FIG. 19
Relation between Absorbing and Radiating Powers.—The exact relation between the absorbing and radiating powers of a surface was first determined by Ritchie by means of an ingenious experiment. Two equal air-tight metal chambers A and B were connected by a glass tube bent twice at right angles as in Fig. 19. A drop of mercury in the horizontal part of this tube acted as an indicator. When one of the vessels became hotter than the other, the air in it expanded and the mercury index moved towards the colder side. Between the two metal chambers a third equal one was mounted which could be heated up by pouring boiling water into it and could thus act as a radiator to the other two. One surface of this radiator was coated with lamp-black and the opposite one with the surface under investigation, e.g. cinnabar. The inner surfaces of the other two vessels were coated in the same way, the one with lamp-black, the other with cinnabar. The middle vessel was first placed so that the lamp-blacked surface was opposite to a cinnabar one, and vice-versa. In this position, when hot water was poured into it no movement of the mercury drop was detected, and therefore the amounts of heat received by the two outer vessels must have been exactly equal. On the one side the heat given out by the cinnabar surface of the middle vessel is only a fraction, equal to its radiating power, of the heat given out by the black surface. All the heat given out by the cinnabar surface to the black surface opposite to it is absorbed, however, while of the heat given out by the black surface to the cinnabar surface opposite it only a fraction is absorbed equal to the absorbing power of the cinnabar surface. Thus on the one side only a fraction is sent out but all of it is absorbed, and on the other side all is sent out and only a fraction absorbed. Since the quantities absorbed are exactly equal, it is obvious that the two fractions must be exactly equal, or the absorbing and radiating powers of any surface are exactly equal. This result is known as Kirchoff's law, and it applies solely to radiation which is caused by temperature. Later experiments have shown that it applies to each individual wave-length, i.e. to any portion of the spectrum which we isolate, as well as to the whole radiation. Thus at any particular temperature let the dotted line in Fig. 20 represent the wave-length—energy curve for a full radiator, and let the solid line represent it for the surface under investigation. Then for any wave-length, ON, the radiating power of the surface would be equal to QN divided by PN.
FIG. 20.
Now a wave-length—energy curve may be as easily constructed for absorbed as for emitted radiation by means of a Langley's bolometer. The strip of the bolometer is first coated with lamp-black and the spectrum of the incident radiation is explored in exactly the same way as is described in Chapter III. The strip is then coated with the surface under investigation and the spectrum is again explored. Since the incident radiation is exactly the same in the two experiments, the differences in the quantities of heat absorbed must be due solely to the difference in the absorbing powers of the two surfaces. In Fig. 21 the dotted line represents the wave-length—energy curve for the radiation absorbed by the blackened bolometer strip, and the solid line the curve for the strip coated with the surface under investigation.
FIG. 21.
The actual form of the curves may and probably will be quite different from the form in Fig. 20, but it will be found for the same wave-length ON that PN/QN is exactly the same in the two figures.