CHAPTER VII

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.

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.

=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.