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Thermometer, Mercurial

THERMOMETER, MERCURIAL 5. The most familiar type of thermometer depends on the apparent expansion of a liquid hermetically sealed in a glass bulb attached to a graduated stem of fine bore. Of all liquidin-glass thermometers those containing mercury are almost invariably selected for scientific purposes, although at first sight mercury would appear to be the least suitable liquid, on account of its small coefficient of expansion. The smallness oi the expansion necessitates an extremely fine bore for the stem, which introduces errors in consequence of the high surface tension of mercury. The considerable density of the liquid also tends to exaggerate the effects of change of position due to variation of the pressure exerted on the interior of the bulb by the liquid column. These errors are small and fairly regular, and can be corrected within certain limits. A much more serious source of trouble, especially at high temperatures, is the imperfect elasticity of the glass, which causes more or less irregular changes in the volume of the bulb. The effect of these changes on the readings of the thermometer is enhanced by the smallness of the expansion of mercury, and might be reduced by employing a more expansible liquid. It is more likely, however, that the defect will be remedied by the construction of thermometers of fused quartz, which is the most perfectly elastic solid hitherto discovered. For work at low temperatures the range of a mercury thermometer is limited by its freezing-point (39 C.).

These are the serious disadvantages attending the use of mercury, but in other respects it possesses so many advantages over alcohol or other substitutes, that it will in all probability continue to be used almost exclusively in thermometers of this type for scientific work. Among its chief advantages may be reckoned its high boiling-point (357 C.), and the absence of evaporation from the top of the thread, which is so serious a source of error with the alcohol thermometer. With mercury the evaporation is almost inappreciable at 100 C., and can in all cases be avoided by exposing the upper parts of the emergent thread to the temperature of the air. Although an evacuated mercury thermometer cannot be safely used at temperatures over 300 C., owing to the breaking up of the thread of liquid in the stem, it has been found possible, by filling the upper part of the stem with nitrogen or carbon dioxide under high pressure, to extend the range to 550 C. A more important advantage for accurate work is the fact that mercury does not wet glass, and avoids any possible errors due to adherent films of liquid on the walls of the tube. This greatly facilitates observations, and also renders it possible to calibrate the thermometer after construction, which cannot be satisfactorily accomplished with other liquids. The process of construction and calibration is further facilitated by the fact that mercury does not dissolve air to any appreciable extent. In consequence of the regularity of expansion of mercury at ordinary temperatures, the scale of the mercury thermometer agrees very closely with that of the gas thermometer. The liquid is very easily obtained in a high state of purity by distillation, and has practically no chemical action on glass. In this respect it is superior to the liquid alloy of potassium and sodium, which has been employed in some high-temperature thermometers, but which rapidly reduces silica at high temperatures. The high conductivity and low specific heat of mercury as compared with most other liquids tend to render the thermometer quick and sensitive in action. Its opacity considerably facilitates accurate reading, and even the smallness of its expansion has one great countervailing advantage, in that the correction for stem-exposure is proportionately reduced. This correction, which (even in the case of mercury) may amount to as much as 40 C. at 550 C., is far the most uncertain in its application, and is the most serious objection to the use of the liquid-in-glass thermometer at high temperatures.

6. Construction. The construction of the most accurate type of mercury thermometer has undergone some changes of detail in recent years. The range of the most accurate standards is generally restricted to the fundamental interval. The length of a degree on the stem can be increased to any extent by enlarging the bulb or diminishing the bore of the stem, but it is found in practice that there is no advantage in making the scale more open than one centimetre to the degree C. in standard instruments, or in increasing the number of divisions beyond ten or at most twenty to the degree. Enlarging the bulb makes the instrument sluggish, and exaggerates the errors due to imperfect elasticity. Diminishing the bore of the tube increases the errors due to capillary friction. Even one centimetre to the degree is an impracticable scale for thermometers graduated continuously from o to 100 C., owing to the excessive length of the stem. In order to secure so open a scale, it is necessary to limit the range to 35, or at most 50. The fixed points o and 100 may still be retained, for purposes of testing and reference, by the device, now commonly employed, of blowing auxiliary bulbs or ampoules on the stem, the volume of which is carefully adjusted to correspond with the number of degrees that it is desired to suppress.

In the best instruments for work of precision the bulb is not blown on the capillary tube itself, but is formed of a separate piece of tube fused on the stem. It is possible in this manner to secure greater uniformity of strength and regularity of dimensions. The thickness of the glass is generally between half a millimetre and one millimetre. The advantage in point of quickness gained by making the glass thin is more than counterbalanced by increased fragility and liability to distortion. The best form of bulb is cylindrical, of the same external diameter as the stem. The bore of the stem should also be cylindrical, and not oval or flattened, in order to diminish errors due to capillarity, and to secure the greatest possible uniformity of section. The glass should be clear, and not backed with opal, both to admit of reading from either side, and to minimize risk of bending or distortion. In the commoner sorts of thermometers, which are intended for rough purposes and to be read without the application of minute corrections, it is not unusual to divide the tube into divisions of equal volume by a preliminary calibration. In the most accurate instruments it is preferable to divide the tube into divisions of equal length, as this can be more accurately effected. The corrections to be applied to the readings to allow for inequalities of bore can be most satisfactorily determined in the case of mercury thermometers by calibrating the tube after the instrument is completed [see CALIBRATION). This correction is known as the " caliaration correction." Instead of being separately determined it may be included in the scale correction by comparison with a standard instrument, such as a platinum-resistance thermometer.

7. Corrections. The corrections to be applied to the readings of a mercury thermometer, in addition to the calibration correcion, may be summarized under the following heads: (i.), Zero, 'ii.) Fundamental Interval, (iii.) Internal and External Pressure, (iv.) Stem Exposure, (v.) Scale Correction, including Poggendorff's correction.

(I) The changes of zero are of two kinds, (a) Secular rise of zero due to gradual recovery from changes or strains acquired by :he bulb during the process of manufacture. This process may be lastened and subsequent changes practically eliminated by annealng the bulb after manufacture, and before final adjustment, at a ligh temperature, such as that of boiling sulphur (about 450 C.). A thermometer which has not been so treated may show a rise of zero amounting to as much as 20 or 30 when exposed for some time to a temperature of 350 C. (b) Temporary depression of zero after each exposure to a high temperature, followed by a slow recovery which may last for days or weeks. The best thermometers of hard glass show a depression of zero amounting to about one-tenth of i C. after exposure to 100 C. In softer glass the depression is usually greater and more persistent, and may amount to half a degree after 100 C. At higher temperatures the depression generally increases roughly as the square of the temperature above o C. It may amount to 2 or 3* at 300 C. The effect cannot be calculated or predicted in any series of observations, because it depends in so complicated a manner on the past history and on the time. It is a most serious difficulty in accurate mercurial thermometry, especially at high temperatures. The most satisfactory method of correction appears to be to observe the zero immediately after each reading, and to reckon the temperature from the variable zero thus observed. The rationale of this procedure is that the depression is produced at the high temperature much more rapidly than the subsequent recovery at the low temperature. The thermometer is taken from the bath and allowed to cool rapidly by free exposure to the air. As soon as it reaches 40 or 50 C., it is plunged in the melting ice, and the lowest point reached is taken as the temporary zero.

The following formulae have been proposed by various observers to represent the depression of zero for different kinds of glass :

Fernet, French cnstal, dz= 0-0040(1/100)' Guillaume, Verre dur, 100 C., d2 = (8886/+io-84f) Bottcher, Cristal dur, 190 C., dz = (797o<+329< 2 )lo~ 7 Jena, 16, iii., dz = (7ioot-8P) io~* .

The symbol dz in these formulae stands for the depression of zero produced by an exposure to a temperature (. The depression is about three times as large in French crystal as in English flint glass, and varies roughly as the square of /. Verre dur and Jena, 16, iii., are varieties of hard glass chosen as standards in France and Germany respectively, on account of the comparatively small depression of zero to which they are liable. At low temperatures, up to 50 C., the depression is very nearly proportional to t, but at temperatures above 100 C. it is necessary to adopt another formula in which the term depending upon P is more important. These formulae are useful as giving an idea of the probable size of the correction in any case, but they cannot be employed in practice except in the simplest cases and at low temperatures. On account of these temporary changes of zero, a mercury thermometer intended for the most accurate work at ordinary temperatures (as in calorimetry) should preferably never be heated above 40" or 50 C., and certainly never above 100 C. Above 100 C. the changes of zero become more irregular and more variable, depending on the rate of cooling and on the sequence of previous observations, so that even if the method of observing the zero after each reading is adopted, the order of precision attainable rapidly diminishes.

(II) Fundamental Interval. The thermometer to be tested is exposed to steam condensing at atmospheric pressure in an apparatus which is often called a " hypsometer," constructed with double walls to protect the inner tube containing the thermometer from any cooling by radiation. The standard atmospheric pressure at which the temperature of the steam is by definition equal to 100 C. is equivalent to that produced by a column of mercury at o C. and 760 millimetres high, the force of gravitation being equal to that at sea-level in latitude 45. The atmospheric pressure at the time of observation is reduced to these units by applying the usual corrections for temperature and gravitation. If the pressure is near 760 mm., the temperature of the steam may be deduced by assuming that it increases at the rate of i C. for 27-2 mm. of pressure. If the pressure is not near 760 mm., the application of the correction is less certain, but is generally taken from Regnault's tables, from which the following data are extracted. Thermometers cannot be satisfactorily tested at an elevated station where the height of the barometer H is less than 700 mm., as the steam point is too uncertain.

A convenient type of hypsometer is shown in fig. I. The boiler B is separate from the steam-jacket A surrounding the thermometer. A gauge G is provided for indicating the steam pressure (difference from atmospheric) and a condenser C for returning the condensed steam to the boiler. The thermometer is observed by the microscope M.

FIG. I. Hypsometer.

steam point. If be the interval in degrees of the scale between the two observations, and if h be the temperature of the steam, the fundamental interval of the thermometer may be taken as loo n/h, provided that t t is nearly 100 C. Since all the readings of a thermometer have to be corrected for the error of the fundamental interval, by dividing by the fundamental interval thus observed and multiplying by 100, it is a matter of some convenience in practice to have the instrument graduated so that the difference between the readings in ice and at 100 C. is very nearly 100 of the stem. The correction can then be applied as a small percentage independently of the other corrections. The method of determining the fundamental interval above described applies to all other kinds of thermometers, except that it is not generally necessary to observe the zero after the steam point. The temperature of the steam t\ should be expressed in the scale of the thermometer tested, if the scale differs appreciably from that of Regnault.

(Ill) Pressure Correction. The corrections for variations of internal and external pressure on the bulb are of some importance in accurate thermometry, but can be applied with considerable certainty at moderate temperatures. The correction for external pressure is assumed to be proportional to the change of pressure, and to be independent of the temperature. It is generally determined by enclosing the thermometer to be tested in a vessel of water,_ and observing the change of reading on exhausting or readmitting the air. The correction is generally between one and two thousandths of a degree per centimetre of mercury change of pressure, but must be determined for each thermometer, as it depends on the nature of the glass and on the form and thickness of the walls of the bulb. The coefficient of the correction for internal pressure is greater than that for external pressure by the difference between the compressibility of mercury and that of glass, and may be calculated from it by assuming this relation. If bt, hi, are the external and internal coefficients, expressed in degrees of temperature per centimetre of mercury, we have the relation 61=60+0-00015, degrees per cm. of mercury . . (6)

The coefficient of internal pressure can also be determined by taking readings in the horizontal and vertical positions when the thermometer is at some steady temperature such as that of ice or steam. The reading of the thermometer is generally reduced to an external pressure of one standard atmosphere, and to an internal pressure corresponding to the horizontal position. It is also possible to include the internal pressure correction in the scale correction, if the thermometer is always read in the vertical position. In addition to the variations of internal pressure due to the column of mercury in the stem, there are variations due to capillarity. The internal pressure is greater when the mercury is rising than when it is falling, and the reading is depressed to an extent depending on the fineness of the bore and the thinness of the walls of the bulb. The capillary pressure does not depend only on the bore of the tube, but also apparently to an even greater extent on the state of the walls of the tube. The least trace of dirt on the glass or on the mercury is capable of producing capillary pressures much greater than would be calculated from the diameter of the tube. Even in the best thermometers, when there are no inequalities of bore sufficient to account for the observed variations, it is seldom found that the mercury runs equally easily in all parts of the stem. These variations of capillary pressure are somewhat capricious, and set a limit to the order of accuracy attainable with the mercury thermometer. It appears that the difference of reading of a good thermometer between a rising and falling meniscus may amount to five or ten thousandths of a degree. The difference may be reduced by continuous tapping, but it is generally best to take readings always on a rising column, especially as the variations in the angle of contact, and therefore in the capillary pressure, appear to be much smaller for the rising meniscus. In ordinary work the zero reading and the steam reading would both generally correspond to a falling meniscus; the former necessarily, the latter on account of the phenomenon of the temporary depression of zero, which causes the thermometer to read higher during the first moments of its exposure to steam than it does when the expansion of the bulb has reached its limit. It is easy to secure a rising meniscus at the steam point by momentarily cooling the thermometer. At the zero point the meniscus generally begins to rise TABLE I. Temperature of Steam at pressures from 790 to 710 mm.

Pressure (corrected) Steam temp. = 100 C.+ 790 + 1-083 780 + 726 770 +365 760 o 750 -.369 740 -742 I-I2O -1-502 -1-888 Approximate formula dti = -0367 (H 760) -oooo2o(H 760)* .

If the barometer has a brass scale correct at o C., and H be the reading in millimetres, the correction for temperature is made approximately by subtracting 0-00163 H mm - If L is the latitude and M the height of the station in metres above the sea-level, the correction for gravitation is approximately made by subtracting (0-0026 cos 2L+o-oooooo2M) H mm.

The zero of the thermometer is observed immediately after the after five or ten minutes. The question, however, is not of much importance, as the error, if any, is regular, and the correction for capillarity is necessarily uncertain.

(IV) Stem-Exposure Correction. When the bulb of a mercury thermometer is immersed in a bath at a temperature /, and a part of the column of mercury having a length of n degrees is exposed to a lower temperature fe, the reading of the thermometer will be lower by aXnX(t h) degrees (nearly) than it would have been if the whole of the mercury and stem had been at the temperature t. The factor a in this expression is the apparent coefficient of expansion of mercury in glass, and varies from -000150 to -000165 for different kinds of glass. In order to apply this correction, it is usual to observe fe by means of an auxiliary " stem-thermometer " with its bulb placed near the middle of the emergent column n. Occasionally stem-thermometers with long thin bulbs are employed to give more nearly the average temperature of the whole emergent column. Owing to conduction along the stem of the thermometer, and to heated vapours near the bath, the mean temperature determined in this manner is generally too low. To allow for this empirically, an arbitrary reduction is often made in the value taken for n or o, but this cannot be regarded as satisfactory for work of precision. The only practical method of reducing the correction is to limit the number of degrees n exposed, or, in other words, to work with thermometers of " limited range." Each of these thermometers must then be corrected by comparison with a standard thermometer free from stem-exposure correction, such as a platinumresistance thermometer. To secure results of any value the correction must be determined at each point under the actual conditions of observation under which the thermometer is to be used. In work of precision it is necessary to use ten or twenty thermometers to cover a range of 300, as this is the only method of securing an open scale and reasonable accuracy as regards stem-exposure. To quote the opinion of C. E. Guillaume, one of the leading authorities on mercurial thermometry: " When this correction is large, it cannot generally be determined with sufficient approximation for measurements of precision. The mercury thermometer should then be replaced by other instruments, among which those based on the variation of the electrical resistance of metals hold the first rank."

(V) Scale Correction. The correction required to reduce the readings of a mercurial thermometer to the normal scale may appropriately be called the " scale correction." One of the chief advantages of the mercurial thermometer for scientific purposes is that its scale agrees very closely with the thermodynamical scale between o and 200 C. The scale corrections of the standard French thermometers of verre dur have been very carefully determined over the range o to 80 C. by P. Chappuis using a constantvolume gas thermometer containing hydrogen (at an initial pressure of one metre of mercury at o C.) as the representative of the normal scale. His observations between o and 80 C. are represented by the quartic equation fc-/.=/(*-IOo) (-61-859+0-47351 /-0-OOII577 f -o, (7)

in which f* and / m represent temperature on the scales of the hydrogen and mercury thermometers respectively. The verre dur mercury thermometer reads 0-112 C. above the hydrogen thermometer at 40 C. where the difference of the scales is a maximum. The scale corrections of the Jena-glass thermometers, deduced by comparison with the French verre dur, appear to be practically of the same magnitude, but show differences of as much as 0-010 C. on either side of the mean. It may be questioned whether it is possible to construct mercury thermometers with scales agreeing more closely than this, owing to inevitable variations in the quality and treatment of the glass. According to Guillaume, the scale of a French cristal thermometer t c differs from that of the standard verre dur t m between oand 50 C., according to the cubic formula' tc-t m = t(ioo-t)(i4-i26-o-03iit)Xio- > . . (8) According to some unpublished observations made by the writer in 1893-1894, the scale of an English flint-glass thermometer, tested by comparison with a platinum thermometer, does not differ from that of the constant-pressure air thermometer by more than one or two hundredths of a degree between o and 100 C. But for the comparison of the scales to be of any value, it would be necessary to study a large number of such thermometers. It is possible to obtain much more consistent results if the thermometers are not heated above 50" C.

The comparisons of the verre dur thermometers with the normal scale at the International Bureau at Paris have not as yet extended beyond loo 8 C. The most important observations on the mercury thermometer above these limits appear to be those of Regnault. The later observations of J. M. Crafts were confined to French thermometers of cristal dur (Comptes Rendus, 1882, 95, p. 863). He found the following deviations from the hydrogen scale: / 150 170 200 230" 250 280 300 330 -< +-25 +-35 -f-27 --02 -- 26 -- 63 -I-2I -2-48 The correction changes sign at about 230 C., owing to the rapid increase in the expansion of mercury. Between o and lo C. it would appear that the coefficient of expansion of glass increases more rapidly than that of mercury.

Poggendorfs Correction. It should be observed that, since in the construction of a mercury thermometer the tube is divided or calibrated so as to read in divisions of equal volume when the whole of the tube is at one temperature, the degrees do not as a matter of fact correspond to equal increments of the apparent expansion of mercury. The scale does not therefore agree in practice with the theoretical formula (i) for the scale of the expansion of mercury, since the expansion is measured in a tube which itself is expanding. A similar argument applies to the method of the weight thermometer, in which the overflow is measured by weight. Even if the expansion of mercury and glass were both uniform, as measured on the thermodynamical scale, the scale of the mercury thermometer, as ordinarily calibrated, would not agree with the thermodynamical scale. The difference can be easily calculated if the actual expansion of mercury and glass is known. The correction is known as Poggendorff's, but is generally included in the scale correction, and is not applied separately. It has the effect of making the thermometer read higher at temperatures between o and 100 than it would if the divisions of the stem did FIG. 2. Differences between Scales of Mercury, and Gas Thermometers and Hydrogen Scale, according to Guillaume and Chappuis.

not expand as the temperature rose. The amount of the correction for verre dur is given by Guillaume as P.C.=i(lOO-/)(23-920+0-0240/)XlO- . . (9)

The value of this correction is between -060 and -080 at 50 C. for different thermometers.

Note - this article incorporates content from Encyclopaedia Britannica, Eleventh Edition, (1910-1911)

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