Prévost's Theory of Exchanges.—In 1792, Prévost of Geneva, when endeavouring to explain the supposed radiation of cold, introduced the line of thought, that any body is not to be regarded as radiating heat only when its temperature is falling, or absorbing heat only when its temperature is rising, but that both processes are continually and simultaneously going on. The amount of heat radiated will depend on the temperature and character of the body itself, while the amount absorbed will depend upon the condition of the surroundings as well as upon the nature of the body. If the amount of heat radiated is greater than the amount absorbed the body will fall in temperature, and vice-versa. This view of Prévost's is called the Theory of Exchanges, and we can see that it is a necessary consequence of our ideas as to the production of heat and light waves by the agitation of electrons in the radiating body.
If the rate of cooling of a body at a certain temperature is measured when it is placed in an enclosure at a lower temperature, it must be borne in mind that the rate of loss of heat is equal to the rate at which heat is radiated minus the rate at which it is absorbed from the enclosure.
A second way in which the heat lost by a body has been measured at different temperatures is by heating a conductor such as a thin platinum strip by means of an electric current, and measuring the temperature to which the conductor has attained. When its temperature is steady, all the energy given to it by the current must be lost as heat, and therefore the electrical energy, which can very easily be calculated, must be equal to the heat radiated by the body minus the heat received from the enclosure.
So many attempts have been made to establish, by one or other of these two methods, the relation between the quantity of heat radiated and the temperature, that it is impossible to give even a passing reference to most of them. Unfortunately, the results do not show the agreement with one another which we would like, but probably the most correct result is that stated by Stefan in 1878, after a close inspection of the experimental results of Dulong and Petit. He stated that the quantity of heat radiated per second by a full radiator is proportional to the fourth power of its absolute temperature.[[1]] Thus the quantity of heat radiated by one square centimetre of the surface of a full radiator whose absolute temperature is T, is equal to ET4, where E is some constant multiplier which must be determined by experiment and which is called the radiation constant. If the absolute temperature of the enclosure in which the surface is placed is T, then the rate at which the surface is losing heat will be E(T4-T14), for it will receive heat at the rate ET14 and will radiate it at the rate ET4.
Stefan's fourth power law has been verified by a number of good experiments, notably those of Lummer and Pringsheim (Congrés International de Physique, Vol. II. p. 78), so that although some experiments do not agree with it, we are probably justified in taking it as correct.
In 1884 Boltzmann added still further evidence in support of this law by deriving it theoretically. He applied to a space containing the waves of full radiation the two known laws which govern the transformation of energy, by imagining the space to be taken through a cycle of compressions and expansions in just the same way as a gas is compressed and expanded in what is known as Carnot's cycle.
Variation of Spectrum with Temperature.—The variation of the character of the spectrum of a full radiator has been determined mainly by the use of Langley's bolometer, but the general nature of the change may be readily observed by the eye.
As the temperature of a full radiator rises it first gives out only invisible heat waves; as soon as its temperature exceeds about 500° C. it begins to emit some of the longest visible rays; and as the temperature rises further, more and more of the visible rays in the spectrum are emitted until, when the radiator is white hot, the whole of the visible spectrum. is produced. Thus the higher the temperature of the radiator the more of the shorter waves are produced.