CHAPTER X.
BOILING-POINT THERMOMETERS.
=91. Ebullition.=--The temperature at which a fluid _boils_ is called the _boiling-point_ of that particular fluid. It is different for different liquids; and, moreover, in the same liquid it varies with certain changes of circumstance. Thus the same liquid in various states of purity would have its boiling temperature altered in a slight degree. There is also an intimate connection with the pressure under which a fluid is boiled, and its temperature of ebullition. Liquids boiled in the open air are subjected to the atmospheric pressure, which is well known to vary at different times and places; and the boiling-point of the liquid exhibits corresponding changes. When the pressure is increased on the surface of any fluid, the temperature of ebullition rises; and with a decrease of pressure, the boiling goes on at a lower degree of heat.
In the case of water, we commonly state the boiling-point to be 212 deg. F.; but it is only so at the level of the sea, under the mean pressure of the atmosphere, represented, in the latitude of London, by a column of 29.905 inches of mercury, at a temperature of 32 deg. F., and when the water is fresh and does not contain any matter chemically dissolved in it. When steam is generated and confined in a boiler, the pressure upon the boiling water may be several times greater than that of the atmosphere. Experimentally it has been found, that if the pressure in the boiler be 25 lbs. on the square inch, the temperature of the boiling water, and of the steam likewise, is raised to 241 deg.; while under the exhausted receiver of an air-pump, water will boil at 185 deg., when the pressure is reduced to 17 inches of mercury.
=92. Relation between the Boiling-Point and Elevation.=--Now, as the atmospheric pressure is diminished by ascent, as shown by the fall of mercury in the barometer, it follows that in elevated localities water, or any other fluid, heated in the open air, will boil at a temperature lower than at the sea-level. Therefore, there must be some relation between the height of a hill, or mountain, and the temperature at which a fluid will boil at that height. Hence, the thermometer, as used to determine the boiling-point of fluids, is also an indicator of the atmospheric pressure; and may be used as a substitute for the barometer in measuring elevations.
If the atmospheric pressure were constant at the sea-level, and always the same for definite heights, we might expect the boiling-points of fluids also to be in exact accordance with height; and the relation once ascertained, we could readily, by means of the thermometer and boiling water, determine an unknown height, or for a known elevation assert the boiling temperature of a liquid. However, as the atmospheric pressure is perpetually varying at the same place, within certain limits, so there are, as it were, sympathetic changes in the boiling temperatures of fluids. It follows from this, that heights can never be accurately measured, either by the barometer or the boiling-point thermometer, by simply observing at the places whose elevations are required. To determine a height with any approach to accuracy, it is necessary that a similar observation should be made at the same time at a lower station, not very remote laterally from the upper, and that they should be many times repeated. When such observations have been very carefully conducted, the height of the upper station above the lower may be ascertained with great precision, as has been repeatedly verified by subsequent trigonometrical measurement of elevations so determined. If the lower station be at the sea-level, of course the absolute height of the upper is at once obtained.
=93. Mountain Thermometer; sometimes called Hypsometric Apparatus.=--We have now to examine the construction of the boiling-point thermometer, and its necessary appendages, as adapted for the determination of heights.
Messrs. Negretti and Zambra's arrangement of the instrument is shown in figures 72 and 73.
The thermometer is made with an elongated bulb, so as to be as sensitive as possible. The scale, about a foot long, is graduated on the stem, and ranges from 180 deg. to 214 deg., each degree being sufficiently large to show the divisions of tenths of a degree. A sliding metallic vernier might perhaps with advantage be attached to the stem, which would enable the observer to mark hundredths of a degree; which, however, he can pretty well do by estimation. The boiler is so contrived as to allow, not only the bulb, but the stem also of the thermometer, to be surrounded by the steam. The arrangement is readily understood by reference to the accompanying diagram, fig. 73.
_C_, is a copper boiler, supported by a tripod stand so as to allow a spirit-lamp, _A_, made of metal to be placed underneath. The flame from the lamp may be surrounded by a fine wire gauze, _B_, which will prevent it being extinguished when experimenting in the external air. _E E E_, is a three-drawn telescope tube, proceeding from the boiler, and open also at top. Another tube, similarly constructed, envelops this, as shown by _D D D_. This tube is screwed to the top of the boiler, and has two openings, one at the top to admit the thermometer, the other low down, _G_, to give vent to the steam. As the steam is generated, it rises in the inner tube, passes down between the tubes, and flows away at _G_. The thermometer is passed down, supported by an india-rubber washer, fitting steam tight, so as to leave the top of the mercury, when the boiling-point is attained, sufficiently visible to make the observation. The telescopic movement, and the mode of supporting the thermometer, enable the observer always to keep the bulb near the water, and the double tube gives all the protection required to obtain a steady boiling-point. Some boiling-point thermometers are constructed with their scales altogether exposed to the air, which may be very cold, and consequently may contract to some extent the thread of mercury outside the boiler. The steam, having the same temperature as the boiling water, keeps the tube, throughout nearly its whole length, at the same degree of heat, in the apparatus described. The whole can be packed in a tin case very compactly and securely for travelling, as in fig. 72.
_Directions for Using._--When the apparatus is required for practical use, sufficient water must be poured into the boiler to fill it about one third, through an opening, _F_, which must be afterwards closed by the screw plug. Then apply the lighted lamp. In a short time steam will issue from _G_; and the mercury in the thermometer, kept carefully immersed, will rise rapidly until it attains a stationary point, which is the boiling temperature. The observation should now be taken and recorded with as much accuracy as possible, and the temperature of the external air must be noted at the same time by an ordinary thermometer.
The water employed should be pure. Distilled water would therefore be the best. If a substance is held mechanically suspended in water, it will not affect the boiling-point. Thus, muddy water would serve equally as well as distilled water. However, as it cannot be readily ascertained that nothing is dissolved chemically when water is dirty, we are only correct when we employ pure water.
=94. Precautions to ensure correct Graduation.=--Those who possess a boiling-point thermometer should satisfy themselves that it has been correctly graduated. To do this, it is advisable to verify it with the reading of a standard barometer reduced to 32 deg. F. The table of "Vapour Tension" (given at p. 62) will furnish the means of comparison. Thus, if the reduced reading of the barometer, corrected also for latitude, be 29.922, the thermometer should show 212 deg. as the boiling-point of water at the same time and place; if 29.745, the thermometer should read 211.7; and so on as per table. In this way the error of the chief point of the scale can be obtained. Other parts of the scale may be checked with a standard thermometer, by subjecting both to the same temperature, and comparing their indications. The graduations as fixed by some makers are not always to be trusted; and this essential test should be conducted with the utmost nicety and care.
Admiral FitzRoy writes, in his _Notes on Meteorology_:--"Each degree of the boiling-point thermometer is equivalent to about 550 _feet of ascent_, or one-tenth to 55 feet; therefore, the smallest error in the graduation of the thermometer itself will affect the height deduced materially.
"In the thermometer which is graduated from 212 deg. (the boiling-point) to 180 deg., similarly to those intended for the purpose of measuring heights, there must have been a starting point, or zero, from which to begin the graduation. I have asked an optician in London how he fixed that zero, the boiling-point. 'By boiling water at my house,' he replied. 'Where is your house?' In such a part of the town, he answered. I said: 'What height is it above the sea?' to which he replied, 'I do not know;' and when I asked the state of the barometer when he boiled the water, whether the mercury was high or low, he said that he had not looked at it! Now, as this instrument is intended to measure heights and to decide differences of some hundred, if not thousand feet upwards, at least one should endeavour to ascertain a reliable starting point. From inquiries made, I believe that the determination of the boiling-point of ordinary thermometers has been very vague, not only from the extreme difficulties of the process itself (which are well known to opticians), but from the radical errors of not allowing for the pressure of the atmosphere at the time of graduation--which may be much, even an inch higher or lower, than the mean, or any _given height_--while the elevation of the place above the level of the sea is also unnoticed. Then there is another source of error, a minor one, perhaps: the inner limit, the 180 deg. point, is fixed only by comparison with another thermometer; it may be right, or it may be very much out, as may be the intermediate divisions; for the difficulty of ascertaining degree by degree is great: and it must be remembered that the measurement of a very high mountain depends upon those inner degrees from 200 deg. down to 180 deg., thereabouts. Hence, the difficulty of making a reliable observation by boiling water seems to be greater than has been generally admitted."
=95. Method of Calculating Heights from Observations with the Mountain Thermometer.=--Having considered how to make observations with the proper care and accuracy, it becomes necessary to know how to deduce the height by calculation. That a constant intimate relation exists between the boiling temperature of water and the pressure of the air, we have already learned. This knowledge is the result of elaborate experiments made by several scientific experimentalists, who have likewise constructed formulae and tables for the conversion of the boiling temperatures into the corresponding pressures of vapour, or, which is equivalent, of the atmosphere, when the operation is performed in the open air. As might be expected, there is not a perfect accord in the results arrived at by different persons. Regnault is the most recent, and his experiments are considered the most reliable.
From Regnault's table of vapour tension, we can obtain the pressure in inches of mercury at 32 deg., which corresponds to the observed boiling-point; or _vice versa_, if required. From the pressure, the height may be deduced by the method for finding heights by means of the barometer.
The following table expresses very nearly the elevation in feet corresponding to a fall of 1 deg. in the temperature of boiling water:--
Boiling Temperatures Elevation in Feet between. for each Degree.
214 deg. and 210-- 520 210 and 200-- 530 200 and 190 550 190 and 180 570
These numbers agree very well with the results of theory and actual observation. The assumption is that the boiling-point will be diminished 1 deg. for each 520 feet of ascent until the temperature becomes 210 deg., then 530 feet of elevation will lower it one degree until the water boils at 200 deg., and so on; the air being at 32 deg.
Let _H_ represent the vertical height in feet between two stations; _B_ and _b_, the boiling-points of water at the lower and upper stations respectively; _f_, the factor found in the above table. Then
_H_ = _f_(_B_ - _b_)
Further, let _m_ be the mean temperature of the stratum of air between the stations. Now, if the mean temperature is less than 32 deg., the column of air will be shorter; and if greater, longer than at 32 deg. According to Regnault, air expands 1/491.13 or .002036 of its volume at 32 deg., for each degree increase of heat. Calling the correction due to the mean temperature of air _C_, its value will be found from the equation,
_C_ = _H_ (_m_ - 32) .002036
Calling the corrected height _H'_, it will be found from the formula,
_H'_ = _H_ + _H_ (_m_ - 32) .002036 that is, _H'_ = _H_ { 1 + (_m_ - 32) .002036 }
and substituting the value of _H_,
_H'_ = _f_(_B_ - _b_) { 1 + (_m_ - 32) .002036 }
Strictly, according to theoretical considerations, there is a correction due to latitude, as in the determination of heights by the barometer; but its value is so small that it is practically of no importance.
If a barometer be observed at one of the stations, the table of vapour tensions (p. 62) will be useful in converting the pressure into the corresponding boiling-point, or _vice versa_; so that the difference of height may be found either by the methods employed for the boiling-point thermometer or the barometer.
In conclusion, it may be remarked that observers who have good instruments at considerable elevations, as sites on mountains or plateaus, would confer a benefit to science, by registering for a length of time the barometer along with the boiling temperature of water, as accurately as possible. Such observations would serve to verify the accuracy of theoretical deductions, and fix with certainty the theoretical scale with the barometer indications.
_Example, in calculating Heights from the Observations of the Boiling-point of Water._--1. At Geneva the observed boiling-point of water was 209 deg.335; on the Great St. Bernard it was 197 deg.64; the mean temperature of the intermediate air was 63 deg.5; required the height of the Great St. Bernard above Geneva.
Method by formula:--
_H'_ = _f_ (_B_ - _b_) { 1 + (_m_ - 32 deg.) .002036 }
In this case _f_ is between 530 and 550, or 540.
_B_ = 209.335 _m_ = 63.5 _b_ = 197.64 32 ------- ----- 11.695 31.5 _f_ = 540 .002036 ------- --------- 6315.3 0.0641340 1.064 1 ------- ----- _H'_ = 6719.5 feet. 1.064 ======
Method by Tables supplied with boiling-point apparatus made by Messrs. Negretti and Zambra:--
209.335 gives 1464 in Table I. 197.64 " 7736 " ---- 6272 63.5 " 1.07 in Table II. ---- Height 6711 ====
=96. Thermometers for Engineers.=--_1st. Salinometer._--Under the circumstances at which fresh water boils at 212 deg., sea water boils at 213 deg.2. The boiling temperature is raised by the chemical solution of any substance in the water, and the more with the increase of matter dissolved.
From a knowledge of this principle, marine engineers make use of the thermometer to determine the amount of salts held in solution by the water in the boilers of sea-going steamers. Common sea-water contains 1/33 of its volume of salt and other earthy matters. As evaporation proceeds, the solution becomes proportionally stronger, and more heat is required to produce steam. The following table from the work of Messrs. Main and Brown, on the Marine Steam-Engine, shows the relation between the boiling-point under the mean pressure of the atmosphere, or 80 inches of mercury, and the proportion of matter dissolved in the water:--
Proportion of Salt in 100 parts of water 0 Boiling-point 212 deg. " " 1/33 " 213.2 " " 2/33 " 214.4 " " 3/33 " 215.5 " " 4/33 " 216.6 " " 5/33 " 217.9 " " 6/33 " 219.0 " " 7/33 " 220.2 " " 8/33 " 221.4 " " 9/33 " 222.5 " " 10/33 " 223.7 " " 11/33 " 224.9 " " 12/33 " 226.0
When the salts in solution amount to 12/33, the water is saturated. It has also been ascertained that, when a solution of 4/33 is attained, incrustation of the substances commences on the boiler. Hence, it is a rule with engineers to expel some of the boiling water, when the thermometer indicates a temperature of 216 deg., and introduce some more cold water, in order to prevent incrustation, which not only injures the boiler, but opposes the passage of heat to the water. The thermometer used for this purpose should be very accurately graduated, and the scale must be considerably higher than, though it need not read much below 212 deg.
_2nd. Pressure Gauge._--The elasticity of gases augments by increase of temperature, and _vice versa_; it follows, therefore, that when steam is generated in a closed boiler, its temperature rises beyond the boiling temperature of 212 deg., owing to the increased pressure upon the water. The law connecting the pressure and the corresponding temperature of steam is the same as that upon which the boiling of fluids under diminished atmospheric pressure takes place. Hence, the indications of the thermometer become exponents of steam pressure. Engineers are furnished, in works on the steam-engine, with tables, from which the pressure corresponding to a given temperature, or the converse, can be obtained by mere inspection.
Fig. 74 represents the thermometer employed as a steam-pressure gauge. It is fitted in a brass case, with screw-plug and washers for closing the boiler when the thermometer is not in use. The scale shows the pressure corresponding to the temperature, from 15 to 120 lbs., above the atmospheric pressure, which is usually taken as 15 lbs. on the square inch.