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The following brief notes on the characteristic behavior of mercury-in-glass thermometers are added to aid the user in understanding the behavior of these thermometers, and to better utilize the information contained in the Reports of Calibration.

8.1. Glass Changes

The changes which occur in the glass of a thermometer bulb after first heating to a high temperature within the acceptable exposure limits of the glass and subsequent cooling to ambient temperatures, are an involved function of time and temperature. They will depend upon the thermal history of the glass (both during manufacture and previous use), the time of exposure to the high temperature, and the rate of cooling. Evidence from many investigations [13, 15, 16] seems to indicate that when a glass is held indefinitely at some fixed temperature, density (and volume) changes proceed toward a preferred density corresponding to a quasi equilibrium condition characteristic of the particular kind of glass and the temperature. Since these changes involve molecular rearrangements, they proceed more rapidly at high temperatures where the viscosity of the glass is lower, and the molecular mobility consequently higher. For this reason, a close approach to quasi equilibrium may be reached in the order of hours at annealing temperatures, while infinite time may be required at much lower temperatures.

If a glass that has been heated to a high temperature is allowed to cool rapidly, it will be seen that equilibrium is not reached at the lower temperatures during cooling, and an equilibrium density more nearly corresponding to the high temperature is "frozen" into the glass. This characteristic behavior of glass has a lasting effect on the performance of liquid-in-glass thermometers. For the entire lifetime of the thermometer it may retain a "memory" of the thermal history at the higher temperatures.

The techniques of good manufacture are designed to produce in the thermometer glass a state which will result in maximum stability for the range of temperature indicated on the scale. To achieve perfect stability for all conditions of use is not possible in thermometer manufacture; therefore, changes in the ice-point readings are observed periodically. The changes observed at the ice point are reflected at all points on the scale by the same magnitude and sign, since they are the result of changes in the bulb volume (see Sec. 5.2) (changes in the stem have very little effect). Because of this behavior of glass, the changes in the bulb volume can be either temporary or permanent.

a. Temporary Changes

Upon heating to a high temperature, the bulb of a thermometer will expand from its initial state. After a short period of time, an equilibrium condition cor

responding to that particular high temperature will appear to be reached. If the thermometer is cooled slowly through critical temperature regions, the glass will nearly return to its initial state, and the icepoint reading will show no change. If, on the other hand, the thermometer is cooled rapidly (such as cooling naturally in still air), the bulb will retain a portion of its expanded condition, and the ice-point reading will be lower than the reading taken before heating. This phenomenon is known as "zero, or icepoint depression." Thermometers which have been heated to high temperatures recover from this icepoint depression in an unpredictable way, and frequently there will be no significant recovery after a period of one year at room temperature. Since the ice-point depression has a reproducible value, icepoint readings may be used reliably to show changes in the volume of the thermometer bulb with time and use, provided the thermometer is allowed to cool in still air and the ice point is taken within a reasonable period of time, not to exceed one hour, after being heated.

Thermometers used below approximately 100 °C will usually exhibit a relatively rapid recovery from the ice-point depression, and the original bulb volume will recover within the equivalent of 0.01 or 0.02 degrees C in approximately 3 days. This phenomenon has an important bearing on the precision attainable with mercury thermometers, and must be taken into consideration, especially in the range of 0 to 100 °C. If a thermometer is used to measure a given temperature, it will indicate an erroneously low value if it has, within a short period of time, previously been exposed to a higher temperature. With the better grades of thermometric glasses the error resulting from this hysteresis will not exceed (in the interval of 0 to 100 °C) 0.01 of a degree for each 10-degree difference between the temperature being measured and the higher temperature to which the thermometer has recently been exposed. With the best glasses the error may only be a few thousandths of a degree for each 10-degree difference. The errors due to this hysteresis become somewhat erratic at temperatures above 100 °C. For these reasons it is customary, in precision thermometry, to apply a scale correction based upon an ice-point reading taken immediately after the temperature measurement (see Sec. 5.2).

Where the range of temperature is small and the time between observations is short (as in the use of calorimetric thermometers), it is more satisfactory, each time the thermometer is used, to first heat to the highest temperature to be measured, so that all of the depression has taken place before the observations are begun. The condition to be observed is that the time required for observations is so short that no appreciable recovery shall have taken place during this time. As this condition is fairly well satisfied in calorimetric work, and as it is the only one for which

interval can be made repeatedly, calorimetric thermometers should be used in this way.

b. Permanent Changes

A "secular change" in thermometer glasses, which may progress with time, results in a non-recoverable decrease in the bulb volume as indicated by an increase in the ice-point reading. At room temperature there may be a gradual change which will continue for years, but at high temperatures the changes will be markedly accelerated. With better grades of thermometer glasses the change will not exceed 0.1 °C over a period of many years, provided the thermometer has not been heated to temperatures above approximately 150 °C. Initially, at high temperatures, the secular change usually progresses more rapidly, but with continued heating and time it tends toward a lower rate of change. The rate of secular change will depend upon the kind of glass used in the thermometer bulb and the particular heat treatment given the thermometer in manufacture. Thermometers manufactured according to good practices will evidence only small secular changes. However, thermometers made of glass unsuitable for the temperature range indicated on the scale, or improperly annealed, may show changes as large as 12 °C or 21 °F after heating for approximately 200 hours at high temperatures [17]. Permanent changes in the bulb volume have also been observed when thermometers have been repeatedly cycled at low temperatures (between -30 and +25 °C) [18].

When using thermometers for high temperature measurements, one must use care to avoid overheating. After only a few minutes of heating the thermometer at a temperature higher than its intended range, the increased gas pressure above the liquid column may cause a permanent distortion of the bulb resulting in lower thermometer indications.

8.2. Pressure Effects

Since glass exhibits elastic properties, the volume of a thermometer bulb will change when either the internal or external pressure changes. Therefore, at a given temperature, the reading of a thermometer in a horizontal position will differ from the reading in a vertical position. Thermometer readings will also vary with altitude. Changes of approximately 0.1 °C (0.2 °F) per atmosphere have been observed for many thermometers 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 approximately 10 percent greater.

Formulas for both external and internal pressure coefficients have been derived by Guillaume [19]. He found the relation,

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the bulb, and k 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. In the above formula, the external pressure coefficient ẞ is defined as the change in scale reading in degrees resulting from a change of 1 mm Hg in external pressure. For Celsius thermometers, Guillaume found a value of 5.2 × 10-5 degrees C/mm Hg for k, but Hall and Leaver [10]. by experiment, found a value approximately 25 percent lower for their thermometers. In cases where an accurate correction is necessary, the value, ẞe, should be determined experimentally. A simple apparatus for this determination is shown in figure 9.

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Practically all theoretical treatments concerning thermometer lag are based on the assumption that Newton's law of cooling is applicable (that the rate of change in the reading of the thermometer is propor tional to the difference between the thermometer temperature and the bath temperature). Consequently, when a thermometer is immersed in any medium, it does not indicate the temperature immediately, but approaches it asymptotically. A detailed discussion of this subject has been given by Harper [20].

If the temperature of the medium is varying uniformly, the thermometer always indicates what the temperature was at some previous time. The thermom

of the medium by an amount which may or may not be negligible, depending upon the rapidity of the temperature variation and the physical characteristics of the thermometer. In this case, the lag, A, 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 is dependent upon the dimensions and material of the thermometer bulb, the medium surrounding the thermometer and the stirring rate of the medium. If a thermometer is suspended in still air, the lag may be as much as 50 times that of the same thermometer when it is immersed in a well-stirred water bath. Since the value of the lag for mercurial thermometers is not large (from 2 to 10 seconds in 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 seconds and another of 8 seconds, are read simultaneously in a bath with the temperature rising at a rate of 0.001 degree in 5 seconds, the former will read 0.001 degree higher than the latter, due to the lag. In the intercomparison of thermometers, the rate of temperature rise can usually be kept small, making the lag correction negligible.

A second interpretation of thermometer lag involves immersing a thermometer in a bath where the temperature of the medium remains constant. A certain time must elapse before the thermometer reading agrees with the temperature of the medium to 0.1 of a degree, and still longer for agreement to be within 0.01 of a degree. In this case the lag, A, is the time required for the original difference in temperature between the thermometer and bath medium to be reduced to 1/e (that is 1/2.7) of itself. In a length of time 4 the difference will be approximately 1.5 percent of the original difference, and in a length of time 7 approximately 0.1 percent. Determinations of A for solid-stem laboratory thermometers, representative of American manufacture, have yielded values of approximately 2 to 3 seconds in a well-stirred water bath. Figure 10 shows the approach of thermometer readings to the water bath temperature for three selected thermometers having different values of A. If the thermometer having λ = 2.2 seconds is initially A at 25 °C. and is immersed in a constant temperature 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 seconds, and within 0.01 °C in 19 seconds. The curve showing X 3.1 was obtained for an American Society for Testing and Materials (ASTM) specification 56C calorimetric thermometer with an outside bulb diameter of 7.9 mm and a bulb length of 44 mm. The value of 2.2 was found for an ASTM 7C thermometer having bulb dimensions of 5.4 by 12 mm. The third curve, where 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 λ lying within the range of the three curves shown. It will be noted that, according to Harper [20], the value

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of λ for a given thermometer in a well stirred oil bath will be approximately twice its value in a water bath.

For a thermometer which is used to measure temperature changes (as in calorimetry), it has been shown by White [21] 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, providing 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, which have no true value of λ, as is explained in the paper referred to above.

8.4. Separated Columns

Many inquiries are received concerning separated mercury columns which occur especially during shipment. Since no means of avoiding such occurrences has yet been found, some directions for joining the mercury may be helpful and are described below.

(a) The bulb of the thermometer may be cooled in a solution of common salt, ice, and water (or other cooling agent) to bring the mercury down slowly into the bulb. If the salt solution does not provide sufficient cooling, carbon dioxide snow (dry ice) may be used. Since the temperature of dry ice is approximately

mately 40 °C (-40 °F), the mercury will solidify. Cool only the bulb and never the stem or mercury column. Moderate tapping of the bulb on a rubber stopper or similar soft spongy object, or the application of centrifugal force, by swinging the thermometer in a short arc (i.e. use of centrifugal force), usually serves to unite the mercury in the bulb. Care must be taken to warm the top of the bulb first, so that pressures in the bulb due to expanding mercury may be

relieved.

(b) If there is a contraction chamber above the bulb or an expansion chamber at the top of the thermometer, the mercury can sometimes 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. (The expansion chamber should never be more than 2/3 full.) 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.

This procedure should not be used if it requires the thermometer to be heated above 260 °C (500 °F) and the bulb should never be heated in an open flame.

(c) As a last resort, especially for thermometers having no expansion chambers, small separated portions of the column can sometimes be dispersed by

the gas to by-pass. The thermometer is heated, and the droplets are collected by the rising mercury

column.

The procedure for thermometers containing organic liquids is similar. Separated liquid in the stem can be vaporized and permitted to drain down the capillary. Another method consists of gently tapping the stem. above the separation against the palm of the hand, forcing the organic liquid to break away from the wall of the capillary and flow down the bore to join the main column.

Minute gas bubbles, which are sometimes found along the surface of the mercury in the thermometer bulb, may be collected by "washing" the bulb with a large gas bubble. Bring all of the mercury into the bulb as outlined in section (a). Hold the thermometer in a horizontal position and gently tap it against the hand to form a large gas bubble. Force the bubble to travel around the walls of the bulb by rotating the thermometer and tapping it against the palm of the hand. When the entire surface has been "washed" rotate the bubble to the top of the bulb and reunite the mercury as described above.

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 of the liquid has been joined is a check of the ice point or some other reference point on the scale.

9. References

[1] "The International Practical Temperature Scale of 1968," Metrologia, Vol. 5, No. 2, 35 (April, 1969).

[2] Calibration and Test Services of The National Bureau of Standards, NBS Spec. Publ. 250 (1970 Edition), Part 5. (Copies available from NBS on request).

[3] Comptes Rendus des Séances de la Treizième Conférence Générale des Poids et Mesures (1967-1968), Resolutions 3 and 4, p. 104.

[4] Stimson, H. F., The International Practical Temperature Scale of 1948, J. Res. Nat. Bur. Stand. (U.S.), 65A (Phys. and Chem.), No. 3, 139-145 (May-June 1961). [5] Based on the data of Osborne, N. S., and Meyers, C. H., A formula and tables for the pressure of saturated water vapor in the range 0 to 374 °C, J. Res. NBS 13, 1 (1934) RP691.

[6] Scott, R. B., and Brickwedde, F. G., A precision cryostat with automatic temperature regulation, BS J. Res. 6, 401 (1931) RP284.

[7] American Society for Testing and Materials Designation E77-72, Calibration at Temperatures Other Than Fixed Points, Section 11.2.

[8] Buckingham, E., The correction for emergent stem of the mercurial thermometer, Bul. BS 8, 239 (1912) S170.

[9] Pemberton, L. H., Further consideration of emergent column correction in mercury thermometry, J. Sci. Instr. 41, 234 (1964).

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

[11] Ween, Sidney, "The Beckmann Differential Thermometer: Its Principles of Construction and Application," Materials Research and Standards, MTRSA, Vol. 12, No. 8, August 1972, p. 31. [12] Thompson, R. D., Recent developments in liquid-in-glass thermometry, Temperature, Its Measurement and Control in Science and Industry 3, Part 1 (Reinhold Publishing Corp., New York, 1962) p. 201.

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

[14] American Society for Testing and Materials Designation C162-56, Standard Definitions of Terms Relating to Glass and Glass Products.

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12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP)

Same as 9.

5. Publication Date

January 1976

6. Performing Organization Code

8. Performing Organ. Report No.

10. Project/Task/Work Unit No.

11. Contract/Grant No.

13. Type of Report & Period
Covered

Final

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

Library of Congress Catalog Card Number: 75-619230
16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant
bibliography or literature survey, mention it here.)

This Monograph, which supersedes NBS Monograph 90, contains information of general
interest to manufacturers and users of liquid-in-glass thermometers. Instructions
explaining how to submit a thermometer to the National Bureau of Standards for
calibration are provided, and the techniques and equipment, such as stirred liquid
comparison baths, used in the calibration procedures are described. A discussion
of important principles of acceptable thermometer design and factors affecting their
use is included. Listed are tables of tolerances reflecting good manufacturing
practices and reasonably attainable accuracies expected with liquid-in-glass
thermometers. The calculation of corrections for the temperature of the emergent
stem is given in detail for various types of thermometers and conditions of use.

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17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper
name; separated by semicolons)
Calibration; emergent stem; liquid-in-glass thermometer; reference point; stirred
liquid comparison bath; temperature scale.

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