Online Encyclopedia
Search over 40,000 articles from the original, classic Encyclopedia Britannica, 11th Edition.
TRANSFERENCE OF
Online EncyclopediaEncyclopedia Home :: TOO-TUM
del.icio.us it!
|
TRANSFERENCE OF See also:HEAT 25. Modes of Transference.—There are three See also:principal modes of transference of heat, namely (r) convection, (2) See also:conduction,. and (3) See also:radiation. (r) In convection, heat is carried or conveyed by the See also:motion of heated masses of See also:matter. The most See also:familiar illustrations of this method of transference are the See also:heating of buildings by the circulation of See also:steam or hot See also:water, or the equalization of temperature of a See also:mass of unequally heated liquid or See also:gas by convection currents, produced by natural changes of See also:density or by artificial stirring. (2) In conduction, heat is transferred by contact between contiguous particles of matter and is passed on from one particle to the next without visible relative motion of the parts of the See also:body. A familiar See also:illustration of conduction is the passage of heat through the See also:metal plates of a See also:boiler from the See also:fire to the water inside, or the transference of heat from a soldering See also:bolt to the See also:solder and the metal with which it is placed in contact. (3) In radiation, the heated body gives rise to a motion of vibration in the See also:aether, which is propagated equally in all directions, and is reconverted into heat when it encounters any obstacle capable of absorbing it. Thus radiation differs from conduction and convection in taking See also:place most perfectly in the See also:absence of matter, whereas conduction and convection require material communication between the bodies concerned. In the See also:majority of cases of transference of heat all three modes of transference are simultaneously operative in a greater or less degree, and the combined effect is generally of See also:great complexity. The different modes of transference are subject to widely different See also:laws, and the difficulty of disentangling their effects and subjecting them to calculation is often one of the most serious obstacles in the experimental investigation of heat. In space void of matter, we should have pure radiation, but it is difficult to obtain so perfect a vacuum that the effects of the residual gas in transferring heat by conduction or convection are inappreciable. In the interior of an opaque solid we should have pure conduction, but if the solid is sensibly transparent in thin layers there must also be an See also:internal radiation, while in a liquid or a gas it is very difficult to eliminate the effects of convection. These difficulties are well illustrated in the See also:historical development of the subject by the experimental investigations which have been made to determine the laws of heat-transference, such as the laws of cooling, of radiation and of conduction. 26. See also:Newton's See also:Law of Cooling.—There is one essential See also:condition See also:common to all three modes of heat-transference, namely, that they depend on difference of temperature, that the direction of the See also:transfer of heat is always from hot to See also:cold, and that the See also:rate of transference is, for small See also:differences, directly proportional to the difference of temperature. Without difference of temperature there is no transfer of heat. When two bodies have been brought to the same temperature by conduction, they are also in See also:equilibrium as regards radiation, and See also:vice versa. If this were not the See also:case, there could be no equilibrium of heat defined by equality of temperature. A hot body placed in an enclosure of See also:lower temperature, e.g. a calorimeter in its containing See also:vessel, generally loses heat by all three modes simultaneously in different degrees. The loss by each mode will depend in different ways on the See also:form, extent and nature of its See also:surface and on that of the 2nciosure, on the manner in which it is supported, on its relative position and distance from the enclosure, and on the nature of the intervening See also:medium. But provided that the difference of temperature is small, the rate of loss of heat by all modes will be approximately proportional to the difference of temperature, the other conditions remaining See also:constant. The rate of cooling or the rate of fall of temperature will also be nearly proportional to the rate of loss of heat, if the specific heat of the cooling body is constant, or the rate of cooling at any moment will be proportional to the difference of temperature. This See also:simple relation is commonly known as Newton's law of cooling, but is limited in its application to comparatively simple cases such as the foregoing. Newton himself applied it to estimate the temperature of a red-hot See also:iron See also:ball, by observing the See also:time which it took to cool from a red heat to a known temperature, and comparing this with the time taken to cool through a known range at See also:ordinary temperatures. According to this law if the excess of temperature of the body above its surroundings is observed at equal intervals of time, the observed values will form a geometrical progression with a common ratio. Supposing, for instance, that the surrounding temperature were o° C., that the red-hot ball took 25 minutes to cool from its See also:original temperature to 20° C., and 5 minutes to cool from 20° C. to 10° C., the original temperature is easily calculated on the See also:assumption that the excess of temperature above o° C. falls to See also:half its value in each See also:interval of 5 minutes. Doubling the value 200 at 25 minutes five times, we arrive at 640° C. as the original temperature. No other method of estimation of such temperatures was available in the time of Newton, but, as we now know, the simple law of proportionality
to the temperature difference is inapplicable over such large
ranges of temperature. The rate of loss of heat by radiation,and also by convection and conduction to the surrounding See also:air, increases much more rapidly than in simple proportion to the temperature difference, and the rate of increase of each follows a different law. At a later date See also:Sir See also: 225 and 337), who observed the rate of cooling of a See also:mercury thermometer from 300° C. in a water-jacketed enclosure at various temperatures from 6° C. to 8o° C. In See also:order to obtain the rate of cooling by radiation alone, they exhausted the enclosure as perfectly as possible after the introduction of the thermometer, but with the imperfect appliances available at that time they were not able to obtain a vacuum better than about 3 or 4 mm. of mercury. They found that the velocity of cooling V in a vacuum could be represented by a See also:formula of the type
V=A(aa–a'o) (5)
in which t is the temperature of the thermometer, and to that of the enclosure, a is a constant having the value 1.0075, and the coefficient A depends on the form of the bulb and the nature of its surface. For the ranges of temperature they employed, this formula gives much better results than Newton's, but it must be remembered that the temperatures were expressed on the arbitrary See also:scale of the mercury thermometer, and were not corrected for the large and uncertain errors of See also:stem-exposure (see See also:THERMOMETRY). Moreover, although the effects of cooling by convection currents are practically eliminated by exhausting to 3 or 4 mm. (since the density of the gas is reduced to 1/2ooth while its viscosity is not appreciably affected), the rate of cooling by conduction is not materially diminished, since the conductivity, like the viscosity, is nearly See also:independent of pressure. It has since been shown by Sir See also: (6) They found that the cooling effect of convection, unlike that of radiation, was independent of the nature of the surface of the thermometer, whether silvered or blackened, that it varied as some See also:power c of the pressure p, and that it was independent of the See also:absolute temperature of the enclosure, but varied as the excess temperature (t–to) raised to the power I'233,„ ,This highly artificial result undoubtedly contains some elements of truth, but could only be applied to experiments similar to those from which it was derived. F. Herve de la Provostaye and P. Q. Desains (Ann. Chico. Phys., 1846, 16, p. 337), in repeating these experiments under various conditions, found that the coefficients A and B were to some extent dependent on the temperature, and that the manner in which the cooling effect varied with the pressure depended on the form and See also:size of the enclosure. It is evident that this should be the case, since the cooling effect of the gas depends partly on convective currents. which are necessarily greatly modified by the form of the enclosure in a manner which it would appear hopeless to See also:attempt to represent by any general formula. 28. Surface Emissivity.—The same remark applies to many attempts which have since been made to determine the general value of the constant termed by See also:Fourier and See also:early writers the " exterior conductibility," but now called the surface emissivity. This coefficient represents the rate of loss of heat from a body per unit See also:area of surface per degree excess of temperature, and includes the effects of radiation, convection and conduction. As already pointed out, the combined effect will be nearly proportional to the excess of temperature in any given case provided that the excess is small, but it is not necessarily proportional to the extent of surface exposed except in the case of pure radiation. The rate of loss by convection and conduction varies greatly with the form of the surface, and, unless the enclosure is very large compared with the cooling body, the effect depends also on the size and form of the enclosure. Heat is necessarily communicated from the cooling body to the layer of gas in contact with it by conduction. If the linear dimensions of the body are small, as in the case of a See also:fine See also:wire, or if it is separated from the enclosure by a thin layer of gas, the rate of loss depends chiefly on conduction. For very fine metallic wires heated by an electric current, W. E. See also:Ayrton and H. Kilgour (Phil. Trans., 1892) showed that the rate of loss is nearly independent of the surface, instead of being directly proportional to it. This should be the case, as See also:Porter has shown (Phil. See also:Hag., See also: The effects of conduction and radiation may be approximately estimated if the conductivity of the gas and the nature and forms of the surfaces of the body and enclosure are known, but the effect of convection in any case can be determined only by experiment. It has been found that the rate of cooling by a current of air is approximately proportional to the velocity of the current, other things being equal. It is obvious that this should be the case, but the result cannot generally be applied to convection currents. Values which are commonly given for the surface emissivity must therefore be accepted with great reserve. They can be regarded only as approximate, and as applicable only to cases precisely similar to those for which they were experimentally obtained. There cannot be said to be any general law of convection. The loss of heat is not necessarily proportional.to the area of the surface, and no general value of the coefficient can be given to suit all cases. The laws of conduction and radiation admit of being more precisely formulated, and their effects predicted, except in so far as they are complicated by convection. 29. Conduction of Heat.—The laws of transference of heat in the interior of a solid body formed one of the earliest subjects of mathematical and experimental treatment in the theory of heat. The law assumed by Fourier was of the simplest possible type, but the mathematical application, except in the simplest cases, was so difficult as to require the development of a new mathematical method. Fourier succeeded in showing how, by his method of See also:analysis, the See also:solution of any given problem with regard to the flow of heat by conduction in any material could be obtained in terms of a See also:physical constant, the thermal conductivity of the material, and that the results obtained by experiment agreed in a qualitative manner with those predicted by his theory. But the experimental determination of the actual values of these constants presented formidable difficulties which were not surmounted till a later date The experimental methods and difficulties are discussed in a See also:special See also:article on CONDUCTION OF HEAT. It will suffice here to give a brief historical See also:sketch, including a few of the more important results by way of illustration. 30. Comparison of Conducting See also:Powers.—That the power of transmitting heat by conduction varied widely in different materials was probably known in a general way from prehistoric times. Empirical knowledge of this See also:kind is shown in the construction of many articles for heating, cooking, &c., such as the See also:copper soldering bolt, or the See also:Norwegian cooking-See also:stove. Oneof the earliest experiments for making an actual comparison of conducting powers was that suggested by See also:Franklin, but carried out by See also:Jan Ingenhousz (Journ. de phys., 1789, 34, pp. 68 and 38o). Exactly similar bars of different materials, See also:glass, See also:wood, metal, &c., thinly coated with See also:wax, were fixed in the See also:side of a trough of boiling water so as to project for equal distances through the side of the trough into the See also:external air. The wax coating was observed to melt as the heat travelled along the bars, the distance from the trough to which the wax was melted along each affording an approximate indication of the See also:distribution of temperature. When the temperature of each See also:bar had become stationary the heat which it gained by conduction from the trough must be equal to the heat lost to the surrounding air, and must therefore be approximately proportional to the distance to which the wax had melted along the bar. But the temperature fall per unit length, or the temperature-gradient, in each bar at the point where it emerged from the trough would be inversely proportional to the same distance. For equal temperature-gradients the quantities of heat conducted (or the relative conducting powers of the bars) would therefore be proportional to the squares of the distances to which the wax finally melted on each bar. This was shown by Fourier and Despretz (Ann. chins. phys., 1822, 19, p. 97). 31. See also:Diffusion of Temperature.—It was shown in connexion with this experiment by Sir H. See also:Davy, and the experiment was later popularized by John See also:Tyndall, that the rate at which wax melted along the bar, or the rate of See also:propagation of a given temperature, during the first moments of heating, as distinguished from the melting-distance finally attained, depended on the specific heat as well as the conductivity. See also:Short prisms of iron and See also:bismuth coated with wax were placed on a hot metal See also:plate. The wax was observed to melt first on the bismuth, although its conductivity is less than that of iron. The See also:reason is that its specific heat is less than that of iron in the proportion of 3 to I1. The densities of iron and bismuth being 7.8 and 9.8, the thermal capacities of equal prisms will be in the ratio •86 for iron to •29 for bismuth. If the prisms receive heat at equal rates, the bismuth will reach the temperature of melting wax nearly three times as quickly as the iron. It is often stated on the strength of this experiment that the rate of propagation of a temperature See also:wave, which depends on the ratio of the conductivity to the specific heat per unit See also:volume, is greater in bismuth than in iron (e.g. See also:Preston, Heat, p. 628). This is quite incorrect, because the conductivity of iron is about six times that of bismuth, and the rate of propagation of a temperature wave is therefore twice as great in iron as in bismuth. The experiment in reality is misleading because the rates of reception of heat by the prisms are limited by the very imperfect contact with the hot metal plate, and are not proportional to the respective conductivities. If the iron and bismuth bars are properly faced and soldered to the See also:top of a copper See also:box (in order to ensure See also:good metallic contact, and exclude a non-conducting film of air), and the box is then heated by steam, the rates of reception of heat will be nearly proportional to the conductivities, and the wax will melt nearly twice as fast along the iron as along the bismuth. A bar of See also:lead similarly treated will show a faster rate of propagation than iron, because, although its conductivity is only half that of iron, its specific heat per unit volume is 2.5 times smaller. 32. See also:Bad Conductors. Liquids and Gases.—See also:Count See also:Rumford (1792) compared the conducting powers of substances used in clothing, such as See also:wool and See also:cotton, See also:fur and down, by observing the time which a thermometer took to cool when embedded in a- - globe filled successively with the different materials. The times of cooling observed for a given range varied from 1300 to 900 seconds for different materials. The See also:low conducting power of such materials is principally due to the presence of air in the interstices, which is prevented from forming convection currents by the presence of the fibrous material. Finely powdered See also:silica is a very bad conductor, but in the compact form of See also:rock crystal it is as good a conductor as some of the metals. According to the kinetic theory of gases, the conductivity of a gas depends on molecular diffusion. See also:Maxwell estimated the conductivity of
air at ordinary temperatures at about 2o,000 times less than that of copper. This has been verified experimentally by See also:Kundt and Warburg, Stefan and See also:Winkelmann, by taking special precautions to eliminate the effects of convection currents and radiation. It was for some time doubted whether a gas possessed any true conductivity for heat. The experiment of T. See also:Andrews, repeated by See also: Difficulty of Quantitative Estimation of Heat Transmitted.—The conducting powers of different metals were compared by C. M. Despretz, and later by G. H. See also:Wiedemann and R. See also:Franz, employing an See also:extension of the method of Jan Ingenhousz, in which the temperatures at different points along a bar heated at one end were measured by thermometers or thermocouples let into small holes in the bars, instead of being measured at one point only by means of melting wax. These experiments undoubtedly gave fairly accurate relative values, but did not permit the calculation of the absolute amounts of heat transmitted. This was first obtained by J. D. See also:Forbes (Brit. Assoc. See also:Rep., 1852; Trans. Roy. Soc. Ed., 1862, 23, p. 133) by deducing the amount of heat lost to the surrounding air from a See also:separate experiment in which the rate of cooling of the bar was observed (see CONDUCTIO.i of HEAT). See also:Clement (Ann. chim. phys., 1841) had previously attempted to determine the conductivities of metals by observing the amount of heat transmitted by a plate with one side exposed to steam at See also:ioo° C., and the other side cooled by water at z8° C. Employing a copper plate 3 mm. thick, and assuming that the two surfaces of the plate were at the same temperatures as the water and the steam to which they were exposed, or that the temperature-gradient in the metal was 92° in 3 mm., he had thus obtained a value which we now know to be nearly zoo times too small. The actual temperature difference in the metal itself was really about o•36° C. The See also:remainder of the 92° drop was in the badly conducting films of water and steam See also:close to the metal surface. Similarly in a boiler plate in contact with See also:flame at 15oo° C. on one side and water at. say, 15o° C. on the other, the actual difference of temperature in the metal, even if it is an See also:inch thick, is only a few degrees. The metal, unless badly furred with incrustation, is but little hotter than the water. It is immaterial so far as the transmission of heat is concerned, whether the plates are iron or copper, The greater See also:part of the resistance to the passage of heat resides in a comparatively quiescent film of gas close to the surface, through which film the heat has to pass mainly by conduction. If a See also:Bunsen flame, preferably coloured with See also:sodium, is observed impinging on a cold metal plate, it will be seen to be separated from the plate by a dark space of a millimetre or less, throughout which the temperature of the gas is lowered by its own conductivity below the temperature of incandescence. There is no abrupt change of temperature in passing from the gas to the metal, but a continuous temperature-gradient from the temperature of the metal to that of the flame. It is true that this gradient may be upwards of r000° C. per mm., but there is no discontinuity. 34. Resistance of a Gas Film to the Passage of Heat.—It is possible to make a rough estimate of the resistance of such a film to the passage of heat through it. Taking the See also:average conductivity of the gas in the film as ro,000 times less than that of copper (about See also:double the conductivity of air at ordinary temperatures) a millimetre film would be See also:equivalent to a thickness of ro metres of copper, or about 1.2 metres of iron. Taking the temperature-gradient as r000° C. per mm. such a film would transmit r gramme-calorie per sq. cm. per sec., or 36,000 kilo-calories per sq. See also:metre per See also:hour. With an area of 100 sq. See also:ems. the heat transmitted at this rate would raise a litre of water from 2o° C. to roo° C. in 800 secs. By experiment with a strong Bunsen flame it takes from 8 to ro minutes to do this, which would indicate that on the above assumptions the equivalent thickness of quiescent film should be rather less than i mm. in this case. The thickness of the film diminishes with the velocity of the burning gases impinging on the surface. This accounts for the rapidity of heating by a See also:blowpipe flame, which is not due to any great increase in temperature of the flame as compared with a Bunsen. Similarly the efficiency of a boiler is but slightly reduced if half the tubes are stopped up, because the increase of See also:draught through the remainder compensates partly for the diminished heating surface. Some resistance to the passage of heat into a boiler is also due to the water film on the inside. But this is of less See also:account, because the conductivity of water is much greater than that of air, and because the film is continually broken up by the formation of steam, which abstracts heat very rapidly. 35. Heating by Condensation of Steam.—It is often stated that the rate at which steam will condense on a metal surface at a temperature below that corresponding to the saturation pressure of the steam is practically See also:infinite (e.g. See also:Osborne See also:Reynolds, Proc. Roy. Soc. Ed., 1893, p. 275), and conversely that the rate at which water will abstract heat from a metal surface by the formation of steam (if the metal is above the temperature of saturation of the steam) is limited only by the rate at which the metal can See also:supply heat by conduction to its surface layer. The rate at which heat can be supplied by condensation of steam appears to be much greater than that at which heat can be supplied by a flame under ordinary conditions, but there is no reason to suppose that it is infinite, or that any discontinuity exists. Experiments by H. L. Callendar and J. T. See also:Nicolson by three independent methods (Proc. Inst. Civ. Eng., 1898, 131, p. 149; Brit. Assoc. Rep. p. 418) appear to show that the rate of See also:abstraction of heat by evaporation, or that of communication of heat by condensation, depends chiefly on the difference of temperature between the metal surface and the saturated steam, and is nearly proportional to the temperature difference (not to the pressure difference, as suggested by Reynolds) for such ranges of pressure as are common in practice. The rate of heat transmission they observed was equivalent to about 8 calories per sq. cm. per sec., for a difference of 20 ° C. between the temperature of the metal surface and the saturation temperature of the steam. This would correspond to a condensation of 530 kilogrammes of steam at roo° C. per sq. metre per hour, or 109 lb per sq. ft. per hour for the same difference of temperature, values which are many times greater than those actually obtained in ordinary surface condensers. The reason for this is that there is generally some air mixed with the steam in a surface See also:condenser, which greatly retards the condensation. It is also difficult to keep the temperature of the metal as much as zo° C. below the temperature of the steam unless a very See also:free and copious circulation of cold water is available. For the same difference of temperature, steam can supply heat by condensation about a thousand times faster than hot air. This rate is not often approached in practice, but the facility of See also:generation and transmission of steam, combined with its, high latent heat and the accuracy of See also:control and regulation of temperature afforded, render it one of the most convenient agents for the distribution of large quantities of heat in all kinds of manufacturing processes. 36. Spheroidal See also:State.—An interesting contrast to the extreme rapidity with which heat is abstracted by the evaporation of a liquid in contact with a metal plate, is the so-called spheroidal state. A small drop of liquid thrown on a red-hot metal plate assumes a spheroidal form, and continues See also:swimming about for some time, while it slowly evaporates at a temperature somewhat below its boiling-point. The explanation is simply that the liquid itself cannot come in actual contact with the metal plate (especially if the latter is above the See also:critical temperature), but is separated from it by a badly conducting film of vapour, through which, as we have seen, the heat is comparatively slowly transmitted even if the difference of temperature is several See also:hundred degrees. If the metal plate is allowed to cool gradually, the drop remains suspended on its See also:cushion of vapour, until, in the case of water, a temperature of about 200° C. is reached, at which the liquid comes in contact with the plate and boils explosively, reducing the temperature of the plate, if thin, almost instantaneously to oo° C. The temperature of the metal is readily observed by a thermo-electric method, employing a See also:platinum dish with a platinum-See also:rhodium wire soldered with See also:gold to its under side. The absence of contact between the liquid and the dish in the spheroidal state may also be shown by connecting one terminal of a See also:galvanometer to the drop and the other through a See also:battery to the dish, and observing that no current passes until the drop boils. 37. Early Theories of Radiation..—It was at one time supposed that there were three distinct kinds of radiation—thermal, luminous and actinic, combined in the radiation from a luminous source such as the sun or a flame. The first gave rise to heat, the second to See also:light and the third to chemical See also:action. The three kinds were partially separated by a See also:prism, the actinic rays being generally more refracted, and the thermal rays less refracted than the luminous. This conception arose very naturally from the observation that the feebly luminous See also:blue and See also:violet rays produced the greatest photographic effects, which also showed the existence of dark rays beyond the violet, whereas the brilliant yellow and red were practically without action on the photographic plate. A thermometer placed in the blue or violet showed no appreciable rise of temperature, and even in the yellow the effect was hardly discernible. The effect increased rapidly as the light faded towards the extreme red, and reached a maximum beyond the extreme limits of the spectrum (Herschel), showing that the greater part of the thermal radiation was al-together non-luminous. It is now a See also:commonplace that chemical action, See also:colour sensation and heat are merely different effects of one and the same kind of radiation, the particular effect produced in each case depending on the frequency and intensity of the vibration, and on the nature of the substance on which it falls. When radiation is completely absorbed by a See also:black substance, it is converted into heat, the quantity of heat produced being equivalent to the See also:total See also:energy of the radiation absorbed, irrespective of the colour or frequency of the different rays. The actinic or chemical effects, on the other See also:hand, depend essentially on some relation between the See also:period of the vibration and the properties of the substance acted on. The rays producing such effects are generally those which are most strongly absorbed. The spectrum of See also:chlorophyll, the See also:green colouring matter of See also:plants, shows two very strong absorption bands in the red. The red rays of corresponding period are found to be the most active in promoting the growth of the plant. The chemically active rays are not necessarily the shortest. Even photographic plates may be made to See also:respond to the red rays by staining them with pinachrome or some other suitable dye. The action of light rays on the retina is closely analogous to the action on a photographic plate. The retina, like the plate, is sensitive only to rays within certain restricted limits of frequency. The limits of sensitiveness of each colour sensation are not exactly defined, but vary slightly from one individualto another, especially in cases of partial colour-See also:blindness, and are modified by conditions of fatigue. We are not here concerned with these important physiological and chemical effects of radiation, but rather with the question of the See also:conversion of energy of radiation into heat, and with the laws of emission and absorption of radiation in relation to temperature. We may here also assume the identity of visible and invisible radiations from a heated body in all their physical properties. It has been abundantly proved that the invisible rays, like the visible, (1) are propagated in straight lines in homogeneous See also:media; (2) are reflected and diffused from the surface of bodies according to the same law; (3) travel with the same velocity in free space, but with slightly different velocities in denser media, being subject to the same law of See also:refraction; (4) exhibit all the phenomena of diffraction and interference which are characteristic of wave-motion in general; (5) are capable of polarization and double refraction; (6) exhibit similar effects of selective absorption. These properties are more easily demonstrated in the case of visible rays on account of the great sensitiveness of the See also:eye. But with the aid of the thermopile or other sensitive See also:radiometer, they may be shown to belong equally to all the radiations from a heated body, even such as are See also:thirty to fifty times slower in frequency than the longest visible rays. The same physical properties have also been shown to belong to electromagnetic waves excited by an electric See also:discharge, whatever the frequency, thus including all kinds of aetherial radiation in the same See also:category as light. 38. Theory of Exchanges.—The apparent concentration of cold by a See also:concave See also:mirror, observed by G. B. Porta and rediscovered by M. A. Pictet, led to the enunciation of the theory of exchanges by See also:Pierre See also:Prevost in 1791. Prevost's leading See also:idea was that all bodies, whether cold or hot, are constantly radiating heat. Heat equilibrium, he says, consists in an equality of ex-change. When equilibrium is interfered with, it is re-established by inequalities of See also:exchange. If into a locality at See also:uniform temperature a refracting or reflecting body is introduced, it has no effect in the way of changing the temperature at any point of that locality. A reflecting body, heated or cooled in the interior of such an enclosure, will acquire the surrounding temperature more slowly than would a non-reflector, and will less affect another body placed at a little distance, but will not affect the final equality of temperature. Apparent radiation of cold, as from a See also:block of See also:ice to a thermometer placed near it, is due to the fact that the thermometer being at a higher temperature sends more heat to the ice than it received back from it. Although Prevost does not make the statement in so many words, it is clear that he regards the radiation from a body as depending only on its own nature and temperature, and as independent of the nature and presence of any adjacent body. Heat equilibrium in an enclosure of constant temperature such as is here postulated by Prevost, has often been regarded as a consequence of See also:Carnot's principle. Since difference of temperature is required for transforming heat into See also:work, no work could be obtained from heat in such a See also:system, and no spontaneous changes of temperature can take place, as any such changes might be utilized for the See also:production of work. This See also:line of reasoning does not appear quite satisfactory, because it is tactitly assumed, in the reasoning by which Carnot's principle was established, as a result of universal experience, that a number of bodies within the same impervious enclosure, which contains no source of heat, will ultimately acquire the same temperature, and that difference of temperature is required to produce flow of heat. Thus although we may regard the equilibrium in such an enclosure as being due to equal exchanges of heat in all directions, the equal and opposite streams of radiation annul and neutralize each other in such a way that no actual transfer of energy in any direction takes place. The state of the medium is everywhere the same in such an enclosure, but its energy of-agitation per unit volume is a See also:function of the temperature, and is such that it would not be in equilibrium with any body at a different temperature.
3o. " Full" and Selective Radiation. See also:Correspondence of Emission and Absorption.—The most obvious difficulties in the
way of this theory arise from the fact that nearly all radiation is more or less selective in See also:character, as regards the quality and frequency of the rays emitted and absorbed. It was shown by J. See also:Leslie, M. See also:Melloni and other experimentalists that many substances such as glass and water, which are very transparent to visible rays, are extremely opaque to much of the invisible radiation of lower frequency; and that polished metals, which are perfect reflectors, are very feeble radiators as compared with dull or black bodies at the same temperature. If two bodies emit rays of different periods in different proportions, it is not at first sight easy to see how their radiations can See also:balance each other at the same temperature. The See also: It follows from this conception that the proportion of the full radiation stream absorbed by any body in such an enclosure must be exactly compensated in quality as well as quantity by the proportion emitted, or that the emissive and absorptive powers of any body at a given temperature must be precisely equal. A good reflector, like a polished metal, must also be a feeble radiator and absorber. Of the incident radiation it absorbs a small fraction and reflects the remainder, which together with the radiation emitted (being precisely equal to that absorbed) makes up the full radiation stream. A partly transparent material, like glass, absorbs part of the full radiation and transmits part. But it emits rays precisely equal in quality and intensity to those which it absorbs, which together with the transmitted portion make up the full stream. The ideal black body or perfect radiator is a body which absorbs all the radiation incident on it. The rays emitted from such a body at any temperature must be equal to the full radiation stream in an isothermal enclosure at the same temperature. Lampblack, which may absorb between 98 to 99 % of the incident radiation, is generally taken as the type of a black body. But a closer approximation to full radiation may be obtained by employing a hollow vessel the internal walls of which are blackened and maintained at a uniform temperature by a steam jacket or other suitable means. If a relatively small hole is made in the side of such a vessel, the radiation proceeding through the See also:aperture will be the full radiation corresponding to the temperature. Such a vessel is also a perfect absorber. Of radiation entering through the aperture an infinitesimal fraction only could possibly emerge by successive reflection even if the sides were of polished metal internally. A thin platinum See also:tube heated by an electric current appears feebly luminous as compared with a blackened tube at the same temperature. But if a small hole is made in the side of the polished tube, the light proceeding through the hole appears brighter than the blackened tube, as though the inside of the tube were much hotter than the outside, which is not the case to any appreciable extent if the tube is thin. The radiation proceeding through the hole is nearly that of a perfectly black body if the hole is small. If there were no hole the internal stream of radiation would be exactly that of a blackbody at the same temperature however perfect the reflecting power, or however low the emissive power of the walls, because the defect in emissive power would be exactly compensated by the internal reflection. Balfour Stewart gave a number of striking illustrations of the qualitative identity of emission and absorption of a substance. Pieces of coloured glass placed in a fire appear to lose their colour when at the same temperature as the coals behind them, because they compensate exactly for their selective absorption by radiating chiefly those See also:colours which they absorb. Rocksalt is remarkably transparent to thermal radiation of nearly all kinds, but it is extremely opaque to radiation from a heated plate of rocksalt, because it emits when heated precisely those rays which it absorbs. A plate of See also:tourmaline cut parallel to the See also:axis absorbs almost completely light polarized in a See also:plane parallel to the axis, but transmits freely light polarized in a perpendicular plane. When heated its radiation is polarized in the same plane as the radiation which it absorbs. In the caseof incandescent vapours, the exact correspondence of emission and absorption as regards wave-length of frequency of the light emitted and absorbed forms the See also:foundation of the See also:science of spectrum analysis. See also:Fraunhofer had noticed the coincidence of a pair of See also:bright yellow lines seen in the spectrum of a See also:candle flame with the dark D lines in the solar spectrum, a coincidence which was afterwards more exactly verified by W. A. See also:Miller. See also:Foucault found that the flame of the electric arc showed the same lines bright in its spectrum, and proved that they appeared as dark lines in the otherwise continuous spectrum when the light from the See also:carbon poles was transmitted through the arc. See also:Stokes gave a dynamical explanation of the phenomenon and illustrated it by the analogous case of resonance in See also:sound. See also:Kirchhoff completed the explanation (Phil. Mug., r86o) of the dark lines in the solar spectrum by showing that the reversal of the spectral lines depended on the fact that the body of the sun giving the continuous spectrum was at a higher temperature than the absorbing layer of gases surrounding it. Whatever be the nature of the selective radiation from a body, the radiation of light of any particular wave-length cannot be greater than a certain fraction E of the radiation R of the same wave-length from a black body at the same temperature. The fraction E See also:measures the emissive power of the body for that particular wave-length, and cannot be greater than unity. The same fraction, by the principle of equality of emissive and absorptive powers, will measure the proportion absorbed of incident radiation R'. If the black body emitting the radiation R' is at the same temperature as the absorbing layer, R=R', the emission balances the absorption, and the line will appear neither bright nor dark. If the source and the absorbing layer are at different temperatures, the radiation absorbed will be ER', and that transmitted will be R'–ER'. To this must be added the radiation emitted by the absorbing layer, namely ER, giving R'–E(R'–R). The lines will appear darker than the background R' if R' is greater than R, but bright if the See also:reverse is the case. The D lines are dark in the sun because the photosphere is much hotter than the See also:reversing layer. They appear bright in the candle-flame because the outside See also:mantle of the flame, in which the sodium See also:burns and See also:combustion is complete, is hotter than the inner reducing flame containing the incandescent particles of carbon which give rise to the continuous spectrum. This qualitative identity of emission and absorption as regards wave-length can be most exactly and easily verified for luminous rays, and we are justified in assuming that the relation holds with the same exactitude for non-luminous rays, although in many cases the experimental See also:proof is less complete and exact. 40. Diuthermancy.—A great See also:array of data with regard to the transmissive power or diathermancy of transparent substances for the heat radiated from various sources at different temperatures were collected by Melloni, Tyndall, Magnus and other experimentalists. The measurements were chiefly of a qualitative character, and were made by interposing between the source. and a thermopile a layer or plate of the substance to be examined. This method lacked quantitative precision, but led to a number of striking and interesting results, which are admirably set forth in Tyndall's Heat. It also gave rise to many curious discrepancies, some of which were recognized as being due to selective absorption, while others are probably to be explained by imperfections in the methods of experiment adopted. The general result of such researches was to show that substances, like water, See also:alum and glass, which are practically opaque to radiation from a source at low temperature, such as a vessel filled with boiling water, transmit an increasing percentage of the radiation when the temperature of the source is increased. This is what would be expected, as these substances are very transparent to visible rays. That the proportion transmitted is not merely a question of the temperature of the source, but also of the quality of the radiation, was shown by a number of experiments. For instance, K. H. Knoblauch (Pogg. Ann., 1847) found that a plate of glass interposed between a spirit See also:lamp and a thermopile intercepts a larger proportion of the radiation from the flame itself than of the radiation from a platinum, See also:spiral heated in the flame, although the spiral is undoubtedly at a lower temperature than the flame. The explanation is that the spiral is a fairly good radiator of the visible rays to which the glass is transparent, but a bad radiator of the invisible rays absorbed by the glass which constitute the greater portion of the heat-radiation from the feebly luminous flame. Assuming that the radiation from the source under investigation is qualitatively determinate, like that of a black body at a given temperature, the proportion transmitted by plates of various substances may easily be measured and tabulated for given plates and sources. But owing to the highly selective character of the radiation and absorption, it is impossible to give any general relation between the thickness of the absorbing plate or layer and the proportion of the total energy absorbed. For these reasons the relative diathermancies of different materials do not admit of any simple numerical statement as physical constants, though many of the qualitative results obtained are very striking. Among the most interesting experiments were those of Tyndall, on the absorptive powers of gases and vapours, which led to a good See also:deal of controversy at the time, owing to the difficulty of the experiments, and the contradictory results obtained by other observers. The arrangement employed by Tyndall for these measurements is shown in Fig. 6. A See also:brass gas and vapours. tube AB, polished inside, and closed with plates of highly diathermanous rocksalt at either end, was fitted with stopcocks C and D for exhausting and admitting air or other gases or vapours. The source of heat S was usually a plate of copper heated by a Bunsen burner, or a Leslie See also:cube containing boiling water as shown at E. To obtain greater sensitiveness for See also:differential measurements, the radiation through the tube AB incident on one See also:face of the See also:pile P was balanced against the radiation from a Leslie cube on the other face of the pile by means of an adjust-able See also:screen H. The radiation on the two faces of the pile being thus balanced with the tube exhausted, Tyndall found that the See also:admission of dry air into the tube produced practically no absorption of the radiation, whereas See also:compound gases such as carbonic See also:acid, See also:ethylene or See also:ammonia absorbed 20 to q0%, and a trace of aqueous vapour in the air increased its absorption 50 to roo times. H. G. Magnus, on the other hand, employing a thermopile and a source of heat, both of which were enclosed in the same exhausted See also:receiver, in order to avoid interposing any rocksalt or other plates between the source and the pile, found an absorption of r r % on admitting dry air, but could not detect any difference whether the air were dry or moist. Tyndall suggested that the apparent absorption observed by Magnus may have been due to the cooling of his radiating surface by convection, which is a very probable source of error in this method of experiment. Magnus considered that the remarkable effect of aqueous vapour observed by Tyndall might have been caused by condensation on the polished internal walls of his experimental tube, or on the rocksalt plates at either end.' The question of ' In reference to this objection, Tyndall remarks (Phil. Meg., 1862, p. 422; Heat, p. 385); " In the first place the plate of See also:salt nearest the source of heat is never moistened, unless the experiments are of the roughest character. Its proximity to the source enables the heat to See also:chase away every trace of humidity from its surface." He therefore took precautions to dry only the circumferential portions of the plate nearest the pile, assuming that the See also:flux of heat through the central portions would suffice to keep them dry. This reasoning is not at all satisfactory, because rocksalt is very hygroscopic and becomes wet, even in unsaturated air, if the vapour pressure is greater than that of a saturated solution of salt at thethe relative diathermancy of air and aqueous vapour for radiation from the sun to the earth and from the earth into space is one of great See also:interest and importance in See also:meteorology. Assuming with Magnus that at least ro% of the heat from a source at loci° C. is absorbed in passing through a single See also:foot of air, a very moderate thickness of See also:atmosphere should suffice to absorb practically all the heat radiated from the earth into space. This could not be reconciled with well-known facts in regard to terrestrial radiation, and it was generally recognized that the result found by Magnus must be erroneous. Tyndall's experiment on the great diathermancy of dry air agreed much better with meteorological phenomena, but he appears to have exaggerated the effect of aqueous vapour. He concluded from his experiments that the water vapour See also:present in the air absorbs at least. ro% of the heat radiated from the earth within ro ft. of its surface, and that the absorptive power of the vapour is about 17,000 times that of air at the same pressure. If the absorption of aqueous vapour were really of this order of magnitude, it would exert a far greater effect in modifying See also:climate than is actually observed to be the case. Radiation is observed to take place freely through the atmosphere at times when the proportion of aqueous vapour is such as would practically stop all radiation if Tyndall's results were correct. The very careful experiments of E. Lecher and J. Pernter (Phil. Mag., Jan. 1881) confirmed Tyndall's observations on the absorptive powers of gases and vapours satisfactorily in nearly all cases with the single exception of aqueous vapour. They found that there was no appreciable absorption of heat from a source at See also:roe C. in passing through r ft. of air (whether dry or moist), but that CO and See also:CO2 at atmospheric pressure absorbed about 8%, and ethylene (olefiant gas) about 50% in the same distance; the vapours of See also:alcohol and See also:ether showed absorptive powers of the same order as that of ethylene. They confirmed Tyndall's important result that the absorption does not diminish in See also:pro-portion to the pressure, being much greater in proportion for smaller pressures in consequence of the selective character of the effect. They also supported his conclusion that absorptive power increases with the complexity of the See also:molecule. But they could not detect any absorption by water vapour at a pressure of 7 mm., though alcohol at the same pressure absorbed 3% and acetic acid ro%. Later researches, especially those of S. P. See also:Langley with the spectro-bolometer on the infra-red spectrum of sunlight, demonstrated the existence of marked absorption bands, some of which are due to water vapour. From the character of these bands and the manner in which they vary with the state of the air and the thickness traversed, it may be inferred that absorption by water vapour plays an important part in meteorology, but that it is too small to be temperature of the plate. Assuming that the vapour pressure of the saturated salt solution is only half that of pure water, it would require an See also:elevation of temperature of ro° C. to dry the rocksalt plates in saturated air at 15° C. It is only See also:fair to say that the laws of the vapour pressures of solutions were unknown in Tyndall's time, and that it was usual to assume that the plates would not become wetted until the See also:dew-point was reached. The writer has repeated Tyndall's experiments with a facsimile of one of Tyndall's tubes in the See also:possession of the Royal See also:College of Science, fitted with plates of rocksalt cut from the same block as Tyndall's, and therefore of the same hygroscopic quality. Employing a reflecting galvanometer in See also:conjunction with a differential bolometer, which is quicker in its action than Tyndall's pile, there appears to be hardly any difference between dry and moist air, provided that the latter is not more than half saturated. Using saturated air with a Leslie cube as source of heat, both rocksalt plates invariably become wet in a See also:minute or two and the absorption rises to ro or 20 % according to the thickness of the film of deposited moisture. Employing the open tube method as described by Tyndall, without the rocksalt plates, the absorption is certainly less than 1% in 3 ft. of air saturated at 20° C., unless condensation is induced on the walls of the tube. It is possible that the walls of Tyndall's tube may have become covered with a very hygroscopic film from the See also:powder of the See also:calcium chloride which he was in the See also:habit of introducing near one end. Such a film would be exceedingly difficult to remove, and would account for the excessive precautions which he found necessary in drying the air in order to obtain the same transmitting power as a vacuum. It is probable that Tyndall's experiments on aqueous vapour were effected by experimental errors of this character.
readily detected by laboratory experiments in a 4 ft. tube, with-out the aid of spectrum analysis.
41. Relation between Radiation and Temperature.—Assuming, in accordance with the reasoning of Balfour Stewart and Kirchhoff, that the radiation stream inside an impervious enclosure at a uniform temperature is independent of the nature of the walls of the enclosure, and is the same for all substances at the same temperature, it follows that the full stream of radiation in such an enclosure, or the radiation emitted by an ideal black body or full radiator, is a function of the temperature only. The form of this function may be determined experimentally by observing the radiation between two black bodies at different temperatures, which will be proportional to the difference of the full radiation streams corresponding to their several temperatures. The law now generally accepted was first proposed by Stefan as an empirical relation. Tyndall had found that the radiation from a See also: Akad. Ber., 1879, 79, p. 421) noticed that the ratio 11.7 is nearly that of the See also:fourth power of the absolute temperatures as estimated by Tyndall. On making the somewhat different assumption that the radiation between two bodies varied as the difference of the fourth powers of their absolute temperatures, he found that it satisfied approximately the experiments of Dulong and Petit and other observers. According to this law the radiation between a black body at a temperature 8 and a black enclosure or a black radiometer at a temperature 0, should be proportional to (04-004). The law was very simple and convenient in form, but it rested so far on very insecure See also:foundations. The temperatures given by Tyndall were merely estimated from the colour of the light emitted, and might have been some hundred degrees in error. We now know that the radiation from polished platinum is of a highly selective character, and varies more nearly as the fifth power of the absolute temperature. The agreement of the fourth power law with Tyndall's experiment appears therefore to be due to a purely accidental error in estimating the temperatures of the wire. Stefan also found a very fair agreement with See also:Draper's observations of the intensity of radiation from a platinum wire, in which the temperature of the wire was deduced from the expansion. Here again the apparent agreement was largely due to errors in estimating the temperature, arising from the fact that the coefficient of expansion of platinum increases considerably with rise of temperature. So far as the experimental results available at that time were concerned, Stefan's law could be regarded only as an empirical expression of doubtful significance. But it received a much greater importance from theoretical investigations which were even then in progress. See also: L. Boltzmann (1884) employing radiation as the working sub-stance in a Carnot See also:cycle, showed that the energy of full radiation at any temperature per unit volume should be proportional to the fourth power of the absolute temperature. This law was first verified in a satisfactory manner by Heinrich Schneebeli (Wied. Ann., 1884, 22, p. 30). He observed the radiation from the bulb of an air thermometer heated to known temperatures through a small aperture in the walls of the See also:furnace. With this arrangement the radiation was very nearly that of a black body. Measurements by J.T. Bottomley, See also:August See also:Schleiermacher, L. C. H. F. Paschen and others of the radiation from electrically heated platinum, failed to give concordant results on account of differences in the quality of the radiation, the importance of which was not fully realized at first. Later researches by Paschen with improved methods verified the law, and greatly extended our knowledge of radiation in other directions. One of the most complete See also:series of experiments onthe relation between full radiation and temperature is that of O. R. Lummer and See also:Ernst See also:Pringsheim (Ann. Phys., 1897, 63, p. 395). They employed an aperture in the side of an enclosure at uniform temperature as the source of radiation, and compared the intensities at different temperatures by means of a bolometer. The fourth power law was well satisfied throughout the whole range of their experiments from -190° C. to 2300° C. According to this law, the rate of loss of heat by radiation R from a body of emissive power E and surface S at a temperature 0 in an enclosure at 0, is given by the formula R = aES (04 -004), where a is the radiation constant. The absolute value of v was determined by F. Kurlbaum using an electric See also:compensation method (Wied. Ann., 1898, 65, p. 746), in which the radiation received by a bolometer from a black body at a known temperature was measured by finding the electric current required to produce the same rise of temperature in the bolometer. K. See also:Angstrom employed a similar method for solar radiation. Kurlbaum gives the value v = 5.32 X 10–5 ergs per sq. cm. per sec. C. Christiansen (Wied. Ann., 1883, 19, p. 267) had previously found a value about 5% smaller, by observing the rate of cooling of a copper plate of known thermal capacity, which is probably a less accurate method. 42. Theoretical Proof of the Fourth Power Law.—The proof given by Boltzmann may be somewhat simplified if we observe that full radiation in an enclosure at constant temperature behaves exactly like a saturated vapour, and must therefore obey Carnot's or Clapeyron's See also:equation given in See also:section 17. The energy of radiation per unit volume, and the radiation-pressure at any temperature, are functions of the temperature only, like the pressure of a saturated vapour. If the volume of the enclosure is increased by any finite amount, the temperature remaining the same, radiation is given off from the walls so as to fill the space to the same pressure as before. The heat absorbed when the volume is increased corresponds with the latent heat of See also:vaporization. In the case of radiation, as in the case of a vapour, the latent heat consists partly of internal energy of formation and partly of external work of expansion at constant pressure. Since in the case of full or undirected radiation the pressure is one-third of the energy per unit volume, the external work for any expansion is one-third of the internal energy added. The latent heat absorbed is, therefore, four times the external work of expansion. Since the external work is the product of the pressure P and the increase of volume V, the latent heat per unit increase of volume is four times the pressure. But by Carnot's equation the latent heat of a saturated vapour per unit increase of volume is equal to the rate of increase of saturation-pressure per degree divided by Carnot's function or multiplied by the absolute temperature. Expressed in symbols we have, B(dP/dO) =L/V =4P, where (dP/dO) represents the rate of increase of pressure. This equation shows that the percentage rate of increase of pressure is four times the percentage rate of increase of temperature, or that if the temperature is increased by 1%, the pressure is increased by 4%. This is equivalent to the statement that the pressure varies as the fourth power of the temperature, a result which is mathematic-ally deduced by integrating the equation. 43. Wien's Displacement Law.—Assuming that the fourth power law gives the quantity of full radiation at any temperature, it remains to determine how the quality of the radiation varies with the temperature, since as we have seen both quantity and quality are determinate. This question may be regarded as consisting of two parts. (1) How is the wave-length or frequency of any given kind of radiation changed when its temperature is altered? (2) What is the form of the See also:curve expressing the distribution of energy between the various wave-lengths in the spectrum of full radiation, or what is the distribution of heat in the spectrum? The researches of Tyndall, Draper, Langley and other investigators had shown that while the energy of radiation of each frequency increased with rise of temperature, the maximum of intensity was shifted or displaced along the spectrum in the direction of shorter wave-lengths or higher frequencies. W. Wien (Ann. Phys., 1898, 58, p. 662), applying Doppler's principle to the adiabatic See also:compression of radiation in a perfectly reflecting enclosure, deduced that the wave-length of each constituent of the radiation should be shortened in proportion to the rise of temperature produced by the compression, in such a manner that the product AB of wave-length and the absolute temperature should remain constant. According to this relation, which is known as Wien's Displacement Law, the frequency corresponding to the maximum See also:ordinate of the energy curve of the normal spectrum of full radiation should vary directly (or the wave-length inversely) as the absolute temperature, a result previously obtained by H. F. See also:Weber (1888). Paschen, and Lummer and Pringsheim verified this relation by observing with a bolometer the intensity at different points in the spectrum produced by a fluorite prism. The intensities were corrected and reduced to a wave-length scale with the aid of Paschen's results on the See also:dispersion formula of fluorite (Wied Ann., 1894, 53, p. 301). The curves in fig. 7 illustrate results obtained by Lummer and Pringsheim (Ber. See also:deaf. ph vs. Ges., 1899, 1, p. 34) at three different temperatures, namely 1377°, 1087° and 836° absolute, plotted on a wave-length See also:base with a scale of microns (µ) or millionths of a metre. The wave-lengths Oa, Ob, Oc, corresponding to the maximum ordinates of each curve, vary inversely as the absolute temperatures given. The constant value of the product AB at the maximum point is found to be 2920 Thus for a temperature of See also:rood° Abs. the maximum is at wave-length 2.92/2; at 20000 the maximum is at 1.46 A. 44. Form of the Curve representing the Distribution of Energy in the Spectrum.—Assuming Wien's displacement law, it follows that the form of the curve representing the distribution of energy in the spectrum of full radiation should be the same for different temperatures with the maximum displaced in proportion to the absolute temperature, and with the total area increased in proportion to the fourth power of the absolute temperature. Observations taken with a bolometer along the length of a normal or wave-length spectrum, would give the form of the curve plotted on a wave-length base. The height of the ordinate at each point would represent the energy included between given limits of wave-length, depending on the width of the bolometer See also:strip and the slit. Supposing that the bolometer strip had a width„ corresponding to -or ,u, and were placed at 1.o µ in the spectrum of radiation at 2000° Abs., it would receive the energy corresponding to wave-lengths between 1•0o and 1.01 µ. At a temperature of r000° Abs. the corresponding part of the energy, by Wien's displacement law, would See also:lie between the limits 2.00 and 2.02 /2, and the total energy between these limits would be 16 times smaller. But the bolometer strip placed at 2•oµ would now receive only half of the energy, or the energy in a See also:band .or µ wide, and the deflection would be 32 times less. Corresponding ordinates of the curves at different temperatures will therefore vary as the fifth power of the temperature, when the curves are plotted on a wave-length base. The maximum ordinates in the curves already given are found to vary as the fifth powers of the corresponding temperatures. The equation representing the distribution of energy on a wave-length base must be of the form E=Cc-5 F(XO) =C©5(Xe)-5F(XB) where F()^9) represents some function of the product of the wave-length and temperature, which remains constant for corresponding wave-lengths when B is changed. If the curves were plotted on a frequency base, owing to the change of scale, the maximum ordinates would vary as the cube of the temperature instead of the fifth power, but the form of the function F would remain unaltered. Reasoning on the See also:analogy of the distribution of velocities among the particles of a gas on the kinetic theory, which is a very similar problem, Wien was led to assume that the function F should be of the form e-`/X0, where e is the base of Napierian logarithms, and c is a constant having the value 14,600 if the wave-length is measured in microns te. This expression was found by Paschen to give a very good approximation to the form of the curve obtained experimentally for those portions of the visible and infra-red spectrum where observations could be most accurately made. The formula was tested in two ways: (1) by plotting the curves of distribution of energy in the spectrum for constant temperatures as illustrated in fig. 7; (2) by plotting the energy corresponding to a given wave-length as a function of the temperature. Both methods gave very good agreement with Wien's formula for values of the product A0 not much exceeding 3000 A method of isolating rays of great wave-length by successive reflection was devised by H. See also:Rubens and E. F. Nichols (Wied. Ann., 1897, 6o, p.418). They found that See also:quartz and o• fluorite possessed the See also:property of selective 4o reflection for rays of wave-length 8.8µ and a0-24µ to 32/2 respectively, so that after four to six reflections these rays could be isolated from a source at any temperature in ''~s';•Ab+ a state of considerable z a a s c q S s,. purity. The residual Fin. 7.—Distribution of energy in the impurity at any See also:stage spectrum of a black body. could be estimated by interposing a thin plate of quartz or fluorite which completely reflected or absorbed the residual rays, but allowed the impurity to pass. H. See also:Beckmann, under the direction of Rubens, investigated the variation with temperature of the residual rays reflected from fluorite employing sources from -8o° to 600° C., and found the results could not be represented by Wien's formula unless the constant c were taken as 26,000 in place of 14,600. In their first series of observations extending to 6 t O.R. Lummer and E. Pringsheim (Dent. phys. Ges., 1899, 1, p. 34) found systematic deviations indicating an increase in the value of the constant c for See also:long waves and high temperatures. In a theoretical discussion of the subject, See also:Lord See also:Rayleigh (Phil. Mag., 1900, 49, p. 539) pointed out that Wien's law would lead to a limiting value CX , of the radiation corresponding to any particular wave-length when the temperature increased to infinity, whereas according to his view the radiation of great wave-length should ultimately increase in direct proportion to the temperature. Lummer and Pringsheim (Dent. phys. Ges., 1900, 2, p. 163) extended the range of their observations to 18 /2 by employing a prism of sylvine in place of fluorite. They found deviations from Wien's formula increasing to nearly 50% at 18 where, however, the observations were very difficult on account of the smallness of the energy to be measured. Rubens and F. Kurlbaum (Ann. Phys., 1901, 4, p. 649) extended the residual reflection method to a temperature range from -190° to 1500° C., and employed the rays reflected from quartz 8.8/1, and rocksalt gi µ, in .^ Em^,m Nigim addition to those ° ~^/„^^~~~®~~ from fluorite. It es ^^11^MEMINI^~I researches ro that these ', 11111111110111INIIIIIIIII rays of great wave- length from a source ^.f^^NM,^^ ^^R at a high temperature ' ^~'^^^ ~Elms tended directly vary as the °^"^^~^^,\'^^ limit tthe absolute ~ ^ ^^ :' =M aote temperature ,; 0 lN•Wi p A 1 G 3 4 5 B/L of the source, as d1e t.See also:net,4arioW.we.TH NN/GR°NS suggested by Lord Flo. 8.--Distribution of energy in the Rayleigh, and could spectrum of full radiation at 2000°Abs. be represented according to formulae of See also:Planck & Wien. not by Wien's formula with any value of the constant c. The simplest type of formula satisfyhtg the required conditions is that proposed by Max Planck (Ann. Phys., 1901, 4, p. 553) namely, 60. nn• s 20 1 0 E which agrees with Wien's formula when 0 is small, where Wien's formula is known to be satisfactory, but approaches the limiting form E=CX-'B/c, when is large, thus satisfying the condition D.C.L. from See also:Oxford (31st of March 1752). He also See also:left MS. proposed by Lord Rayleigh. The theoretical See also:interpretation of notes on See also:Burmann's and See also:Martyn's See also:editions of See also:Virgil, on See also:Euripides, this formula remains to some extent a matter of future investiga- See also:Catullus, See also:Tibullus, and the greater part of See also:Hesiod. In some of tion, but it appears to satisfy experiment within the limits of these he adopts the whimsical name Dexiades Ericius. His observational error. In order to compare Planck's formula Revisal of Shakespear's See also:Text (1765) was an See also:answer to the " in-graphically with Wien's, the distribution curves corresponding See also:solent dogmatism " of See also:Bishop See also:Warburton. The See also:Essay towards a to both formulae are plotted in fig. 8 for a temperature of 2000° See also:Demonstrative Proof of the Divine Existence, Unity and Attributes abs., taking the value of the constant (1740) was intended to combat the opinions of See also:Voltaire, See also: may be applied to find the energy for HEATH, See also:NICHOLAS (c. 1501-1578), See also:archbishop of See also:York and any other wave-length or temperature, lord See also:chancellor, was See also:born in See also:London about 15o1 and graduated by simply altering the wave-length B.A. at Oxford in 1519. He then migrated to See also:Christ's College, scale in.inverse ratio to the See also:tempera- See also:Cambridge, where he graduated B.A. in 1520, M.A. in 1522, and See also:ture, or vice versa. Thus to find the was elected See also:fellow in 1524. After holding See also:minor preferments distribution curve for loco° abs., it is he was appointed See also:archdeacon of See also:Stafford in 1534 and graduated only necessary to multiply all the D.D. in 1535. He then accompanied See also:Edward See also:Fox (q.v.), bishop See also:numbers in the wave-length scale of , of See also:Hereford, on his See also:mission to promote a theological and See also:political fig. 8 by 2; or to find the variation understanding with the Lutheran princes of See also:Germany. His curve for wave-length 6othe numbers on the temperature scale selection for this See also:duty implies a readiness on Heath's part to of fig. 9 should be divided by 2. The ordinate scales must be proceed some distance along the path of reform; but his dealings increased in proportion to the fifth power of the temperature, or with the See also:Lutherans did not confirm this tendency, and Heath's inversely as the fifth power of the wave-length respectively subsequent career was closely associated with the cause of re-in See also:figs. 8 and 9 if See also:comparative results are required for different action. In 1539, the See also:year of the Six Articles, he was made bishop temperatures or wave-lengths. The results hitherto obtained of See also:Rochester, and in 1543 he succeeded See also:Latimer at See also:Worcester. for cases other than full radiation are not sufficiently simple and His Catholicism, however, was of a less rigid type than See also:Gardiner's
definite to admit of profitable discussion in the present article. and See also:Bonner's; he See also:felt something of the force of the See also:national BTBLIOGRAPHV.—It would not be possible, within the limits of an antipathy to See also:foreign See also:influence, whether ecclesiastical or See also:secular,
article like the present, to give tables of the specific thermal properties and was always impressed by the See also:necessity of national unity, of different substances so far as they have been ascertained by ex-
so far as was possible, in matters of faith. Apparently he made
periment. To be of any use, such tables require to be extremely no difficulty about carrying out the earlier reforms of Edward VI., detailed, with very full references and explanations with regard to
the value of the experimental See also:evidence, and the limits within which and he accepted the first See also:book of common See also:prayer after it had the results may be relied on. The quantity of material available been modified by the See also:House of Lords in a See also:Catholic direction.
is so enormous and its value so varied, that the most elaborate tables His definite See also:breach with the See also:Reformation occurred on the grounds, on which four centuries later See also:Leo XIII. denied the Catholicity of the reformed See also:English See also: Like Sir See also: Among See also:modern textbooks, Preston's Theory of Heat and Poynting and See also:Thomson's Heat are the best known, and have been brought well up to date. Sections on heat are included in all the general text-books of Physics, such as those of See also:Deschanel (translated by Everett), Ganot (translated by See also:Atkinson), See also:Daniell, See also:Watson,&c. Of the original investigations on the subject, the most important have already been cited. Others will be found in the collected papers of See also:Joule, See also:Kelvin and Maxwell. See also:Treatises on special branches of the subject, such as Fourier's Conduction of Heat, are referred to in the separate articles in this See also:encyclopaedia dealing with See also:recent progress, of which the following is a See also:list: See also:CALORIMETRY, CONDENSATION OF GASES, CONDUCTION OF HEAT, DIFFUSION, See also:ENERGETICS, See also:FUSION, LIQUID GASES, RADIATION, RADIOMETER, SOLUTION, See also:THERMODYNAMICS, See also:THERMOELECTRICITY, TIIERMOMFTRY, VAPORIZATION. For the See also:practical aspects of heating see HEATING. (H. L. Additional information and CommentsThere are no comments yet for this article.
» Add information or comments to this article.
Please link directly to this article:
Highlight the code below, right click, and select "copy." Then paste it into your website, email, or other HTML. Site content, images, and layout Copyright © 2006 - Net Industries, worldwide. |
|
|
[back] TRANSFER (from Lat. transferre, to bear across, car... |
[next] TRANSFORMERS |