RADIATION PYROMETERS
=General Principles.=—It is a common experience that the heat
radiated by a substance increases as its temperature rises; and it
would obviously be an advantage if the temperature of a hot body could
be deduced from the intensity of its radiations, as the measurement
could then be made from a distance, without the necessity of placing a
pyrometer in contact with the heated substance. At temperatures above
1000° C., when difficulties are experienced either with the metals
or protecting sheaths of thermo-electric or resistance pyrometers,
the advantage gained would become more conspicuous as the temperature
increased. A brief survey of our knowledge of the relations between
radiant energy and temperature will indicate how this desired end may
be achieved.
Any substance at a temperature above absolute zero (-273° C.) radiates
energy to its surroundings by means of ether waves. Below 400° C. these
waves produce no impression on the retina of the eye, and the radiating
body is therefore invisible in a dark room. Above 400° C., however, a
proportion of visible waves are emitted; and as the temperature rises
the effect on the retina is enhanced, and the body increases in
brightness. The difference between the non-luminous and luminous waves
is merely one of wave-length, the shorter wave-lengths being visible
to the eye; and both represent radiant energy. In addition to giving
out radiant energy, a substance receives waves from its surroundings,
which it absorbs in greater or less degree, and which when absorbed
tend to raise the temperature of the receiving substance. A number of
objects in a room, all at the same temperature, are therefore radiating
energy to one another, and equality of temperature is established when
each object receives from its surroundings an amount of energy equal
to that which it radiates. A hot substance radiates more energy than
a cold one; thus if a hot iron ball be hung in a room it will radiate
more energy to its surroundings than it receives from them, and will
therefore cool until the outgoing energy is balanced by the incoming,
when its temperature will be equal to that of the other objects in the
room.
The rate at which a substance emits or takes up radiant energy depends
upon the nature of its surface. A rough, black surface, such as may
be obtained by holding an object in the smoke from burning camphor,
radiates and absorbs heat with greater freedom than any other; whilst
a polished, metallic surface, which acts as a reflector, is worst of
all in these respects. Even a surface of finely divided soot, however,
does not completely absorb all the radiations which fall upon it, but
exhibits a small degree of reflection. An “absolute black surface,” if
such could be found, would be totally devoid of reflecting power, and
would absorb all the radiant energy incident upon it; and conversely
would radiate all energy reaching it from its under side, without
reflecting any back, or allowing any to pass through in the manner that
light waves are transmitted through a transparent substance. No such
perfect surface is known; but, as Kirchoff showed, it is possible to
make a radiating arrangement which will give the same numerical result
for the energy radiated as would be obtained by a perfect surface at
the same temperature. Such an arrangement is termed a “black body,” and
radiations from it are designated “black-body radiations.”
[Illustration: FIG. 42.—BLACK-BODY RADIATIONS.]
Any enclosure, if opaque to radiant energy, and kept at a constant
temperature, constitutes a black body, and radiations received from the
interior through a small opening in the side are black-body radiations.
Fig. 42 represents such an enclosure; in which, to show the application
to pyrometry, a body A is indicated opposite to an opening in the side,
through which radiations escape from the surface of A. If this surface
were “perfect,” all the waves falling upon it would be completely
absorbed and completely radiated; but to prevent change of temperature
the energy radiated must balance the energy received. If, on the other
hand, the surface of A were a polished metal, the waves falling upon
it from the sides of the enclosure would in the main be reflected; but
here again the energy leaving the surface must equal the amount
received if the temperature be constant. It follows, therefore, that if
no alteration in temperature occur, the energy leaving the surface of A
is independent of the nature of that surface; and the amount escaping
through the opening will therefore be the same, whatever be the
character of the surface opposite the opening. With a good radiating
surface the rays from the enclosure will first be absorbed and then
radiated through the opening; in the case of a poor radiating surface,
the rays will be directly reflected through the opening; the total
energy escaping being the same in either case. It will be seen later
that radiation pyrometers are based upon black-body radiations; and it
is important to note that the arrangement under discussion is realised
in a furnace at a constant temperature, in which A might represent
an object such as a block of steel. It happens, therefore, that the
condition of perfect radiation is attained by the appliances in
everyday use; and, moreover, black-body radiations can always be
secured by placing a tube, closed at one end, in the heated space,
and receiving the radiations through the open end; for this again
represents an enclosure at a constant temperature. Similarly,
radiations from a solid in the interior of the tube of the electric
furnace shown in fig. 29 will be of the same description, and we can
therefore apply with accuracy any instrument based upon black-body
radiations, knowing that the same may be readily realised in practice.
The law connecting the energy radiated by a substance, under given
conditions, with its temperature, was variously stated by different
observers until Stefan, in 1879, deduced the true relation from certain
experimental data obtained by Tyndall. Stefan concluded that the
figures given by Tyndall indicated that the energy radiated by a given
solid varied as the fourth power of its absolute temperature. Numerous
experiments, under different conditions, showed that the fourth-power
law did not apply to all kinds of surfaces or circumstances; but a
strong confirmation of its truth when applied to black-body radiations
was forthcoming in 1884, when Boltzmann showed, from thermodynamic
considerations, that the quantity of energy radiated in a given time
from a perfect radiator must vary as the fourth power of its absolute
thermodynamic temperature. Certain assumptions made by Boltzmann in
this investigation were subsequently justified by experiment; and
numerous tests under black-body conditions have since amply verified
the law. It is upon the Stefan-Boltzmann law that radiation pyrometers
are based; the energy received by radiation from the heated substance,
under black-body conditions, being measured by the instrument, and
translated into corresponding temperatures on its scale.
Expressed in symbols, the fourth-power law takes the form—
E = K(T_{1}^4 - T_{2}^4),
where E is the total energy radiated; T_{1} the absolute temperature
of the black body; T_{2} the absolute temperature of the receiving
substance, and K a constant depending upon the units chosen. If E be
expressed as watts per square centimetre, the value of K is 5·6 ×
10^{-12}; if in calories per square centimetre per second, the value is
1·34 × 10^{-12}. The introduction of the temperature of the receiving
substance, T_{2}, is rendered necessary by the fact, previously cited,
that energy will be radiated back to the hot body, and the net loss
of energy will evidently be the difference between that which leaves
it and that which returns to it from the receiving substance. If
T_{2} were absolute zero, the energy leaving the black body would be
KT_{1}^4; whereas if T_{2} were equal to T_{1}, the loss of energy
would be nil, as a substance cannot cool by radiation to a lower
temperature than its surroundings. The temperatures T_{1} and T_{2}
refer to the thermodynamic scale (page 9), but as the gas scale is
practically identical, Centigrade degrees may be used, measured from
absolute zero, or -273°. An example is appended to illustrate the
application of the law:—
_Example._—To compare the energy radiated through an opening
in the side of a furnace at temperatures of 527°, 727°,
and 927° C. respectively, to surroundings at 27° C.
The quantities will be as
K(800^4 - 300^4) : K(1000^4 - 300^4) : K(1200^4 - 300^4).
since 273 must be added to each temperature to convert
into absolute degrees. Dividing each by K, and expanding
in each case, the ratio becomes
(4096 - 81) × 10^8 : (10000 - 81) × 10^8 : (20736 - 81) × 10^8.
Dividing each by 10^8 and subtracting, the result is
4015 : 9919 : 20655, or 1 : 2·47 : 5·12.
It will be noted in the above example that the effect of the
surrounding temperature, taken as 27° C., is small in quantity,
and becomes proportionately less as the temperature of the furnace
increases. If T_{2} had been ignored in the calculation, the amounts of
energy radiated would have appeared as
1 : 2·44 : 5·06.
It will be seen later, that in calculating the temperature scale of a
radiation pyrometer, the temperature of the surroundings is for this
reason not taken into account. Fig. 43 is a graphic illustration of the
fourth-power law.
[Illustration: FIG. 43.—ENERGY RADIATED BY A BLACK BODY AT
DIFFERENT TEMPERATURES.]
When the relation between temperature and quantity of energy radiated
is known, any instrument which will indicate the amount of the
radiations it receives may be used to measure temperatures. The ray,
for example, may be focused on a thermal junction, which will be heated
in proportion to the amount of energy incident upon it, and when
connected to a millivoltmeter will cause deflections proportional to
the energy it receives. A thin strip of metal might be used in place
of a junction, and by measuring its resistance the heating effect
of the radiations, and hence the amount thereof, may be deduced. A
third method would be to focus the rays on to a compound strip of two
metals, which by altering in shape could be made to furnish a clue to
the quantity of energy received by it. In theory, it is only necessary
to allow the radiations to fall on the working part of any instrument
for measuring low temperatures, when the rise in temperature produced
may be taken as proportional to the energy received, and the thermal
condition of the radiating body deduced from the fourth-power law.
In practice, however, it is desirable that the receiving thermometer
should be small in size; of low thermal capacity, so as to respond
rapidly; and capable of giving a sensitive indication—hence an
ordinary mercury thermometer would be unsuitable for this purpose. A
thermopile, placed at a fixed distance, would fail owing to the cold
junctions gradually warming up by conduction through the pile. The
part receiving the radiations should be coated with lamp-black, so
that practically all the waves impinging upon it, whether luminous or
non-luminous, may be absorbed, and the energy they represent utilised
in producing a rise in temperature.
=Practical Forms of Radiation Pyrometers: Féry’s Instruments.=—In
the year 1902 Féry introduced a pyrometer in which the rays were
focused by the aid of a lens upon a small, blackened thermal
junction, in the same way that the rays of the sun may be focused
by a burning-lens. The junction was connected to a special form of
d’Arsonval galvanometer, which recorded the E.M.F. developed. By taking
the readings of the galvanometer as proportional to the temperature of
the junction—that is, to the radiant energy impinging upon it—the
temperature of the source could be calculated from the fourth-power
law. The drawback to the use of this instrument was the fact that a
proportion of the rays was absorbed by the glass, this proportion,
moreover, varying at different temperatures, so that the fourth-power
law could not be applied with accuracy. By using a fluorspar lens in
place of glass, this error was overcome, but the cost of a good lens
of this material being high, its use in ordinary workshop practice
was rendered prohibitive on account of the price. A number of these
pyrometers, furnished with glass lenses, and calibrated by comparison
with a standard possessing a fluorspar lens, were placed on the market,
but were superseded in 1904, when Féry hit upon the plan of focusing
the rays by means of a concave mirror, thus overcoming the error due to
absorption by the glass lens. This plan, which serves admirably, has
since been adopted in most radiation pyrometers.
=Féry’s Mirror Pyrometer.=—This instrument is shown in
longitudinal and also in cross section in fig. 44. A concave mirror, M,
which has a gilt reflecting surface, is placed at one end of a metal
tube, and is fastened to a rack which engages in a pinion moved by
the milled-head, P, so that on turning P, a longitudinal movement is
imparted to the mirror. A small, blackened thermal junction, shown at
the centre of the cross section, and consisting of a copper disc to
which wires of copper or iron and constantan are fastened, receives the
rays after reflection, and may be brought into focus by suitably moving
the mirror.
[Illustration: FIG. 44.—FÉRY’S MIRROR PYROMETER. SECTION.]
[Illustration: FIG. 45.—FÉRY’S MIRROR PYROMETER. END VIEW.]
The wires pass to terminals _b_ and _b´_ on the outside of the tube,
from which leads are taken to the indicator. In order to discover
when the junction is in the focus of the mirror, an eye-piece, O, is
fitted in the end of the tube, which enables the junction to be seen,
magnified, through a hole in the centre of M. By means of an optical
device placed near the junction, the image of the sighted object,
produced by M, is reflected in two portions to the eye-piece O. When
the junction is exactly in the focus of M, a circular image is seen
round the junction; when out of focus, the appearance presented is
that of two semi-circles not coinciding laterally. The adjustment
consists in moving the mirror until the separate semi-circles produce a
continuous circle; a method at once simple and definite. The front end
of the pyrometer is shown in fig. 45, in which it will be seen that the
entrance may be partially closed by a diaphragm, or left entirely open,
as required. The diaphragm is used to cut off a definite proportion of
the radiations, and is used for very high temperatures, at which, with
full aperture, the indicator needle would be urged beyond the limits
of the scale. On the indicator two separate temperature scales are
provided, one referring to full, and the other to partial aperture.
The same end might be achieved by inserting a suitable resistance in
series with the indicator: but in this case the junction might be
unduly heated, and possibly damaged thereby. The proportions of the
pyrometer are such that at the highest temperatures measured the heat
incident on the junction never raises it above 110° C. Although the
intensity of radiations diminishes as the square of the distance, the
quantity impinging on the junction is, within limits, independent of
the distance: This arises from the property of concave mirrors with
respect to the relation between the size of an image and the distance
of the object producing it. If _r_ = the radius of the mirror, _u_
the distance of the object, and _v_ the distance of the image, both
measured from the centre of the mirror, the relation 1/_u_ + 1/_v_ =
2/_r_ holds for a concave mirror, and when two of these are known the
third may be calculated. Further, if _d_ be the linear dimension of
an object, and _d_{1}_ that of its image, the relation _d_/_d_{1}_
= _u_/_v_ also holds, and from these two expressions all the points
arising in connection with the Féry pyrometer may be determined, as
will best be made clear by examples.
_Example I._—To find the position of the image of an object
formed by a mirror of 6 inches radius, with object at
distance (_a_) 10 feet, (b) 20 feet.
Reducing to inches, and applying in the formula
1 1 2 1 1 1
────── + ────── = ─────── , ──── + ─────── = ───
_u_ _v_ _r_ 120 _v_ 3
and
1 1 1
─── + ───── = ───
240 _v_ 3
from which the values of _v_ are 3-1/13 inches and 3-1/26
inches respectively, a difference of only 1/26 of an inch.
If _u_ were 6 inches, _v_ would also be 6 inches; if u
were infinity, _v_ would be 3 inches. The movement of
the image, when an object is brought towards it from a
great distance, would in the mirror under notice be from
3 inches away to 6 inches away, and at distances of 10
feet and upwards would only differ in position by small
fractions of an inch.
_Example II._—To find the area of the image of a circular
opening, 1 foot in diameter, formed by a mirror of 6
inches radius distant from the opening (_a_) 10 feet;
(_b_) 20 feet.
Since _d_ _u_
──────── = ───── ; then, from the results of
_d_{1}_ _v_
Example 12 120
──────── = ──────── at 10 feet distance,
_d_{1}_ (3-1/13)
and 12 240
─────── = ──────── at 20 feet.
_d_{1}_ (3-1/26)
Hence the linear dimensions, _i.e._ the diameters of
the circular images, will be 0·308 and 0·152 inch
respectively; and the areas 0·074 and 0·0182 square inch.
These areas are to each other practically as 4 : 1.
That is, the area of the image decreases in size directly
as the _square_ of the distance of the object; the squares
of the distances being 100 and 400, or as 1 : 4; whereas
the areas of the images are as 4 : 1.
_Example III._—To find, for a 6-inch mirror, and a junction
of 1/10th of an inch in diameter, the greatest distance
at which the mirror may be placed from an opening 1 foot
in diameter, so as to give an image not less than the
junction.
From Example I it is evident that at any distance
exceeding 20 feet the position of the image will only be
a minute and negligible fraction over 3 inches; hence _v_
may be taken as 3.
Applying values in the formula _d_ _u_
─────── = ───── and
_d_{1}_ _v_
taking _d_{1}_ as equal to the diameter of the junction,
= 0·1 inch,
12 _u_
─── = ──── , and _u_ = 360 inches, or 30 feet.
0·1 3
Beyond this distance the image would be less than the junction. The
conclusions to be drawn from the foregoing examples are: (1) that the
amount of energy received by the junction does not vary, provided the
image overlaps it; and (2) that the limiting distance at which a
correct reading can be secured is that at which the size of the image
is equal to that of the junction. Thus, taking distances of 10 and 20
feet, as in Example II; at the former distance the energy striking
the mirror is four times as great as with the latter; but, on the
other hand, the area of the image at 10 feet distance is four times
as great as that obtained at 20 feet. Hence, at the greater distance,
the proportion of the image impinging on the junction is four times as
great, and the fact that only ¼ the amount of energy strikes the mirror
is thus counterbalanced. All the reflected rays which fail to strike
the junction are ineffective, and pass out through the entrance of the
tube.
[Illustration: FIG. 46.—FÉRY’S SPIRAL.]
The two-scale form of instrument described above is extremely useful
for general purposes, but when all the temperatures to be controlled
fall within the limit of one of the scales, it is simpler and cheaper
to dispense with the diaphragm, and to use an indicator furnished with
one scale only. The single-scale mirror pyrometer is for this reason
more generally employed for industrial purposes; and the Cambridge and
Paul Instrument Company now make a pivoted indicator for use with full
aperture, which is less liable to damage than one which possesses a
suspended coil.
[Illustration: FIG. 47.—FÉRY’S SPIRAL PYROMETER. SECTION.]
=Féry’s “Spiral” Radiation Pyrometer.=—This instrument differs
from the preceding merely in the fact that the rays are focused on a
small spiral, formed of a compound strip of two metals, fixed at one
end and furnished with a pointer at the free-moving end (fig. 46). The
effect of alterations of temperature on this spiral are to cause it to
coil up or uncoil, according to whether the temperature rises or falls.
This movement is magnified by the pointer, the end of which moves over
a dial graduated to read temperatures directly. This arrangement is
shown in section in fig. 47, where C is the mirror, E the eye-piece, S
the spiral, P the pointer, and D the dial, viewed through the window W.
The appearance of the apparatus when viewed from the front is shown
in fig. 48. The advantage gained by the use of the spiral is that the
instrument is self-contained, no galvanometer being necessary; but, on
the other hand, the indications are not so exact, an error of 20° C.
being probable at temperatures over 1000° C. In using this pyrometer,
it is observed that after focusing the hot substance, the pointer moves
rapidly for a time and then pauses, after which it again commences to
creep along the scale. The temperature indicated at the moment the
pause occurs is generally taken as the reading, but this is not always
correct.
[Illustration: FIG. 48.—FÉRY’S SPIRAL PYROMETER. FRONT VIEW.]
The creeping movement is probably due to the whole instrument, and
the air in the interior, becoming heated by the entering rays, and by
proximity to the hot source. In a number of trials made by the author,
it was noticed that when the instrument was allowed to stand near the
furnace for some time before using, thereby attaining the temperature
existing in the vicinity, the “creep” almost entirely vanished. All
things considered, the spiral form of Féry’s pyrometer must be regarded
as more portable but less accurate than that in which the rays are
received on a thermal junction.
=Foster’s Fixed-Focus Radiation Pyrometer.=—The necessity for
focusing, common to all Féry’s radiation pyrometers, is obviated in
Foster’s pyrometer, which, however, cannot be used from so great a
distance. The principle involved in the fixed-focus pyrometer is that
the amount of energy received by a concave mirror and focused on a
thermal junction will not vary so long as the area of the surface
sending rays to the mirror, through a fixed opening, increases as the
square of the distance. This will be understood from fig. 49, in which
C is the mirror, D a thermal junction fixed so as to be in the focus of
the opening E F, and A B the heated surface. The lines joining E and
F to the edge of the mirror intersect in a point G, and provided the
lines G E and G F, if produced, fall within the heated surface A B,
the quantity of energy falling on D will always be the same. A cross
section of the cone G A B is a circle; and if A B be twice as far
away from G as E F, the areas of the circles of which A B and E F are
diameters will be in the ratio 4: 1. But as A B is twice as far from
G as E F, the intensity of its radiations will be as 1: 4; and hence
loss of radiating power is exactly balanced by increase in area.
[Illustration: FIG. 49.—PRINCIPLE OF FOSTER’S FIXED-FOCUS PYROMETER.]
In the actual instrument the tube in which the mirror is placed is
blackened internally, so that no rays reach the mirror by reflection
from it. The diameters of the opening E F and the mirror C are such
that the perpendicular from G on to A B is ten times the length of A
B. Hence, if the heated object be 6 inches in diameter, the limiting
distance of G is 10 × 6 = 60 inches. The position of the point G
is indicated by a ring on the outside of the tube, and in taking a
measurement the tube is brought well within the distance prescribed,
which is in all cases ten times the diameter of the heated object.
Temperatures are read from a galvanometer connected to the thermal
junction, the whole arrangement being portable, as shown in figs. 50
and 51, which represent the instrument in use.
[Illustration: FIG. 50.—FOSTER’S PYROMETER, MOUNTED ON STAND.]
The advantages derived from the use of a fixed focus instrument are
simplicity and cheapness; but, as many occasions arise in practice
in which focusing on an object is a necessity, Foster’s pyrometer
must be regarded as a simplified apparatus not capable of the wider
applications of Féry’s instruments, but of great service in many cases.
Whipple has recently adapted the Féry spiral pyrometer to produce
an instrument with a fixed focus, by fastening the instrument to a
fireclay tube, on the closed end of which the pyrometer is permanently
focused. This form is specially useful for determining the temperature
of molten metals, into which the end of the fireclay tube is plunged,
thus giving true black-body conditions.
[Illustration: FIG. 51.—FOSTER’S PYROMETER, IN USE.]
=Paul’s Radiation Pyrometer.=—Thwing, in America, has introduced
a radiation pyrometer in which the rays from the furnace enter the wide
end of a cone, and by internal reflection are brought to the apex,
at which a thermal junction is located. Paul, in this country, has
marketed a similar instrument, the action of which is shown in fig. 52,
where E is a tube containing a polished cone, C, at the apex of which
is fixed a thermal junction, T. Rays from the hot source A A´ enter the
tube at D, and pass into the cone, being finally reflected on to T,
which is connected to the indicator. So long as the lines joining the
outside of the cone with the extremities of the entrance D, crossing at
O, fall within the hot source, A A´, the reading will be the same at
all distances. Fig. 53 shows the actual pyrometer, mounted on a tripod.
[Illustration: FIG. 52.—PRINCIPLE OF PAUL’S RADIATION PYROMETER.]
=Indicators for Radiation Pyrometers.=—When the radiations are
focused on a thermal junction, the temperature of which is raised
in consequence, the E.M.F. developed is in accordance with the laws
discussed in Chapter II, and any thermo-electric indicator, if
sufficiently sensitive, will serve for the purposes of a radiation
pyrometer. The effect on the galvanometer is influenced by: (1) the
nature of the junction; (2) the size of the mirror or cone; and (3)
the highest temperature attained by the junction. The indicators used
in connection with radiation pyrometers are of the pivoted type, which
can now be made sufficiently sensitive to give full-scale deflection
for a rise of 100° C. in the temperature of the junction. For the
junction itself, Heil’s alloy (zinc and antimony in atomic proportions)
partnered with constantan has been used, owing to the high E.M.F.
developed; but cases of deterioration of this alloy have been noted,
causing it to be replaced by some makers by iron. Two iron or copper
constantan junctions in series give an E.M.F. for a rise of 100° C.,
sufficient to work a pivoted indicator, and are preferable to Heil’s
couple for a radiation pyrometer.
[Illustration: FIG. 53.—PAUL’S RADIATION PYROMETER.]
=Calibration of Indicators for Radiation Pyrometers.=—The
deflections on the indicators are due to the E.M.F. generated, which is
proportional to the difference in temperature between the hot and cold
junctions. If both these are at the same temperature—say, 20° C.—the
deflection is zero; and on allowing the radiations to fall on the hot
junction its temperature is raised by an amount depending upon the
intensity of the radiations—say, to 90° C. The deflection produced is
then due to a difference of (90-20) = 70°, the radiations having raised
the temperature of the hot junction 70° above its surroundings. If the
surroundings (including the cold junction or junctions) had been at
15° to commence with, the hot junction under the same conditions would
have risen to 85°, giving again a difference of 70°, and thus causing
the same deflection as before. Provided both hot and cold junctions are
located so as to attain the same atmospheric temperature in the absence
of radiations, a given quantity of energy impinging on the hot junction
will always produce in it the same _excess_ temperature, and will
therefore give rise to the same deflection at all ordinary atmospheric
temperatures. As the junctions are so arranged in radiation pyrometers
as to fulfill this condition, no correction for fluctuations in the
cold junctions is necessary. The deflections, therefore, correspond to
excess temperatures of the hot junction, which in turn are directly
proportional to the energy received by the junction. Readings in
millivolts on the indicator thus represent directly the proportions
of energy received by the hot junction, 4 millivolts corresponding to
twice the energy, which produces 2 millivolts, and so on; and hence the
millivolt scale becomes an energy scale.
In order to translate energy into corresponding temperatures, the
fourth-power law must be applied. If E_{1} correspond to an absolute
temperature T_{1} on the part of the black body from which radiations
are received, and E_{2} correspond to another temperature T_{2}, the
following relations will hold good:
E_{1} = K(T_{1}^4 - _x^4_), and E_{2} = K(T_{2}^4 - _x^4_),
where _x_ is the temperature of the surroundings receiving the
radiations. As previously pointed out (see Example on page 140), the
term _x^4_ may be ignored for the range of high temperatures measured
by a radiation pyrometer, hence E_{1} = KT_{1}^4, and E_{2} = KT_{2}^4;
and therefore E_{1}/E_{2} = T_{1}^4/T_{2}^4. But, as shown above,
readings in millivolts on the indicator are directly proportional to
the energy received, and if R_{1} and R_{2} = millivolts due to E_{1}
and E_{2}, the relation R_{1}/R_{2} = T_{1}^4/T_{2}^4 is then obtained.
In order to prepare a temperature scale from this relation, it is
necessary to take one correct reading at a known temperature, after
which the remainder of the scale may be marked by calculation, as shown
in the example appended:—
_Example._—A tube closed at one end is at 927° C. (1200°
abs.), and gives a deflection corresponding to 2
millivolts on the indicator. To find the temperatures
which would yield deflections due to 1, 3, 4, and 5
millivolts.
Taking the case of 1 millivolt and applying in the formula
R_{1} T_{1}^4 2 1200^4
───── = ───────, ─── = ─────── ;
R_{2} T_{2}^4 1 T_{2}^4
1200^4
from which T_{2}^4 = ────── and T_{2} = 1009° abs.
2
= 736° C. Similarly, 3 millivolts represent 1055° C.;
4 millivolts = 1154° C.; and 5 millivolts = 1236° C. These
values are readily obtained by the use of four-figure
logarithms.
Having calculated the temperature corresponding to each whole
millivolt, a curve may be plotted to represent millivolts against
corresponding temperatures, and intermediate values deduced from it.
Evidently, the standard reading must be taken with great accuracy,
as the whole scale hinges upon it; and for this purpose an accurate
resistance or thermo-electric pyrometer may be used, placed inside
the tube of an electric furnace, and the radiation pyrometer sighted
on a thin sheet of iron placed just in front of the naked junction. A
check at the higher readings of the scale is necessary, as an exact
realisation of the fourth-power law is seldom obtained in practice.
This may be taken in the same manner, as thermocouples may now be
calibrated directly against the gas scale up to 1550° C., thus enabling
the gas-scale reading to be transferred to the radiation pyrometer.
For delicate readings over a given range, the scale of a mirror
galvanometer may be calibrated in this manner, sufficient resistance
having first been added in series to ensure that at the highest
temperature employed the spot of light will remain on the scale.
[Illustration: FIG. 54.—RECORD OBTAINED WITH RADIATION PYROMETER.]
=Recorders for Radiation Pyrometers.=—Any of the thermo-electric
recorders described in Chapter II may be applied to radiation
pyrometers, the chart being suitably divided according to the
fourth-power law. When taking a record, the pyrometer is fixed on a
stand or bracket and focused on the desired spot. Fig. 54 is an example
of a record taken with a Thread recorder and Féry pyrometer, in which
the division of the temperature scale according to the fourth-power law
will be noticed. It is possible to arrange that the working temperature
shall lie on the open part of the scale, by adjusting the sensitiveness
of the galvanometer accordingly before calibrating.
=Management of Radiation Pyrometers.=—It is not advisable to
place a radiation pyrometer in the hands of an unskilled observer, as
intelligent oversight is required if good results are to be secured.
Care must be taken to adjust the galvanometer needle to zero before
taking a reading, and the needle should always be locked during
transit. When focusing on an object in a furnace it is necessary to
make certain that the red image seen is actually that of the object,
which may be done by moving the pyrometer until the side of the
object, or some special feature, is visible in the eye-piece, when
the pyrometer may be moved until the image surrounds the junction.
Occasions may arise, as in taking the temperatures of various zones
of a rotary cement-kiln or other furnace, in which it is required to
focus the mirror for a specified distance; in which case the author
has adopted the plan of placing a fixed pointer opposite the milled
head which controls the mirror (P, fig. 44) and focusing the bars of
a window at measured distances, marking the same on the milled head
opposite the pointer; and it would be a convenience if all radiation
pyrometers were thus marked initially. A good check to correct
focusing in the case of a heated object is to alter the focus in both
directions, and finally to adjust to the maximum reading, which should
correspond to the true focus.
Great care should be taken not to damage the mirror. If, in a workshop,
the surface become covered with dirt, this should be removed by gentle
brushing with a camel-hair brush or by blowing air over the mirror. The
focusing device should never be strained beyond its working limits;
when these are reached, the pyrometer should be moved bodily until the
object can be correctly sighted within the ordinary limits of the
movement of the milled head. If metallic fumes or dense smoke intervene
between the furnace and the pyrometer, the radiations will be impeded
and the temperature recorded will be too low; and in such cases the
pyrometer should be placed at the open end of a tube and sighted upon
the closed end, which should terminate at the spot under observation.
In all cases it must be borne in mind that the indications only apply
to black-body conditions. If a block of steel be sighted inside a
furnace, and then be removed to the exterior and again sighted,
the external reading will be much less than the internal, owing to
the inferior radiating power of the surface, which now derives no
assistance from the furnace. All readings should therefore be taken
whilst the object is still in the furnace, or (as in taking the
temperature of molten metal in a ladle) a fireclay tube with a closed
end inserted in the mass may be used, and readings taken through the
open end. Statements are sometimes made that the difference between
external readings and black-body readings is constant for a given
surface, and that the one may be translated into the other; but this is
true only for unchanging surfaces, such as platinum, and seldom applies
to ordinary working surfaces. As black-body conditions are so easy to
ensure, it is simpler and safer always to arrange to take observations
under such conditions, rather than to trust a relation seldom constant
in practice.
When using a radiation pyrometer for a number of furnaces, fireclay
tubes, closed at one end, may be inserted in each, so that the closed
end terminates at the working spot, the open end being left flush
with the exterior of the furnace. The diameter of such tubes will
depend upon the length and also upon the make of the pyrometer; in all
cases the image of the closed end must be large enough to overlap the
receiving junction or spiral. Information on this point can always be
obtained from the makers, or can be discovered by trial with openings
of known diameter. When using the pyrometer to obtain temperatures
in the interior of the tube of an electric furnace, such as that
illustrated in fig. 29, a solid object, such as a short fireclay
cylinder, or a piece of graphite, should be placed in the middle of the
tube, and focused on the junction.
=Special Uses of Radiation Pyrometers.=—For regular use at
temperatures above 1000° C. or 1850° F. the radiation pyrometer will
be found to be more useful than instruments of the thermo-electric
or resistance type as the latter undergo deterioration owing to the
continuous action of the furnace gases, which becomes more marked
as the temperature increases. Examples of industrial processes in
which 1000° C. is considerably exceeded are the manufacture of glass,
pottery, and cement, the treatment of special steels, and the casting
of metals and alloys. Even for temperatures between 750° and 1000° C.
a radiation pyrometer may be used, but is not so convenient for this
range as a thermo-electric instrument. There is no upper limit to the
instrument, which may be calibrated by the fourth-power law to the
highest temperature attainable, that of the electric arc, which has
been found to be 3720° C. by the use of a Féry radiation pyrometer.
Measurements may therefore be made beyond the limits of thermal
junctions, such as the temperature of electric furnaces and of thermit
in the mould, and of molten steel before pouring, thus opening out
the possibility of accurate control at extremely high temperatures.
There is always a danger, however, of the cold junction becoming
unduly heated when near to large masses at very high temperatures, and
serious errors may arise from this cause. Two examples may be cited
to illustrate the usefulness of the radiation pyrometer in practice:
(1) the hardening of steel projectiles; and (2) the determination of
the temperature of the clinkering zone in a rotary cement kiln. In
(1) the projectile is brought to a given spot near the brink of the
furnace, where it is in the focus of a radiation pyrometer, and when
at the specified temperature is raked out of the furnace and drops
into an oil-trough. It has been found that a difference of 10° C. from
the standard temperature at which the projectiles should be quenched
may cause a serious lowering of the penetrative power of the finished
projectile; and hence a radiation pyrometer, which may readily be
sighted on each individual shell, is the best to use for this purpose.
In (2) the hottest spot may be found by focusing the pyrometer to
different distances up the kiln, and, by taking a record, any fall in
temperature due to defect of coal or air supplies, or to excessive
feed of raw material, may be detected, thus furnishing information
from which the process may be regulated to the best advantage. At the
temperatures prevailing in such kilns—1300° to 1450° C., or 2370°
to 2640° F., according to the nature of the kiln—a Féry radiation
pyrometer is quite sensitive to changes of 10° C. or 18° F., and the
author has found it to be entirely satisfactory in this connection.
The adaptability of radiation pyrometers to all temperatures above a
red heat, combined with the absence of deterioration, renders these
instruments of great value, and the possibility of obtaining records is
a further recommendation. The radiation method, however, is not suited
to the purposes of an installation, as even if mirrors and junctions
could be constructed so as to be identical, the arrangement would be
very costly. A cheap adaptation of the radiation principle, by means
of which a number of furnaces, such as a set of cement-kilns, could be
controlled from a centre, would be of great advantage, and would add
further to the general utility of this class of pyrometer.