 19.99 19. 97 20.03 20.04 19.89 Observer B reading left to right 19.88 19.99 19. 97 20.04 20. 05 19.90 Observer B reading right to

left 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 B

Mean ice points

Calculations of corrections

Correction to standards +0. 12

20.01

+0.04

20. Ols Mean temperature, each

standard _ Mean temperature of all readings 20. 01 +0.04

Corrections to test thermometers... +0. 02 -0.02 -0.03

The first observations are the ice points of the

thermometers under test. These are entered in

the upper part of the table. The thermometers

are then mounted in the comparison bath between

the 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 each

observation. Two observers (A and B) are used,

first with one observer reading and the other

recording, and next with the observers interchanged. Observer A reads in the order left to right as the thermometers appear in the table and

then repeats the observations in the order right to

left. Observer B then immediately reads in the same manner. The observations are spaced

imiformly in time so that, with the bath temperature increasing linearly with time, the mean of the

observations with any one thermometer will

correspond to the mean temperature of the comparison bath during the observations of all of the

thermometers. Immediately after the comparison

observations, ice points are taken of the two

standards. 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 mean

temperatiu-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 then

repeated at the next higher test point and so on untn corrections are obtained at a sufficient number 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 same

except that only one standard is used, the same

resistance thermometer being read foiu* times in

place of the separate observations of two hquidin-glass standards.

Ice-point readings are not usually taken vtdth each test point on the scale. For thermometers

not graduated above 300 °C or 600 °F, ice points

taken before the first test point on the scale and

after the last point will usually suffice. With

high-temperature thermometers, however, it is the

practice to take an ice point and then test immediately 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 point

is found that is greater than the expected accuracy

of the thermometer, the thermometer is deemed

unsuitable for calibration and further tests are unnecessary.

The corrections obtained in this manner apply

as long as the ice point remains the same as that

observed during calibration. Subsequent changes

in the ice point will be a result of small changes in

the glass which affect the volume of the thermometer 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 volume

can 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 that

observed at the time of calibration, the other

reported corrections to the scale can confidently

be taken to be higher (or lower) by the same

amount.

5.4. Corrections for Emergent Stem

The proper application of scale corrections as reported in NBS Reports presents no difficulties in cases where thermometers are calibrated and

iised under conditions of total immersion. In such

cases the temperature of the thermometer, including the stem up to the top of the mercury thread,

is definitely specified and the corrections as given

apply when the thermometer is used at total

immersion. Instances frequently occur, however,

where some part of the mercury column is emergent from the region whose temperatiue is being

measured. In these cases the emergent part of

the stem may be in an environment, not only in

which the temperature is markedly different from

that of the thermometer bidb, but in which pronounced temperature gradients may be present.

If such a situation exists in the use of a thermometer which has been calibrated at total immersion,

a correction may be calculated to account for the

difference in temperatm"e between the bulb and

the emergent stem. The calculation of this correction requires a reliable estimate of the mean

temperattu-e of the emergent stem, which, for the

best work, will be made from measurements. But

if the stem temperature measiu-ements are not

repeated each time the thermometer is used, the

acciu"acy of the correction will depend upon the

constancy of the stem temperature over periods

of time. For example, if the emergent stem is exposed to the air above a liquid bath, variations

in ambient temperature and air circulation can

cause significant variations in the temperature of

the emergent stem. The same situation occiirs in the case of partialimmersion thermometers. For this type of thermometer, the reported scale corrections apply only

for the indicated depth of immersion and a particular stem temperature. If the thermometer is then used under conditions where the mean stem

temperature is different, the reported scale corrections are not applicable, and a stem teniperature

correction is required.

The following paragraphs describe methods

for determining stem temperatm-es and calculating

corrections. For a known or assumed condition,

the use of these formulas wiU indicate the importance of the stem correction in relation to a desired

accuracy, and the corrections can then be applied

as necessary.

a. Measurement of Emergent- Stem Temperature

The mean temperatiu*e of the emergent stem

may be measured approximately by means of one

or more small auxiliary thermometers suspended

near the emergent stem, or more acciu"ately by

11
exposing a similar stem and capillary mercury

column beside the emergent stem and thus measuring its mean temperature [5, 6]. This is con- veniently carried out with a faden thermometer

("thread thermometer") in which the expansion

of the mercury in a capillary tube (bulb) is measured in a stiU finer capillary stem.

The methods used at the NBS in calibration

work are based upon the use of faden thermometers

whenever possible. These thermometers have

very long bulbs (5 to 20 cm) with wall thicknesses

and bore sizes nearly the same as the stem of an

ordinary thermometer. If a faden thermometer

is placed beside a thermometer to be observed, at such a height that the top of the faden thermometer bulb is at the same level as the top of the

mercury column in the thermometer, the faden

thermometer reading will give approximately the

mean temperature of the adjacent portion of the

thermometer stem and mercury thread. For

example, a faden thermometer with a 10-cm bulb

wiU 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-immersion

thermometer 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 the

mercmy column in a total immersion thermometer

extends a short distance above the surface of the

bath to permit reading. In this case a correction

must be calculated for the emergent part of the

mercury column. If the stem temperature of a partial-immersion thermometer is to be measured, one or more faden thermometers are mounted so

as to indicate the mean stem temperature between

the immersion mark and the top of the mercury

column, as shown in figure 8(b). If faden thermometers are not available, an estimate of the

stem temperatm-e can be made with auxiliary

thermometers as in figure 8(c).

In calcvdating the correction for the emergent

stem, 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 by

measm-ement of a portion of the thermometer

scale. This measm-ement should be made over

the portion of the graduated scale which was

adjacent to the faden bulb. This is particularly

important with high-temperature thermometers

where the length of a degree is generally not the same at aU parts of the scale.

b. Formula for Total-Immersion Thermometers

When a thermometer, which has been graduated

and calibrated for use at total immersion is actually

used at partial immersion, the correction for the

emergent stem may be calculated by the general

formula,

stem correction = jfiLTi (T—t),

7^.

FADEN THERMOMETER

l-'BULB 7777

FADEN -THERMOMETER

BULB

. LIQUID COLUMN

OF THERMOMETER

IMMERSION LEVEL

(b) PARTIAL IMMERSION

7777';

(c) PARTIAL IMMERSION

AUXILIARY THERMOMETERS

LIQUID COLUMN

OF THERMOMETER

(a) TOTAL IMMERSION

Figure 8.- -Schemes for measurement of emergent stem

temperature.

where

K= differential expansion coefficient of mercury

(or other thermometric liquid) in the particular kind of glass which the thermometer is made (see table 3)

n = number of thermometer scale degrees adjacent to the faden thermometer,

^ = average temperatiu-e of n degrees of the

thermometer stem (faden thermometer

reading)

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, the

change in K with temperature for one glass may

reasonably be inferred from the change for another

glass.

Calculation of the stem correction may be

illustrated by the following example

A total-immersion thermometer reads 90° C in a bath when immersed to the 80 °C graduation

mark 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. 000164

100 .000158 .000164

ISO .000158 .000165 200 .000159 .000167 2S0 . 000161 . 000170 300 .000164 .000174

350 .000178 400 .000183 450 .000188

For Fahrenheit thermometers

0° 0.000088 0.000091 200 .000088 .000091 300 .000088 .000092 400 .000089 .000093

500 .000090 .000095 600 .000092 .000097 700 .000100 800 . 000103

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 X

30(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 the

correction is +

If a faden thermometer were not available in the above example, the emergent-stem temperatiu'e could be estimated by suspending a small

auxiliary thermometer above the bath adjacent to the main thermometer and with its bulb centered

at about the level of the 85° graduation. The

reading of the auxiliary thermometer will then

approximate the mean temperature of the 10 deg C

(80° to 90 °C) emergent from the bath. For this

condition n = 10. If the auxiliary thermometre

reads 60 °C, the stem correction =0.00016X

10(90-60) = +0.048 or +0.05 °C. This method

will usually not be as reliable as the method using

a faden thermometer [6].

c. Formula for Partial-Immersion Thermometers

The scale corrections for partial-immersion thermometers calibrated at the Bureau are reported

for the conditions of immersion to the depth of the

immersion mark on the thermometer and, unless

otherwise requested, for the unspecified stem

temperatures resulting from the particular environments prevailing over the comparison baths in the

course of the calibration. Frequently, however,

thermometers are submitted for calibration with a

request for scale corrections which are applicable to a

specified mean temperature of the emergent stem. In such cases the emergent stem temperatures are measiired during the process of calibration. The

calibration observations are then corrected as necessary to account for any differences found

between the stem temperatures observed during

test and the specified stem temperature for which

the scale corrections are to apply. In this case, the magnitude of the stem correction is proportional to the difference between the specified and

observed stem temperatures and may be calculated

for Celsius mercurial thermometers by means of

the relation,

stem correction = 0.000 1 6w (Up — toba)

where

tgp = specified mean temperature of emergent stem

(for which reported scale corrections

apply),

^oba = observed mean temperature of emergent

stem, n = number of scale degrees equivalent to the

length of emergent stem. The above relation, of course, may also be used

to correct the indications of a partial-immersion

thermometer when used under stem-temperature

conditions other than specified ones for which the

scale corrections apply. In using the formula it should be noted that n applies to the whole length

of emergent stem, i.e., from the immersion mark

to the top of the mercury column. The un- graduated length between the immersion mark and

the first graduation on the scale must therefore be

evaluated in terms of scale degrees and included in the value of n. For purposes of computing the emergent-stem

correction, the value of K may be considered , as depending on the average of T and t, that is iT+t)/2. Values of as a function of iT+t)/2

for two widely used thermometer glasses are given in table 3. If the kind of glass is not known, K may be taken as 0.00016 for Celsius mercury

thermometers and 0.00009 for Fahrenheit thermometers.

d. Formula for Calorimeter Thermometers

The stem correction is often important when

thermometers are used for differential temperature measurements, as in calorimetry. In this case, provided the mean temperature of the stem

remains constant, the correction may be computed

from the following formula, involving the differ- ence of the initial and final readings

s tern 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, respectively,

d=T,-T„

5'= scale reading to which the thermometer is immersed,

and ^=mean temperature of the emergent

stem.

This correction must be applied (added if +,

subtracted if —) to the difference of the readings

to 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; and

the stem temperature was 20 °C. Then the

correction is 0.00016X5 (25 + 30-20 — 20) = +0.012 °C. The difference between and

is 5°. The true difference between the initial and

final 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 thermometer is immersed to near the zero on its scale and

that 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 the

other symbols have the same meanings as

for calorimeter thermometers.

A Beckmann thermometer of the ordinary type

should not be used with any part of the lower

portion of the stem exposed, as this part may

contain 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 the

stem emergent from the bath, the necessary

correction may be computed from the above

formula, provided S in the formula is replaced by

S+m, where m is the number of degrees the

temperature of the thermometer must be lowered

to 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 be

the case with thermometers having the zero graduation at the top of the scale, the differential

stem correction may be calculated from the above

formula if S is replaced by S+m. The formula is applicable whether the point of immersion is on

the scale or below it, provided the points at which

readings are made are above the point to which

the thermometer is immersed.

6. Common Thermometers and Factors Affecting Their Use

In this section common types of high-grade

thermometers 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 4

through 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 become

apparent when all factors are considered. For

example, if one keeps expanding the scale for more

precise reading by reducing the capillary-bore

diameter, a practical limit is reached beyond

which capillary forces, in combination with the

elasticity of the thermometer bulb, will prevent a smooth advance or retreat of the mercury column.

Particularly with a slowly falling temperature, the

movement of the mercury meniscus may be found

to 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. Excessively elliptical or flattened bores are not

recommended. Thus increasing the length of a degree on the scale, for practical bulb sizes, improves thermometric performance to a certain

point only, beyond which the precision of reading

may readily be mistaken for accuracy in temperature measurement. A study of the effects of bulb

and capillary dimensions on thermometer per- formance, made by Hall and Leaver [7], provides

valuable guidelines for design purposes.

Other factors such as ice-point changes, unless

exactly accounted for, and differences in external

pressm-e may also account for inaccuracies much

greater than the imprecision with which a scale

having 0.1- or 0.2-deg graduations may be read.

6.L Total-Immersion Thermometers

Thermometers pointed and graduated by the

manufacturer to read correct temperatures when

the bulb and entire liquid column in the stem are exposed to the temperature to be measured are known as "total-immersion" thermometers.

While these thermometers are designed for immersion of all the mercury, it is not necessary, and

in some cases not desirable, that the portion of the

stem above the meniscus be immersed. The

heating of this portion to high temperatures might

cause excessive gas pressures resulting in erroneous

readings if not permanent damage to the bulb.

In practice a short length of the mercury column

often must be left emergent from the bath (or

region) so that the meniscus will be visible when

the temperature is being measured. If a large

enough temperature difference exists between the

bath and its surroundings, an appreciable temperature gradient may be found in the thermometer

stem near the surface of the bath for which a

correction to the thermometer reading may be

required. The condition becomes more serious

when a thermometer designed and calibrated for

total immersion is intentionally used at partial

immersion, that is with a significant portion of the

liquid column at a temperature different from

that of the bath. The reading will be too low or

too high depending upon whether the surrounding

temperature is lower or higher than that of the

bath. For a total-immersion thermometer so used, an emergent stem correction must be determined and applied in addition to the calibration

corrections. The correction may be as large as 20 Celsius degrees (36 Fahrenheit degrees) if the

length of emergent liquid column and the differ- ence in temperature between the bath and the

space 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 are chosen to be indicative of good manufacturing

practice. These tolerances are based on the fact

that in the manufacture of thermometers certain

small errors in pointing and graduation are

inevitable, and also that the indications of thermometers are subject to variations due to the

inherent properties of the glass. The tolerances

14
Table 4. -Tolerances for Celsius total-immersion mercury

thermometers

Temperature range in degrees Graduation Tolerance Accuracy Correcinterval 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.

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 100 Above 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 300 Above 300 up to 500

0 up to 300 Above 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 in degrees Graduation

interval in degrees

Tolerance

in degrees

Accuracy

in degrees Corrections stated to

Thermometers graduated under 300 °F

32 up to 300

32 up to 300

32 up to 212

2.0

1.0 or 0.6

.2 or .1

1.0

1.0 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 212 Above 212 up to 600 }

2 or 1

r 1.0

I 2.0

0. 2 to 0. 5.5 0.2

.2

Thermometers graduated above 600 °r

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

32 up to 600 Above 600 up to 950

}

} 2orl

/ 4.0

I 7.0

/ 3.0

1 6.0

0. 6 to 1. 0

1. to 2.

0. 2 to 1.

. 6 to 1. 0

0.6

.5

.2

.2

must be sufl&ciently restrictive to insure to the

user a satisfactory high-grade thermometer but at the same time must not cause undue manufacturing 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. The

intent of this requirement is to eliminate thermometers having large corrections of alternating

signs, which would lead to uncertainties in the

interpolation of scale corrections between calibration points.

Tables 4 and 5 also give suitable values for the

subdivisions and the accuracy which may be ex- pected. The word "accuracy" used in these tables

refers to the best values attainable in the use of the thermometer when all corrections are applied.

The final columns state the decimal figures to which the corrections are given for thermometers

calibrated by the Bureau. They are stated to somewhat higher precision than can be attained

with certainty in calibrating the thermometers.

They are so-stated to avoid the possibility of an

additional uncertainty due to rounding off.

6.2. Partial- Immersion Thermometers

In many instances it is required to measure

temperatm-es under conditions where it is inconvenient or impossible to use a liquid-in-glass thermometer at total immersion. For such uses partial-immersion thermometers are designed with

scales graduated to indicate true temperatures

when the thermometers are immersed to specified

depths. No stem temperature correction is necessary, therefore, when these thermometers are used with the same depth of immersion and

emergent-stem temperature for which they are

calibrated. Unless otherwise stated, each Report

of Calibration issued by the Bureau gives corrections that apply for the temperatures prevailing

above the comparison baths. When such a thermometer is to be used with a different stem temperature, the necessary emergent stem correction

must be calculated as shown in section 5.4.c. The accuracy attained with this type of thermometer wiU usually be significantly less than that

possible with total-immersion thermometers. This

is particularly the case when partial-immersion

thermometers are used with stem temperatures

greatly different than the temperature being measured. An unsteady or irreproducible environment

surrounding the emergent stem, together with the

inherent difficulty of estimating or measuring the

emergent-stem temperature with sufficient accuracy, can contribute markedly to the uncertainty

of a given thermometer indication. For this rea- son tables 6 and 7 show that accuracies expected

of partial-immersion thermometers are not so high

as those for total-immersion thermometers nor are the calibration corrections stated so precisely.

6.3. Low-Temperature Thermometers

The lowest temperature to which a mercuryfUled 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 lower

temperatures 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 thermometers

for temperatures down to about — 56 °C ( — 69 °F)

The freezing temperature of the alloy is critically

affected in the neighborhood of the eutectic by

the amount of thallium present. Small differences

in composition, resulting in either too much or too little thallium, have the effect of markedly

raising the freezing point of the alloy. It is therefore difficult to achieve the lowest freezing temperature in practice. In addition, some thermometers 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-immersion mercury thermometers

Temperature range in degrees Graduation

interval in degrees •

Toler- ance in degreesAccuracy i> in degreesCorrections stated to

Thermometers not graduated above 150 °C

0 up to 100

0 up to 150

1. 0 or 0.

1. 0 or 0.

1.0

1.0

0. 1 to 0.

0. 1 to 0.

0.

0.

Thermometers not graduated above 300 °C

0 up to 100 Above 100 up to 300

1.0

1.0 1.0

1.5

0. 1 to 0.

. 5 to 1.

0.1

.2

Thermometers graduated above 300 °C

0 up to 300 Above 300 up to 500. } - 0 or 1.0. 5 to 1.

1. 0 to 2. 0.5.5

Table 7.

Tolerances for Fahrenheit partial-immersion mercury 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 212 32 up to 300 - -2. 0 or 1.

2. 0 or 1. 2.02.0

0. 2 to 0. 5

0. 2 to 1.

0.2

0.2

Thermometers not graduated above 600 °F

32 up to 212 Above 212 up to 6002. 0 or 1.

2. 0 or 1. 2.0 3.0

0. 2 to 0. 5

1. 0 to 2. 0 0.2.5

Thermometers graduated above 600 °F

32 up to 600 Above 600 up to 950 }

5. 0 or 2.

r 5.0

\ 10.0

1. 0 to 2.

2. 0 to 3. 0 1.0

1.0

» Partial-immersion thermometers are sometimes graduated in smaller

intervals 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 considered to be as reliable as merciiry-thallium-fiUed

thermometers, they serve to extend the range

below — 56 °C. Some of these Hquids are used as low as -200 °C (-328 °F).

Alcohol, toluene, and pentane have all been

used as fluids for low-temperature thermometers.

All of these fluids, however, have limitations of one kind or another. Other organic liquids, alone

or in mixtvires, have been found by some manufacturers to show better characteristics for particular

applications.

All of these organic liquids have the disadvantage of wetting the bore of the thermometer tubing

which may lead to significant error in the indications of such thermometers if sufficient precautions

are not taken. Any liquid that wets the tube will

leave a film on the wall as the meniscus falls, the

thickness of the film being dependent among other

things on the viscosity of the liquid, the interfacial

action between the liquid and glass, and the rate at

which the thermometer is cooled. Where possible

the rate of cooling should be slow with the bulb

cooled first. In this way the viscosity of the filling fluid in the thermometer bore is kept as low as possible until the final temperature is reached, thus

minimizing the amount of liquid left behind on the

wall. Even so, sufficient time should be allowed

for drainage from the wall to be essentially completed. Under adverse conditions it may take an hour or more before the effect of drainage ends.

In addition to good drainage characteristics, a

satisfactory low-temperature fluid should be free of water, dirt, or other foreign material which

will separate out at temperatures for which the

thermometer is graduated. Furthermore, lowtemperature thermometers are frequently designed for use up to room temperature or above.

In these cases the vapor pressure of the filling

Uquid becomes important. A low vapor pressure

is necessary to prevent distillation of the Uquid

at the higher temperatures. Any dye added to improve the visibility of the thermometer Uquid

should be chosen for good color fastness with

respect to Ught cxposm-e or chemical action with

the thermometer liquid.

Tolerances applicable to low-temperature thermometers are given in tables 8 and 9.

6.4. Beckmann Thermometers

A metastatic, or Beckmann thermometer is usually of the enclosed-scale type, so constructed

that portions of the mercury may be removed

from, or added to, the bulb permitting the same

thermometer to be used for differential measure- ments in various temperature ranges. The scales are kept short, usually to 5 or 6 deg C, although some micro types have a scale of only 3 deg C.

The "setting" of such a thermometer refers to the

temperatiire 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 temperature

change is different. It follows that two equal

changes in temperature at different settings cause

different indications on the scale. Therefore a

"setting factor" must always be used to convert

reading differences into true temperature differ- ences whenever the thermometer is used at any

setting different from the one at which its scale was calibrated. These setting factors combine

corrections for the different changes in volume of

different quantities of mercury during equal temperature 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 American

equivalent. Corning normal. The scale calibrations for Beckmann thermometers as reported by

the Bureau are applicable to a setting of 20 °C, and

the factor is consequently 1 .0000 at this temperature. For a setting of any other temperature the

observed temperature difference must be multi16
Table 8.

Tolerances for low-temperature total-immersion thermometers Table 10.

Setting factors for Beckmann thermometers

Temperature

range in degrees

Type of Graduation Toler- Accuracy

thermometer interval in ance in in degrees

degrees degrees

Corrections stated 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-immersion

thermometers

Temperature Type of Graduation Toler- Accuracy Corrange in thermometer interval in ance in in degrees rections degrees degrees degrees stated to

Celsius thermometers

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

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.

.5

liquid.

plied by the appropriate factor from the table. An example is given below the table. In a common design of the Beckmann thermometer the large bulb is joined to the fine capillary, backed by the mUk-glass scale, by a

capillary of much larger diameter. When such an

instrument 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 be

actually measiu-ed. When an estimate can be

made of the temperatiu-e of the emergent stem,

however, a correction may be calculated as described in section 5.4. e. Tolerance requirements for Beckmann thermometers are given in table 11. Under the heading "Accuracy of interval in degrees" is given the estimated accuracy attainable in the measurement of any interval within

Setting Factor Setting Factor

°C "C

0 0. 9934 55 1. 0096

5 .9952 60 1. 0107

10 .9969 65 1.0118

15 .9985 70 1. 0129

20 1. 0000 75 1. 0139

25 1. 0015 80 1. 0148 30 1. 0030 85 1. 0157 35 1. 0044 90 1. 0165

40 1. 0058 95 1. 0172

45 1. 0071 100 1. 0179

50 1. 0084

As an illustration, suppose the following observations were made;

Setting = 25''C. Lower reading =2. 058° Stem tempera- Upper reading =5. 127° ture=24° Lower Upper

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

5.119

2. 063

Difierence = 3.056 Difference multiplied by setting

factor (1.0015) = 3.061 Emergent stem correction (see ac- companying-stem correction sheet) =-|-. 004 Corrected difference = 3. 065 Table 11. -Tolerances for Beckmann and calorimeter thermometers

Gradua- Allowable change Accuracy of Cor- Type of tion in- in correction in interval in rections thermometer terval in degrees degrees stated to degrees

Beckmann 0.01 °c 0.01 over 0.5° 0. 002 to 0. 005 0.001 Interval for setting of 20 °C Bomb calorimeter.. .01 °c 0.02 over 1.5° .005 to .01 .002 interval Do__ - .02 °C 0.02 over 1.5° .005 to .01 .002 interval Do .05 °F 0.04 over 2.5° .01 to .02 .005 interval Gas calorimeter .1 °r 0.16 over a 5° .02 to .05 .02 interval

the limits of the scale. No tolerances for scale error are given although

it is desirable that the scale error be no greater

than 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 thermometers which are used for acciurate differential

measurements. Since the accuracy of these thermometers at any one temperature is of less importance than the accuracy of the temperature

intervals, no reference point is required.

Table 11 gives the scale tolerances required of some typical calorimeter thermometers. No

tolerances 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 thermometer

shall be of good design, material, and workmanship

and shall be permanently marked with a serial

number which will uniquely identify the thermometer with its Report of Calibration. No

attempt is made to list specifically all possible

17
defects of design and workmanship, since some

latitude for juogment must be reserved for indi-

\ddual cases as they arise. Certain important

requirements of general applicability can be

singled out, however, and these are described

below.

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 made

of glass suitable for use in the temperature range

for which the thermometer is graduated. In addition, the thermometer must be adequately an- nealed so that continued use will not greatly

change its indications. This is especially important for a thermometer graduated above 300 °C or 600 °F. The quality of the thermometer glass

and the adequacy of the annealing process may be

judged in part by the stability of reference-point

readings (such as ice points).

A method of test for bulb stability is described

in The American Society for Testing and Materials' Method E77.

Table 12 lists some types of glasses commonly

used in the manufacture of thermometer bulbs

with reasonable upper temperature limits of their

use. These estimates by Thompson [8] are based

upon 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 than

130 °C (234 °F) below the strain point of the

glass. Thermometers may be used intermittently,

however, up to within 70 °C (126 °F) of the stram

point 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 a high strain point, such as that of borosilicate glass or higher, result in better thermometer performance and stability even in thermometers used at temperatures much lower than the exposure limits

given in table 12.

Table 12.

Temperature exposure limits for various thermometer glasses^

Exposure limits Strain point Continuous Intermittent

°C "C °F "C °F

Corning normal 7560 500 370 700 b430* b805* Kimble R 6 490 360 680 420 790 Jena 16 III 495 365 690 425 796 Corning borosilicate 8800 529 400 750 460 860 Jena borosilicate 2954 548 420 790 480 900 Corning 1720 668 540 1006 600 1110 Jena Supremax 2955 665 535 995 595 1100

• From reference 18).

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

for the stem.

All high-temperature thermometers should be

filled with a dry inert gas under sufficient pressure

to prevent separation of the mercury at any

temperature for which the scale is graduated.

Total-immersion thermometers graduated above

150 °C or 300 °F must be gas fSled to minimize

the distillation of mercury from the top of the

column. Gas filling for lower temperatures is optional, but is strongly recommended.

7.2. Scale Design and Workmanship

Thermometers of the soUd-stem type shall have

the graduation marks etched directly on the stem

and so located as to be opposite the enamel back.

In thermometers of the enclosed-scale type, the

graduated scale must be securely fastened to prevent relative displacement between scale and

and capillary (for example, by fusing the scale to the enclosing tube) or, if this is not done, a mark

should be placed on the outer tube to locate the

scale and indicate at any time whether the scale

is in its original position. The graduation marks

shall be clear cut, straight, of uniform width, and

in a plane perpendicular to the axis of the

thermometer.

The scale shall be graduated either in 1.0-,

0.5-, 0.2-, or 0.1-deg intervals, or in decimal

multiples 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-deg

intervals, or in 0.25-deg intervals further subdivided, are sometimes difficult to read and their

elimination is desirable. Thermometers graduated

in 0.1- or 0.2-deg intervals, or decimal multiples

of these, should have every fifth mark longer than

the 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 marks

consisting of alternating short and intermediate

marks, with every tenth mark distinctly longer

the others, and numbering at every 10th or 20th

mark.

The scale must not be extended to temperatures

for which the particular thermometer glass is unsuited. For example, a thermometer of borosilicate glass graduated to 500 °C (932 "F) would

be ruined in a short time if used at that temperature.

7.3. Scale Dimensions

Coarse graduation marks do not represent good

design. Optimum line width, however, depends

in some measure upon the use for which a particular thermometer is intended. If the thermometer

indications' are to be observed precisely, for example 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 may

be acceptable.

In addition, the graduation marks must not be

too closely spaced. The closest permissible spacing depends upon the fineness and clearness of the marks. In no case should the distance between

center lines of adjacent graduation marks on an

etched-stem thermometer be less than 0.4 mm.

The minimum permissible interval between graduation marks for an enclosed-scale thermometer

is 0.3 mm if the lines are ruled on a mUk-glass

scale; for other scales the minimum is 0.4 mm.

The minimum in no case represents good design,

and well-designed thermometers will have graduation 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-y

in the main biilb or a capillary enlargement,

graduation marks placed over parts of the capillary

that have been changed by manufacturing operations, 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 between

graduations and enlargements in the bore are considered as minimum hmits commensurate with

good 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-mm

length if the graduation is above 100 °C (212 °F).

(b) A 5-mm length of unchanged capillary

between an enlargement and the graduation next

below, except at the top of the thermometer.

(c) A 10-mm length of unchanged capillary

between an enlargement, other than the bulb, and

the graduation next above, if the graduation is not above 100 °C (212 °F) ; a 30-mm length if the

graduation is above 100 °C (212 °F).

(d) A 10-mm length of unchanged capillary

above the highest graduation, if there is an

expansion 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 mm

of unchanged capUlary.

7.4. Reference Point on Scale

Thermometers graduated above 150 °C or 300

°F, or precision thermometers expected to be used

with an accuracy better than 0.1 °C or 0.2 °F,

when calibrated for the measurement of actual

temperatures rather than temperature diflferences,

must have a reference point at which the thermometer can be conveniently retested from time to time. From these reference-point tests, the effects of changes in bulb volume on the thermometer

indications may be followed throughout the life of the thermometer and the proper corrections

applied at any time. If no suitable reference point

such as the ice or steam point is included in the

range of the main scale, a short auxiliary scale including a fixed point shall be provided. To

avoid making the thermometer unduly long, a contraction chamber may be introduced between

the auxiliary scale and the main scale. The graduations on an auxiliary scale must extend for a short

interval both above and below the reference point.

Similarly, when the main scale ends near a temperature to be used as a reference point, the

graduations must be continued for a short interval

above or below the reference point as the case may be. Any auxiliary scale must have graduations

identical to those of the main scale, both di- mensionally and in terms of temperature.

Reference points are not needed on thermometers intended for differential measurements

(such as calorimeter thermometers) nor on

thermometers not graduated above 150 °C or 300 °F if these are not to be calibrated to an

accuracy better than 0.1 °C or 0.2 °F.

7.5. Marking of Partial -Immersion

Thermometers

Partial-immersion thermometers will not be

calibrated unless plainly marked "partial immersion", or its equivalent (for example, "76-mm

immersion"), and unless a conspicuous line is engraved on the stem to indicate the depth to which the thermometer is to be immersed. This

mark must not be less than 13 mm above the top

of the bulb. Special partial-immersion thermometers adapted to instruments which fix definitely

the manner for use (for example, viscometers and

flash-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 behavior of such thermometers and in a better utili- zation of the information contained in the Reports

of Calibration.

8.1. Glass Changes

The changes which occur in thermometer bulb

glass 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 manufacture 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 indefinitely at some fixed temperature, density (and

v'olume) changes proceed more or less slowly

toward a preferred density corresponding to a quasi equilibrium condition characteristic of the

particular kind of glass and the temperature.

Since these changes involve molecular rearrangements, they proceed more rapidly at high temperatures where the viscosity of the glass is lower

and the molecular mobUity consequently higher.

Thus a close approach to quasi equilibrium may

be 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 minutes

from some high temperature, equilibrium is not

reached 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 liquidin-glass thermometers. For its entire lifetime, a thermometer may retain a "memory" of its thermal history at the higher temperatures experienced diu-ing manufacture. The techniques of

good manufacture, therefore, are designed to produce 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 and

sign 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 kinds

resulting 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 equihbrium

condition corresponding to that particular high

temperature If the thermometer is then cooled

sufficiently slowly through critical temperature

regions, the glass will return to close to its initial state, and the ice point reading will show no

change 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". Thermometers

which have been heated to high temperatures

recover from this ice-point depression in an unpredictable way, and frequently there wiU be no

significant recovery after a year's time at room

temperature. The ice-point depression has a reproducible value, however, for a thermometer

cooled in stiU air, so that the ice point, taken from

time-to-time immediately (within about 1 hour)

following cooling in this manner, may be used

reliably to show changes in thermometer bulb

volume with time and use. On the other hand, thermometers used only up

to about 100 °C win usually exhibit a relatively

rapid recovery from the ice-point depression, and

the original bulb volume wUl be recovered within

the equivalent of 0.01 or 0.02 deg C in about

3 days. This phenomenon has an important

bearing on the precision attainable with mercury

thermometers and most be taken into consideration in precision thermometry, especially in the

interval 0 to 100 deg C. Thus, if a thermometer is used to measure a given temperature, it will read

lower than it otherwise would if it has a short

time previously been exposed to a higher temperature. With the better grades of thermometric

glasses the error resulting from this hysteresis wiU

not exceed (in the interval 0 to 100 deg) 0.01 of a degree for each 10-deg difference between the

temperatiu-e being measured and the higher temperature to which the thermometer has recently

been exposed and with the best glasses only a few

thousandths of a degree for each 10-deg difference.

The errors due to this hysteresis become somewhat

erratic at temperatures much above 100 °C. For

the reasons briefly set forth above it is customary,

in precision thermometry, to apply a scale correction based upon an ice point reading taken immediately after the temperatiu"e measurement.

b. Permanent Changes

A second type of change in thermometer

glasses, known as the "secular change," results in a non-recoverable decrease in bulb volume which

may progress with time even at room temperatiu-e,

but which is markedly accelerated at high temperatmes. This type of change is evidenced by

an increase in the ice point reading. At low to moderate temperatures there may be a gradual

change which will continue for years. With

better grades of thermometer glasses the change wiU

not exceed 0.1 °C in many years, provided the

thermQmeter has not been heated to temperatures

above about 150 °C. In addition, permanent

changes in bulb volumes have sometimes been

observed with thermometers which have been

repeatedly cycled at low temperatures, for example

between -30 and -f25 °C [13]. At high temperatures the secular change usually progresses more

rapidly at first, but, with continued heating,

tends toward lower rate of change with time. The

rate of secular change wiU be dependent upon the

kind of glass used in the thermometer bulb and

the particular heat treatment given the ther- mometer in manufacture. Thermometers manu20
factured according to good practices wUl evidence

only small secular changes, but thermometers

made 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 thermometers

care 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 may

cause a permanent distortion of the bulb resulting

in lower thermometer indications.

8.2. Pressure Effects

Since glass exhibits elastic properties, the volume

of a thermometer bulb will change with change of pressure, either internal or external. Therefore,

at the same temperature, the reading of a thermometer in a horizontal position will be different

than its reading in a vertical position. Thermometer readings will change also with altitude

or when the external pressure is changed in some

other way. Changes of about 0.1 °C (0.2 °F) per

atmosphere have been found for many ther- mometers with bulb diameters between 5 and

7 mm. This value can be used with some confidence for estimating the probable effect of an

external 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 defined

as 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 thermometers, Guillaume found a value of 5.2X10~®

degrees C/mm Hg for k, but Hall and Lever [7], by

experiment, found a value about 25 percent lower

for their thermometers.

In cases where an accurate correction is necessary, (3e should be determined experimentally. A

simple apparatus for the determination is shown in

figure 9. The internal pressure coefficient /3j is more diffi- cult to determine accmrately but may be calculated

from 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 external pressure coefficient.

8.3. Lag

Practically all theoretical treatments of the

question of thermometer lag are based on the

assumption that Newton's law of cooling (i.e., that the rate of change in the reading of the

thermometer is proportional to the difference between thermometer temperature and bath temperature) holds for the thermometer. It is an immediate consequence of this law that when a thermometer is immersed in any medium it does

not take up the temperature immediately, but

approaches it asymptotically. A certain time

must elapse before the thermometer reading agrees

with the temperature of the medium to 0.1 deg,

still longer to 0.01 deg, the temperature remaining

constant. If the temperature is varying, the thermometer always indicates, not the true temperature,

but what the temperature of the medium was at some

previous time. The thermometer readings are thus

said to "lag" behind the temperature by an amount

which may or may not be negligible, depending

upon the rapidity of temperature variation and the

physical characteristics of the thermometer. A

more complete treatment of this subject has been

given by Harper [16]. For a thermometer immersed in a bath, the

temperatiu"e of which is changing uniformly, the

lag may be defined as the interval in seconds

between the time when the bath reaches a given

temperature and the time when the thermometer

indicates that temperature. This lag X is dependent upon the dimensions and material of the

thermometer 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 the same 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, one

having 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 water

bath for three thermometers with typical lag constants.

former will read 0.001 degree higher than the

latter, due to the lag. In the intercomparison of

thermometers the rate of temperature rise may

nearly always be kept so small that this lag

correction is negligible.

If a thermometer at a given initial temperature

is plunged into a bath at a different temperature,

the lag, X, is the time required for the original

difference in temperature between thermometer

and 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 laboratory

thermometers representative of American manufacture have yielded values of about 2 to 3

seconds in a weU-stirred water bath. Figure 10

shows the approach of thermometer readings to the water bath temperature for 3 selected thermometers having different values of X. For

example, if the thermometer for which X=2.2

sec is initially at 25 °C and then is immersed in a bath at 75 °C, the thermometer reading will be

within 0.05 °C (0.1 percent of 50 °C) of the bath

temperature in 15 sec and within 0.01 °C in 19

sec. The curve for X=3.1 was obtained for an American Society for Testing and Materials

(ASTM) specification 56C calorimeter thermometer with a bulb diameter (outside) of 7.9 mm and

bulb length of 44 mm. The value of X=2.2 was

found for an ASTM 7C thermometer having bulb

dimensions of 5.4 by 12 mm. The third curve,

for X=1.7, was obtained for a bulb with dimensions

of 5.4 by 34 mm. It is probable that most solid

stem thermometers of American manufacture will have values of X lying within the range covered by

the 3 curves shown.

According to Harper [16] the value of X for a given thermometer in a well stirred oil bath will

be about twice its value for a water bath.

When a thermometer is used to measure changes

of temperature, as in calorimetry, it has been

shown Dy White [17] that the lag enters into the

observations in such a way as to be eliminated

from the results in applying the usual radiation

corrections. Therefore the lag need not be

considered, provided only that the initial and final readings are made when the temperature is varying

uniformly. This is not strictly true, however, in

the case of some Beckmann thermometers that

have no true value of X, as has been explained in

the paper referred to above.

8.4. Separated Columns

Many inquiries are received concerning separated mercury columns, particularly after shipment. Since no means of avoiding such occur- rences has yet been found, some directions for joining the mercury may be helpful. The mercury

may separate somewhat more readily in thermometers which are not pressure-fiUed, but it can be more easily joined smce there is little gas

to separate the liquid. The process of joining

broken columns consists of one or a series of manipulations which may be effective, and these are

briefly described here.

(a) The bulb of the thermometer may be cooled

in a solution of common salt, ice, and water (or

other cooling agent) to bring the mercury down

into the bulb. Moderate tapping of the bulb on a paper pad or equally firm object or the application

of centrifugal force usually serves to unite the

merciu^y in the bulb. If the salt solution does

not provide sufficient cooling, carbon dioxide snow (dry ice) may be used. Since the temperature of dry ice is about —78 °C (-108 °F) and

mercury freezes at about —40 °C (—40 °F) it will cause the mercury to soUdify. Care must be

taken to warm the top of the bulb first so that

pressiores in the bulb due to the expanding

mercury may be relieved.

(b) If there is a contraction chamber above the

bulb or an expansion chamber at the top of the

thermometer the mercury can sometines be

united by warming the bulb until the column

reaches the separated portions in either enlargement. 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 more

readily accomplished if the quantity in either

cavity has first been shattered into droplets by

tapping the thermometer laterally against the

hand.

22
(c) As a last resort, especially for thermometers

having 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 then

be drained down the bore. The latter process is aided by cooling the bulb. All of these manipulations require patience, and experience is helpful,

but they will yield results if care is used. A

convenient method of ascertaining that all the

liquid 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 Temperature Scale of 1948, J. Res. NBS 65A, 1939 (1961).

[3] N. S. Osborne and C. H. Meyers, A formula an

tables 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 cryostat with automatic temperature regulation, BS

J. 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 emergent

column correction in mercury thermometry, J. Sci. Instr. 41, 234 (1964).

[7] J. A. Hall and V. M. Leaver, The design of mercury

thermometers for calorimetry, J. Sci. Instr. 36, 183 (1959).

[8] R. D. Thompson, Recent developments in liquid-inglass thermometry. Temperature, Its Measurement

and 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 changes

in thermometer glasses, J. Am. Ceram. Soc. 35, 67

(1952).

[10] American Society for Testing and Materials Designation C 162-56, Standard Definitions of Terms Relating to Glass and Glass Products.

[11] H. R. Lillie and W. W. Shaver, Method of tempering

glass, U.S. Patent No. 2,148,630 (Feb. 28, 1939).

[12] L. C. Liberatore, Method of stabilizing the molecular arrangement of glass thermometers, U.S. Patent No. 2,610,445 (Sept. 16, 1952).

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

[14] E. L. Ruh and G. E. Conklin, Thermal stability in ASTM thermometers, ASTM Bui. No. 233, 35

(Oct. 1958).

[15] C. E. Guillaume, Traits Practique de la Thermom6trie, 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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