Part 24

CALORESCENCE (from the Lat. _calor_, heat), a term invented by John Tyndall to describe an optical phenomenon, the essential feature of which is the conversion of rays belonging to the dark infra-red portion of the spectrum into the more refrangible visible rays, i.e. heat rays into rays of light. Such a transformation had not previously been observed, although the converse phenomenon, i.e. the conversion of short waves of light into longer or less refrangible waves, had been shown by Sir G.G. Stokes to occur in fluorescent bodies. Tyndall's experiments, however, were carried out on quite different lines, and have nothing to do with fluorescence (q.v.). His method was to sift out the long dark waves which are associated with the short visible waves constituting the light of the sun or of the electric arc and to concentrate the former to a focus. If the eye was placed at the focus, no sensation of light was observed, although small pieces of charcoal or blackened platinum foil were immediately raised to incandescence, thus giving rise to visible rays.

The experiment is more easily carried out with the electric light than with sunlight, as the former contains a smaller proportion of visible rays. According to Tyndall, 90% of the radiation from the electric arc is non-luminous. The arc being struck in the usual way between two carbons, a concave mirror, placed close behind it, caused a large part of the radiation to be directed through an aperture in the camera and concentrated to a focus outside. In front of the aperture were placed a plate of transparent rock-salt, and a flat cell of thin glass containing a solution of iodine in carbon bisulphide. Both rock-salt and carbon bisulphide are extremely transparent to the luminous and also to the infra-red rays The iodine in the solution, however, has the property of absorbing the luminous rays, while transmitting the infra-red rays copiously, so that in sufficient thicknesses the solution appears nearly black. Owing to the inflammable nature of carbon bisulphide, the plate of rock-salt was found to be hardly a sufficient protection, and Tyndall surrounded the iodine cell with an annular vessel through which cold water was made to flow. Any small body which was a good absorber of dark rays was rapidly heated to redness when placed at the focus. Platinized platinum (platinum foil upon which a thin film of platinum had been deposited electrolytically) and charcoal were rendered incandescent, black paper and matches immediately inflamed, ordinary brown paper pierced and burned, while thin white blotting-paper, owing to its transparency to the invisible rays, was scarcely tinged. A simpler arrangement, also employed by Tyndall, is to cause the rays to be reflected outwards parallel to one another, and to concentrate them by means of a small flask, containing the iodine solution and used as a lens, placed some distance from the camera. The rock-salt and cold water circulation can then be dispensed with.

Since the rays used by Tyndall in these experiments are similar to those emitted by a heated body which is not hot enough to be luminous, it might be thought that the radiation, say from a hot kettle, could be concentrated to a focus and employed to render a small body luminous. It would, however, be impossible by such means to raise the receiving body to a higher temperature than the source of radiation. For it is easy to see that if, by means of lenses of rock-salt or mirrors, we focused all or nearly all the rays from a small surface on to another surface of equal area, this would not raise the temperature of the second surface above that of the first; and we could not obtain a greater concentration of rays from a large heated surface, since we could not have all parts of the surface simultaneously in focus. The desired result could be obtained if it were possible, by reflection or otherwise, to cause two different rays to unite without loss and pursue a common path. Such a result must be regarded as impossible of attainment, as it would imply the possibility of heat passing from one body to another at a higher temperature, contrary to the second law of thermodynamics (q.v.). Tyndall used the dark rays from a luminous source, which are emitted in a highly concentrated form, so that it was possible to obtain a high temperature, which was, however, much lower than that of the source.

A full account of Tyndall's experiments will be found in his _Heat, a Mode of Motion_. (J. R. C.)

CALORIMETRY, the scientific name for the measurement of quantities of heat (Lat. _calor_), to be distinguished from thermometry, which signifies the measurement of temperature. A calorimeter is any piece of apparatus in which heat is measured. This distinction of meaning is purely a matter of convention, but it is very rigidly observed. Quantities of heat may be measured indirectly in a variety of ways in terms of the different effects of heat on material substances. The most important of these effects are (_a_) rise of temperature, (_b_) change of state, (_c_) transformation of energy.

§ 1. The rise of temperature of a body, when heat is imparted to it, is found to be in general nearly proportional to the quantity of heat added. The _thermal capacity_ of a body is measured by the quantity of heat required to raise its temperature one degree, and is necessarily proportional to the mass of the body for bodies of the same substance under similar conditions. The _specific heat_ of a substance is sometimes defined as the thermal capacity of unit mass, but more often as the ratio of the thermal capacity of unit mass of the substance to that of unit mass of water at some standard temperature. The two definitions are identical, provided that the thermal capacity of unit mass of water, at a standard temperature, is taken as the unit of heat. But the specific heat of water is often stated in terms of other units. In any case it is necessary to specify the temperature, and sometimes also the pressure, since the specific heat of a substance generally depends to some extent on the external conditions. The methods of measurement, founded on rise of temperature, may be classed as _thermometric methods,_ since they depend on the observation of change of temperature with a thermometer. The most familiar of these are the method of mixture and the method of cooling.

§ 2. The _Method of Mixture_ consists in imparting the quantity of heat to be measured to a known mass of water, or some other standard substance, contained in a vessel or calorimeter of known thermal capacity, and in observing the rise of temperature produced, from which data the quantity of heat may be found as explained in all elementary text-books. This method is the most generally convenient and most readily applicable of calorimetric methods, but it is not always the most accurate, for various reasons. Some heat is generally lost in transferring the heated body to the calorimeter; this loss may be minimized by performing the transference rapidly, but it cannot be accurately calculated or eliminated. Some heat is lost when the calorimeter is raised above the temperature of its enclosure, and before the final temperature is reached. This can be roughly estimated by observing the rate of change of temperature before and after the experiment, and assuming that the loss of heat is directly proportional to the duration of the experiment and to the average excess of temperature. It can be minimized by making the mixing as rapid as possible, and by using a large calorimeter, so that the excess of temperature is always small. The latter method was generally adopted by J.P. Joule, but the rise of temperature is then difficult to measure with accuracy, since it is necessarily reduced in nearly the same proportion as the correction. There is, however, the advantage that the correction is rendered much less uncertain by this procedure, since the assumption that the loss of heat is proportional to the temperature-excess is only true for small differences of temperature. Rumford proposed to eliminate this correction by starting with the initial temperature of the calorimeter as much below that of its enclosure as the final temperature was expected to be above the same limit. This method has been very generally recommended, but it is really bad, because, although it diminishes the absolute magnitude of the correction, it greatly increases the uncertainty of it and therefore the probable error of the result. The coefficient of heating of a calorimeter when it is below the temperature of its surroundings is seldom, if ever, the same as the coefficient of cooling at the higher temperature, since the convection currents, which do most of the heating or cooling, are rarely symmetrical in the two cases, and moreover, the duration of the two stages is seldom the same. In any case, it is desirable to diminish the loss of heat as much as possible by polishing the exterior of the calorimeter to diminish radiation, and by suspending it by non-conducting supports, inside a polished case, to protect it from draughts. It is also very important to keep the surrounding conditions as constant as possible throughout the experiment. This may be secured by using a large water-bath to surround the apparatus, but in experiments of long duration it is necessary to use an accurate temperature regulator. The method of lagging the calorimeter with cotton-wool or other non-conductors, which is often recommended, diminishes the loss of heat considerably, but renders it very uncertain and variable, and should never be used in work of precision. The bad conductors take so long to reach a steady state that the rate of loss of heat at any moment depends on the past history more than on the temperature of the calorimeter at the moment. A more serious objection to the use of lagging of this kind is the danger of its absorbing moisture. The least trace of damp in the lagging, or of moisture condensed on the surface of the calorimeter, may produce serious loss of heat by evaporation. This is another objection to Rumford's method of cooling the calorimeter below the surrounding temperature before starting. Among minor difficulties of the method may be mentioned the uncertainty of the thermal capacity of the calorimeter and stirrer, and of the immersed portion of the thermometer. This is generally calculated by assuming values for the specific heats of the materials obtained by experiment between 100° C. and 20° C. Since the specific heats of most metals increase rapidly with rise of temperature, the values so obtained are generally too high. It is best to make this correction as small as possible by using a large calorimeter, so that the mass of water is large in proportion to that of metal. Analogous difficulties arise in the application of other calorimetric methods. The accuracy of the work in each case depends principally on the skill and ingenuity of the experimentalist in devising methods of eliminating the various sources of error. The form of apparatus usually adopted for the method of mixtures is that of Regnault with slight modifications, and figures and descriptions are given in all the text-books. Among special methods which have been subsequently developed there are two which deserve mention as differing in principle from the common type. These are (1) the constant temperature method, (2) the continuous flow method.

[Illustration: FIG. 1.]

The _constant temperature method of mixtures_ was proposed by N. Hesehus (_Jour. Phys._, 1888, vii. p. 489). Cold water at a known temperature is added to the calorimeter, immediately after dropping in the heated substance, at such a rate as to keep the temperature of the calorimeter constant, thus eliminating the corrections for the water equivalent of the calorimeter and the external loss of heat. The calorimeter is surrounded by an air-jacket connected to a petroleum gauge which indicates any small change of temperature in the calorimeter, and enables the manipulator to adjust the supply of cold water to compensate it. The apparatus as arranged by F.A. Waterman is shown in fig. 1 (_Physical Review,_ 1896, iv. p. 161). A is the calorimetric tube, B the air-jacket and L the gauge. H is an electric heater for raising the body to a suitable temperature, which can swing into place directly over the calorimeter. W is a conical can containing water cooled by ice I nearly to 0°, which is swung over the calorimeter as soon as the hot body has been introduced and the heater removed. The cold water flow is regulated by a tap S with a long handle O, and its temperature is taken by a delicate thermometer with its bulb at G. The method is interesting, but the manipulations and observations involved are more troublesome than with the ordinary type of calorimeter, and it may be doubted whether any advantage is gained in accuracy.

[Illustration: Fig. 2.]

The _continuous flow method_ is specially applicable to the important case of calorific value of gaseous fuel, where a large quantity of heat is continuously generated at a nearly uniform rate by combustion. Fig. 2 illustrates a recent type of gas calorimeter devised by C.V. Boys (_Proc. R.S.,_ 1906, A. 77, p. 122). The heated products of combustion from the burner B impinge on a metal box H, through which water is circulating, and then pass downwards and outwards through a spiral cooler which reduces them practically to the atmospheric temperature. A steady stream of water enters the apparatus by the inflow thermometer O, flows through the spiral coolers N and M, and finally through the box H, where it is well mixed before passing the outflow thermometer P. As soon as a steady state is reached, the difference of temperature between the outflow and inflow thermometers, multiplied by the current of water in grammes per minute gives the heat per minute supplied by combustion. The gas current is simultaneously observed by a suitable meter, which, with subsidiary corrections for pressure, temperature, &c., gives the necessary data for deducing calorific value.

A continuous flow calorimeter has been used by the writer for measuring quantities of heat conveyed by conduction (see CONDUCTION OF HEAT), and also for determining the variation of the specific heat of water. In the latter case two steady currents of water at different temperatures, say 0° and 100° are passed through an equalizer, and the resulting temperature measured without mixing the currents, which are then separately determined by weighing. This is a very good method of comparing the mean specific heats over two ranges of temperature such as 0-50, and 50-100, or 0-20 and 20-40, but it is not so suitable as the electric method described below for obtaining the actual specific heat at any point of the range.

§ 3. _Method of Cooling._--A common example of this method is the determination of the specific heat of a liquid by filling a small calorimeter with the liquid, raising it to a convenient temperature, and then setting it to cool in an enclosure at a steady temperature, and observing the time taken to fall through a given range when the conditions have become fairly steady. The same calorimeter is afterwards filled with a known liquid, such as water, and the time of cooling is observed through the same range of temperature, in the same enclosure, under the same conditions. The ratio of the times of cooling is equal to the ratio of the thermal capacities of the calorimeter and its contents in the two cases. The advantage of the method is that there is no transference or mixture; the defect is that the whole measurement depends on the assumption that the rate of loss of heat is the same in the two cases, and that any variation in the conditions, or uncertainty in the rate of loss, produces its full effect in the result, whereas in the previous case it would only affect a small correction. Other sources of uncertainty are, that the rate of loss of heat generally depends to some extent on the rate of fall of temperature, and that it is difficult to take accurate observations on a rapidly falling thermometer. As the method is usually practised, the calorimeter is made very small, and the surface is highly polished to diminish radiation. It is better to use a fairly large calorimeter to diminish the rate of cooling and the uncertainty of the correction for the water equivalent. The surface of the calorimeter and the enclosure should be permanently blackened so as to increase the loss of heat by radiation as much as possible, as compared with the losses by convection and conduction, which are less regular. For accurate work it is essential that the liquid in the calorimeter should be continuously stirred, and also in the enclosure, the lid of which must be water-jacketed, and kept at the same steady temperature as the sides. When all these precautions are taken, the method loses most of the simplicity which is its chief advantage. It cannot be satisfactorily applied to the case of solids or powders, and is much less generally useful than the method of mixture.

§ 4. _Method of Fusion._--The methods depending on change of state are theoretically the simplest, since they do not necessarily involve any reference to thermometry, and the corrections for external loss of heat and for the thermal capacity of the containing vessels can be completely eliminated. They nevertheless present peculiar difficulties and limitations, which render their practical application more troublesome and more uncertain than is usually supposed. They depend on the experimental fact that the quantity of heat required to produce a given change of state (e.g. to convert one gramme of ice at 0° C. into water at 0° C., or one gramme of water at 100° C. into steam at 100° C.) is always the same, and that there need be no change of temperature during the process. The difficulties arise in connexion with the determination of the quantities of ice melted or steam condensed, and in measuring the latent heat of fusion or vaporization in terms of other units for the comparison of observations. The earlier forms of ice-calorimeter, those of Black, and of Laplace and Lavoisier, were useless for work of precision, on account of the impossibility of accurately estimating the quantity of water left adhering to the ice in each case. This difficulty was overcome by the invention of the Bunsen calorimeter, in which the quantity of ice melted is measured by observing the diminution of volume, but the successful employment of this instrument requires considerable skill in manipulation. The sheath of ice surrounding the bulb must be sufficiently continuous to prevent escape of heat, but it must not be so solid as to produce risk of strain. The ideal condition is difficult to secure. In the practical use of the instrument it is not necessary to know both the latent heat of fusion of ice and the change of volume which occurs on melting; it is sufficient to determine the change of volume per calorie, or the quantity of mercury which is drawn into the bulb of the apparatus per unit of heat added. This can be determined by a direct calibration, by inserting a known quantity of water at a known temperature and observing the contraction, or weighing the mercury drawn into the apparatus. In order to be independent of the accuracy of the thermometer employed for observing the initial temperature of the water introduced, it has been usual to employ water at 100° C., adopting as unit of heat the "mean calorie," which is one-hundredth part of the heat given up by one gramme of water in cooling from 100° to 0° C. The weight of mercury corresponding to the mean calorie has been determined with considerable care by a number of observers well skilled in the use of the instrument. The following are some of their results:--Bunsen, 15.41 mgm.; Velten, 15.47 mgm.; Zakrevski, 15.57 mgm.; Staub, 15.26 mgm. The explanation of these discrepancies in the fundamental constant is not at all clear, but they may be taken as an illustration of the difficulties of manipulation attending the use of this instrument, to which reference has already been made. It is not possible to deduce a more satisfactory value from the latent heat and the change of density, because these constants are very difficult to determine. The following are some of the values deduced by well-known experimentalists for the latent heat of fusion:--Regnault, 79.06 to 79.24 calories, corrected by Person to 79.43; Person, 79.99 calories; Hess, 80.34 calories; Bunsen, 80.025 calories. Regnault, Person and Hess employed the method of mixture which is probably the most accurate for the purpose. Person and Hess avoided the error of water sticking to the ice by using dry ice at various temperatures below 0° C., and determining the specific heat of ice as well as the latent heat of fusion. These discrepancies might, no doubt, be partly explained by differences in the units employed, which are somewhat uncertain, as the specific heat of water changes rapidly in the neighbourhood of 0° C; but making all due allowance for this, it remains evident that the method of ice-calorimetry, in spite of its theoretical simplicity, presents grave difficulties in its practical application.

One of the chief difficulties in the practical use of the Bunsen calorimeter is the continued and often irregular movement of the mercury column due to slight differences of temperature, or pressure between the ice in the calorimeter and the ice bath in which it is immersed. C.V. Boys (_Phil. Mag._, 1887, vol. 24, p. 214) showed that these effects could be very greatly reduced by surrounding the calorimeter with an outer tube, so that the ice inside was separated from the ice outside by an air space which greatly reduces the free passage of heat. The present writer has found that very good results may be obtained by enclosing the calorimeter in a vacuum jacket (as illustrated in fig. 3), which practically eliminates conduction and convection. If the vacuum jacket is silvered inside, radiation also is reduced to such an extent that, if the vacuum is really good, the external ice bath may be dispensed with for the majority of purposes. If the inner bulb is filled with mercury instead of water and ice, the same arrangement answers admirably as a Favre and Silbermann calorimeter, for measuring small quantities of heat by the expansion of the mercury.

[Illustration: Fig. 3.]

The question has been raised by E.L. Nichols (_Phys. Rev._ vol. 8, January 1899) whether there may not be different modifications of ice with different densities, and different values of the latent heat of fusion. He found for natural pond-ice a density 0.9179 and for artificial ice 0.9161. J. Vincent (_Phil. Trans._ A. 198, p. 463) also found a density .9160 for artificial ice, which is probably very nearly correct. If such variations of density exist, they may introduce some uncertainty in the absolute values of results obtained with the ice calorimeter, and may account for some of the discrepancies above enumerated.