STANDARDS OF TEMPERATURE
=The Absolute or Thermodynamic Scale of Temperatures.=—All
practical instruments for measuring temperatures are based on some
progressive physical change on the part of a substance or substances.
In a mercury thermometer, the alteration in the volume of the liquid
is used as a measure of hotness; and similarly the change in volume
or pressure on the part of a gas, or the variation in resistance to
electricity shown by a metal, and many other physical changes, may be
employed for this purpose. In connection with the measurement of high
temperatures, many different physical principles are relied upon in the
various instruments in use, and it is of the greatest importance that
all should read alike under the same conditions. This result would not
be attained if each instrument were judged by its own performances. In
the case of a mercury thermometer, for example, we may indicate the
amount of expansion between the temperatures of ice and steam at 76
centimetres pressure, representing 100° Centigrade, by _a_; and then
assume that an expansion of 2_a_ will signify a temperature of 200°,
and so on in proportion. Similarly, we may find the increase in
resistance manifested by platinum between the same two fixed points,
and indicate it by _r_, and then assume that an increase of 2_r_ will
correspond to 200°. If now we compare the two instruments, we find
that they do not agree, for on placing both in a space in which the
platinum instrument registered 200°, the mercury thermometer would show
203°. A similar, or even greater, discrepancy would be observed if
other physical changes were relied upon to furnish temperature scales
on these lines, and it is therefore highly desirable that a standard
independent of any physical property of matter should be used. Such a
standard is to be found in the thermodynamic scale of temperatures,
originally suggested by Lord Kelvin. This scale is based upon the
conversion of heat into work in a heat engine, a process which is
independent of the nature of the medium used. A temperature scale
founded on this conversion is therefore not connected with any physical
property of matter, and furnishes a standard of reference to which all
practical appliances for measuring temperatures may be compared.[1]
When readings are expressed in terms of this scale, it is customary to
use the letter K in conjunction with the number: thus 850° K would mean
850 degrees on the thermodynamic scale.
When existing instruments are compared with this standard, it is found
that a scale based on the assumption that the volume of a gas free
to expand, or the pressure of a confined gas, increases directly as
the temperature is in close agreement with the thermodynamic scale.
It may be proved that if the gas employed were “perfect,” a scale in
exact conformity with the standard described would be secured; and
gases which approach nearest in properties to a perfect gas, such
as hydrogen, nitrogen, and air, may therefore be used to produce a
practical standard, the indications of which are nearly identical with
the thermodynamic scale. If any other physical change be chosen, such
as the expansion of a solid, or the increase in resistance of a metal,
and a temperature scale be based on the supposition that the change
in question varies directly as the temperature, the results obtained
would differ considerably from the absolute standard. For this reason
the practical standard of temperature now universally adopted is an
instrument based on the properties of a suitable gas.
=The Constant Volume Gas Thermometer.=—In applying the properties
of a gas to practical temperature measurement, we may devise some
means of determining the increase in volume when the gas is allowed to
expand, or the increase in pressure of a confined gas may be observed.
The latter procedure is more convenient in practice, and the instrument
used for this purpose is known as the constant volume gas thermometer,
one form of which is shown in fig. 1. The gas is enclosed in a bulb B,
connected to a tube bent into a parallel branch, into the bend of which
is sealed a tap C, furnished with a drying cup. The extremity of the
parallel branch is connected to a piece of flexible tubing T, which
communicates with a mercury cistern which may be moved over a scale,
the rod G serving as a guide. In using this instrument the bulb B
is immersed in ice, and the tap C opened. When the temperature has
fallen to 0° C., the mercury is brought to the mark A by adjusting
the cistern, and the tap C then closed. The bulb B is now placed in
the space or medium of which the temperature is to be determined, and
expansion prevented by raising the cistern so as to keep the mercury
at A. When steady, the height of the mercury in the cistern above the
level of A is read off, and furnishes a clue to the temperature of B.
If the coefficient of pressure of the gas used (in this case, air) be
known, the temperature may be calculated from the equation
P_{1} = P_{0}(1 + _bt_),
where P_{1} is the pressure at _t_°; P_{0} the pressure at 0°; and _b_
the coefficient of pressure; that is, the increase in unit pressure
at 0° for a rise in temperature of 1°. Thus if P_{0} = 76 cms.; _b_ =
0·00367; height of mercury in cistern above A = 55·8 cms.; then
P_{1} = (76 + 55·8) = 131·8 cms.,
and by inserting these values in the above equation _t_ is found to be
200°. In the instrument described, P_{0} is equal to the height of the
barometer, since the tap C is open whilst the bulb is immersed in ice.
The coefficient of pressure may be determined by placing the bulb in
steam at a known temperature, and noting the increased pressure. In the
equation given, P_{1}, P_{0}, and _t_ are then known, and the value of
_b_ may be calculated.
[Illustration: FIG. 1.—CONSTANT VOLUME AIR THERMOMETER.]
In using this instrument for exact determinations of temperature,
allowance must be made for the expansion of the bulb, which causes a
lower pressure to be registered than would be noted if the bulb were
non-expansive. Again, the gas in the connecting tube is not at the same
temperature as that in the bulb; an error which may be practically
eliminated by making the bulb large and the bore of the tube small.
The temperature of the mercury column must also be allowed for, as the
density varies with the temperature. When the various corrections have
been made, readings of great accuracy may be secured.
When applied to the measurement of high temperatures, the bulb must
be made of a more infusible material than glass. Gold, porcelain,
platinum, and quartz have been used by different investigators, but
the most reliable material for temperatures exceeding 900° C. has
been found to be an alloy of platinum with 20 per cent. of rhodium.
The most suitable gas to use inside the bulb is nitrogen, which is
chemically inert towards the materials of the bulb, and is not absorbed
by the metals mechanically. When measuring high temperatures with this
instrument, a considerable pressure, amounting to 1 atmosphere for
every increase of 273 degrees above the ice point, is requisite to
prevent expansion of the nitrogen; and this pressure tends to distort
the bulb and so to falsify the indications. This trouble has been
overcome by Day, who surrounded the bulb by a second larger bulb, and
forced air or nitrogen into the intervening space until the pressure
on the exterior of the thermometer bulb was equal to that prevailing
in the interior. Even then it was not found possible to secure higher
readings than 1550° C., as the bulb commenced to alter in shape owing
to the softening of the material. This temperature represents the
highest yet measured on the gas scale; but by using a more refractory
material, such as fused zirconia, it may be found possible to extend
this range to 2000° C. or more. Experiments in this direction are
very desirable, in order that high-reading pyrometers may be checked
directly against the gas scale.
=Fixed Points for Calibration of Pyrometers.=—It is evident
that the gas thermometer is totally unsuited for use in workshops
or laboratories when a rapid determination of a high temperature is
required. Its function is to establish fixed points or temperature
standards, by means of which other instruments, more convenient to
use, may be graduated so as to agree with each other and with the gas
scale itself. The temperature scales of all modern pyrometers are thus
derived, directly or indirectly, from the gas thermometer. In the
table on next page, a number of fixed points, determined by various
observers, is given; the error, even at the highest temperatures,
probably not exceeding ±2° C.
In preparing the temperature scale of a pyrometer for practical
use, the instrument is subjected successively to a number of the
temperatures indicated in the table, and in this manner several fixed
points are established on its scale. The space between these points is
then suitably subdivided to represent intermediate temperatures.
TABLE OF FIXED POINTS.
──────────────────┬────────────────────┬───────┬──────
Substance. │Physical Condition. │ Deg. │ Deg.
│ │ Cent. │ Fahr.
──────────────────┼────────────────────┼───────┼───────
Water (ice) │ At Melting Point │ 0 │ 32
Water │ ” Boiling ” │ 100 │ 212
Aniline │ ” ” ” │ 184 │ 363
Naphthalene │ ” ” ” │ 218 │ 424
Tin │ ” Melting ” │ 232 │ 449
Lead │ ” ” ” │ 327 │ 620
Zinc │ ” ” ” │ 419 │ 786
Sulphur │ ” Boiling ” │ 445 │ 833
Antimony │ ” Melting ” │ 631 │ 1167
Aluminium │ ” ” ” │ 657 │ 1214
Common Salt │ ” ” ” │ 800 │ 1472
Silver (in air) │ ” ” ” │ 955 │ 1751
Silver (free from │ │ │
oxygen) │ ” ” ” │ 962 │ 1763
Gold │ ” ” ” │ 1064 │ 1947
Copper (in air) │ ” ” ” │ 1064 │ 1947
Copper (Graphite │ │ │
covered) │ ” ” ” │ 1084 │ 1983
Iron (pure) │ ” ” ” │ 1520 │ 2768
Palladium │ ” ” ” │ 1549 │ 2820
Platinum │ ” ” ” │ 1755 │ 3190
──────────────────┴────────────────────┴───────┴───────
It is necessary to point out that the figures given in the table refer
only to pure substances, and that relatively small quantities of
impurities may give rise to serious errors. The methods by which the
physical condition to which the temperatures refer may be realised in
practice will be described in the succeeding chapter.
=National Physical Laboratory Scale.=—Exact agreement with regard
to fixed points has not yet been arrived at in different countries, and
an effort to co-ordinate the work of the National Physical Laboratory,
the United States Bureau of Standards, and the Reichsanstalt, with a
view to the formation of an international scale, was interrupted by the
war. In 1916 the National Physical Laboratory adopted a set of fixed
points on the Centigrade thermodynamic scale, in conformity with which
all British pyrometers have since been standardised. It will be seen
that the figures differ very slightly from those given in the previous
table, which represent the average results of separate determinations
in different countries.
NATIONAL PHYSICAL LABORATORY SCALE (1916).
────────────────────┬──────────────────────────┬────────┬──────
Substance. │ Physical Condition. │ Deg. │ Deg.
│ │ Cent. │ Fahr.
────────────────────┼──────────────────────────┼────────┼──────
Water (ice) │ At Melting Point │ 0 │ 32
Water │ ” Boiling ” (760 mm.)│ 100 │ 212
Naphthalene │ ” ” ” ” │ 217·9 │ 424
Benzophenone │ ” ” ” ” │ 305·9 │ 582
Zinc │ ” Melting ” │ 419·4 │ 787
Antimony │ ” ” ” │ 630 │ 1166
Common Salt │ ” ” ” │ 801 │ 1474
Silver (in reducing │ │ │
atmosphere) │ ” ” ” │ 961 │ 1761
Gold │ ” ” ” │ 1063 │ 1945
Copper (in reducing │ │ │
atmosphere) │ ” ” ” │ 1083 │ 1982
────────────────────┴──────────────────────────┴────────┴──────
For higher temperatures the melting points of nickel (1452° C.) and
palladium (1549° C.) are employed, but the accuracy in these cases is
not so certain as with the substances named in the table. A useful
point, intermediate between copper and nickel, has been established
by E. Griffiths, and is obtained by heating nickel with an excess of
graphite, when a well-defined eutectic is formed which freezes at 1330°
C., or 2426° F.
=Temperatures above the Present Limit of the Gas Thermometer.=—As
it is not yet possible to compare an instrument directly with the
gas thermometer above 1550° C., all higher temperatures must be
arrived at by a process of extrapolation. By careful observation of a
physical change at temperatures up to the limit of 1550° C., the law
governing such change may be discovered; and assuming the law to hold
indefinitely, higher temperatures may be deduced by calculation. An
amount of uncertainty always attaches to this procedure, and in the
past some ludicrous figures have been given as the result of indefinite
extrapolation. Wedgwood, for example, by assuming the uniform
contraction of clay, gave 12001° C., or 21637° F., as the melting point
of wrought iron, whereas the correct figure is 1520° C., according
to the gas scale. Even in recent times, the extrapolation of the law
connecting the temperature of a thermal junction with the electromotive
force developed, obtained by comparison with the gas scale up to 1100°
C., led Harker to the conclusion that the melting point of platinum
was 1710° C., a figure 45 degrees lower than that now accepted. The
laws governing the radiation of energy at different temperatures,
however, appear to be capable of mathematical proof from thermodynamic
principles, and temperatures derived from these laws are in reality
expressed on the absolute or thermodynamic scale. Extrapolation of
these laws, when used to deduce temperatures by means of radiation
pyrometers, appears to be justified; but it is still desirable to
extend the gas scale as far as possible to check such instruments.
Assuming the radiation laws to hold, it is possible to determine the
highest temperatures procurable, such as that of the electric arc, with
a reasonable degree of certainty.
[1] For a fuller account of the thermodynamic scale, see the author’s
treatise _Heat for Engineers_, pp. 391-2.