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.
[Illustration: Fig. 72.]
[Illustration: Fig. 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.
[Illustration: Fig. 74.]
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.