CALORIMETRIC PYROMETERS
=General Principles.=—If a piece of hot metal, of known weight
and specific heat, be dropped into a known weight of water at a
temperature _t_{1}_, which rises to _t_{2}_ in consequence, the
temperature of the hot metal, _t_{0}_, can be obtained by calculation,
as shown by the following example:—
_Example._—A piece of metal weighing 100 grams, and of
specific heat 0·1, is heated in a furnace and dropped
into 475 grams of water, contained in a vessel which
has a capacity for heat equal to 25 grams of water. The
temperature of the water rises from 5° to 25° C. To find
the temperature of the furnace.
The heat lost by the metal is equal to that gained by the
water and vessel. Equating these,
100 × 0·1 × (_t_{0}_ - 25) = (475 + 25) × (25 - 5)
from which _t_{0}_ = 1025° C.
The above calculation, which applies generally to this method, depends
for its accuracy upon a correct knowledge of the specific heat of the
metal used. This value is far from constant, increasing as the
temperature rises, and the result will only be correct when the average
value over a given range is known.
The metal used in the experiment should not oxidise readily, and should
possess a high melting point. Platinum is most suitable, but the cost
of a piece sufficiently large would considerably exceed that of a
thermo-electric or other outfit. Nickel is next best in these respects,
and is now generally used for the calorimetric method, up to 1000° C.
The specific heat varies to some extent in different specimens, but
can be determined for the ranges involved in practical use. This may
be done by heating a given weight to known temperatures and plunging
into water, the result being obtained as in the foregoing example,
_t_{0}_ in this case being known and the specific heat calculated. From
a series of such determinations, a curve may be plotted connecting
specific heat and temperature range, from which intermediate values may
be read off.
[Illustration: FIG. 65.—SPECIFIC HEAT OF NICKEL OVER RANGES FROM 0° C.]
Regnault, who first suggested the calorimetric method for high
temperature measurement, attempted to measure the specific heat of iron
over different ranges, with a view to using this metal in the process.
Owing to the absence of reliable means of determining the experimental
temperatures, however, Regnault’s values were considerably in error.
For the range 0 to 1000° C. he gave the average specific heat of iron
as 0·126, a figure much below the truth. Thus, if a piece of iron
be heated to 970° C., as measured by the thermo-electric method,
and dropped into water, the temperature calculated from an assumed
specific heat of 0·126 will be found to be 1210°, or 240° too high. The
values now employed are obtained by experiments with a thermo-electric
pyrometer, so that temperatures deduced by the calorimetric method
agree, within the limits of manipulative error, with those of the
standard scale. The accompanying curve, fig. 65, shows the average
specific heat of nickel over all ranges between 0° and 1000° C., and
from this curve the correct figure to use in the calculation for any
range may be determined. Thus for a furnace between 800° and 900° C.
the specific heat would be taken as 0·136; and although the choice
of the value to be taken involves a knowledge of the temperature
within 100°, no difficulty arises in practice, as it is easy to judge
this limit by experience at temperatures below 1000° C In the most
approved forms of calorimetric pyrometers for industrial purposes
the temperature of the hot metal may be read directly from a scale,
prepared in accordance with the value applying to the specific heat at
various ranges.
Copper and iron are still used to a limited extent in these pyrometers,
but lose continuously in weight by oxidation, the scales of oxide
falling off when quenched, necessitating weighing before each test
to ensure accuracy. Nickel oxidises very little below 1000 C., and
as the thin film of oxide which forms does not readily peel off, the
weight may increase slightly. Quartz would probably be more suitable
than metals, not being altered by heating and quenching, but does not
appear to have been tried for this purpose. Another possible material
is nichrom, which resists oxidation below 1000° C. The weight of the
solid should be at least 1/20 of that of the water, in order to ensure
a tangible rise in temperature, and the thermometer should be capable
of detecting 1/20 of a degree C. The rise in temperature should not be
so great as to cause the water to exceed the atmosphere in temperature
by more than 4° or 5° C., as otherwise radiation losses would have a
marked effect. The limits of accuracy of the method will be shown by
reference to examples.
_Example I._—A piece of nickel, weighing 100 grams, is
placed in a furnace, and after heating dropped into 2000
grams of water at 10° C., contained in a vessel of water
equivalent 50 grams. The temperature rises to 16·25° C.
The specific heat of nickel for the range is 0·137. To
find the temperature of the furnace and the limits of
accuracy, the thermometer being readable to 1/20° C.
Equating heat lost by the nickel to that gained by the
water and vessel:—
100 × 0·137 × (_x_ - 16·25) = 2050 × (16·25 - 10·0)
from which _x_ = 952° C.
If the error in each thermometer reading amounted to
1/40° the maximum difference in the above calculation is
obtained by introducing the altered values as under:—
100 × 0·137 × (_x_ - 16·225) = 2050 × (16·225 - 10·025)
when _x_ = 944° C.
The maximum error due to a possible incorrect reading of
1/40° is therefore less than 1 per cent.
_Example II._—The loss of heat by radiation in transferring
100 grams of nickel at 927° C., possessing a surface of
30 square centimetres, and with radiating power 0·7 of a
black body, may be shown by the fourth-power law to be 50
calories per second (see page 139). If two seconds were
occupied in the transfer, the error from this cause would
be 1 in 130; and adding this to the thermometric error,
the total is less than 2 per cent.
=Practical Forms of Calorimetric Pyrometers.=—When required
to estimate the temperature of a muffle furnace or other laboratory
appliance, a sheet-copper vessel of about 1500 c.c. capacity may be
used. This should rest on wooden supports in a second similar vessel,
about 2 inches wider, which acts as a shield against radiation. A
cylinder of nickel about 1½ inches long, and 1¼ inches in diameter,
with a hole of ½-inch diameter in the centre, is suitable for test
purposes. This may conveniently be heated in a nickel crucible; and
when transferring to the water the crucible may be grasped with a pair
of tongs, and tilted so as to allow the cylinder to drop into the
water. When used in a tube furnace, a length of thin nickel wire may
be attached to the cylinder to enable withdrawal to be accomplished
rapidly, allowance being made for the weight of the heated wire. The
transfer should be accomplished as speedily as possible, to avoid
radiation errors. The figure to be used to represent the specific heat
of nickel may be obtained from the curve (fig. 65), when the range
to be measured is approximately known. The water equivalent of the
vessel and thermometer should be determined as follows:—Place in the
vessel one-half the quantity of cold water used in the experiment—say
750 c.c.—and note the temperature (_t_{1}_) after stirring with the
thermometer. Then add an equal quantity of water at a temperature
(_t_{2}_) about 10° higher than _t_{1}_ Mix thoroughly with the
thermometer, and note the temperature of the mixture (_t_{3}_). Check
results may be obtained by varying the proportions of cold and warm
water, the total quantity always being equal to that used for quenching
the hot nickel. If W_{1} = the weight of cold water, and W_{2} that of
the warm, the water equivalent (_x_) is obtained from the equation
W_{2} (_t_{2}_ - _t_{3}_) - W_{1}(_t_{3}_ - _t_{1}_)
_x_ = ─────────────────────────────────────────────────────
_t_{3}_ - _t_{1}_.
This figure represents the weight of water equal in thermal capacity to
the vessel, and in a pyrometric measurement is added to the weight of
water taken.
In industrial practice, it is desirable to dispense, if possible, with
the necessity for calculations, so that a reading may be taken by
an unskilled observer. The earliest form of calorimetric pyrometer,
patented by Byström in 1862, consisted of a lagged zinc vessel into
which a piece of platinum was dropped, and a table was provided from
which the temperature of the furnace could be read by noting the rise
in temperature of the water. The modern industrial form, made by Messrs
Siemens, will now be described.
[Illustration: FIG. 66.—SIEMENS’ CALORIMETRIC OR “WATER” PYROMETER.]
=Siemens’ Calorimetric or “Water” Pyrometer.=—Fig. 66 shows
this instrument in longitudinal and transverse section. It consists
of a double copper vessel, the inner containing water, and the outer
provided with a handle. The space between is lagged with felt, to
prevent escape of heat from the water. The thermometer, _b_, is
protected by a perforated brass tube from damage that might be caused
on dropping in the hollow nickel cylinder, _d_. Opposite the stem
of the thermometer is placed a sliding-piece _c_, on which a
temperature scale is marked. In using the instrument, the specified
quantity of water is placed in the inner vessel, and the pointer on _c_
brought opposite to the top of the mercury column in the thermometer.
The nickel cylinder, which has been heated in a crucible or muffle
in the furnace, is then dropped in, and the vessel shaken to secure
an equal temperature throughout the water. When the thermometer is
stationary, the mark on _c_ opposite the top of the mercury gives the
temperature of the furnace, the scale on _c_ having previously been
marked from calculations made for each 50 degrees. The correctness of
the reading evidently depends upon the accuracy with which _c_ has
been calibrated, an operation which involves taking into account the
water equivalent of the vessel and the variation of the specific heat
of nickel at different temperatures. Allowing for the sources of error
attaching to the method, results by this pyrometer cannot be guaranteed
to better than 2 or 3 per cent, at 900° or 1000° C., but in cases
where this degree of inaccuracy is not of importance, the instrument
may be used with advantage. As no calculation is necessary, the
determination may be made in the workshop by any workman who exercises
care in conducting the operation. Copper and iron cylinders are
sometimes supplied instead of nickel, but are not to be recommended,
as they decrease in weight with each test, and necessitate the use
of a multiplying factor to convert the reading on _c_ into the true
temperature.
=Special Uses of Calorimetric Pyrometers.=—The great drawback
to the calorimetric method is that each observation necessitates a
separate experiment, involving time and labour. The accuracy, moreover,
is not comparable with that obtainable by the use of a thermo-electric
or resistance pyrometer; and practically the only recommendation
is the low initial cost of the outfit. When an occasional reading
of temperature, true to 3 per cent., suffices, the calorimetric
pyrometer may be used; and in special laboratory determinations the
method will frequently be found of value. Considering the low cost of
thermo-electric pyrometers at the present time, it is probable that
the calorimetric method will be entirely superseded in industrial
practice, as the former method gives a continuous, automatic reading,
and is capable of furnishing records. Many firms have already replaced
their “water” pyrometers by the more accurate and useful appliances now
available.