Читать книгу Pyrometry: A Practical Treatise on the Measurement of High Temperatures - Charles R. Darling - Страница 6

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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 2a 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 2r 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

P₁ = P₀(1 + bt),

where P₁ is the pressure at t°; P₀ 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 P₀ = 76 cms.; b = 0·00367; height of mercury in cistern above A = 55·8 cms.; then

P₁ = (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, P₀ 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, P₁, P₀, and t are then known, and the value of b may be calculated.

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	At Melting Point	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.