CHAPTER XXIX.

RADIANT HEAT.

305. Radiation.-When two bodies at different temperatures are brought opposite to each other, an unequal exchange of heat takes place through the intervening distance; the temperature of the hotter body falls, while that of the colder rises, and after some time the temperature of both becomes the same. This propagation of heat across an intervening space is what is meant by radiation, and the

heat transmitted under these conditions is called radiant heat. Instances of heat communicated by radiation are the heat of a fire received by a person sitting in front of it, and the heat which the earth receives from the sun.

This last instance shows us that radiation as a means of propagating heat is independent of any ponderable medium. But since the solar heat is accompanied by light, it might still be questioned whether dark heat could in the same way be propagated through a vacuum.

This was tested by Rumford in the following way:-He constructed a barometer (Fig. 279), the upper part of which was expanded into a globe, and contained a thermometer hermetically sealed into a hole at the top of the globe, so that the bulb of the thermometer was at the centre of the globe. The globe was thus a Torricellian vacuum-chamber. By melting the tube with a blow-pipe, the globe was separated, and was then immersed in a vessel containing hot water, when the thermometer was immediately observed to rise to a temperature evidently higher than could be

due to the conduction of heat through the stem. The heat had therefore been communicated by direct radiation through the vacuum between the sides of the globe and the bulb a of the thermometer.

306. Radiant Heat travels in Straight Lines. In a uniform medium the radiation of heat takes place in straight lines. If, for instance, between a thermometer and a source of heat, there be placed a number of screens, each pierced with a hole, and if the screens be so arranged that a straight line can be drawn without interruption from the source to the thermometer, the temperature of the latter immediately rises; if a different arrangement be adopted, the heat is stopped by the screens, and the thermometer indicates no effect.

The heat which travels along any one straight line is called a ray of heat. Thus we say that rays of heat issue from all points of the surface of a heated body, or that such a body emits rays of heat.

Such language may be thought to imply the hypothesis that heat is a substance (caloric) which is accumulated in bodies, and emitted by them in all directions. A ray of heat would thus consist of a series of molecules of caloric issuing forth one after the other in a straight line. But, in fact, the definition which we have just given of a ray of heat is independent of any hypothesis, and is simply experimental; it amounts merely to the expression of the incontestable fact that the direction of radiation is rectilinear. Whatever idea we may form about the nature of heat, it must be such as to imply this rectilinear propagation.

It is now generally admitted that both heat and light are due to a vibratory motion which is transmitted through space by means of a fluid called ether. According to this theory the rays of light and heat are lines drawn in all directions from the origin of motion, and along which the vibratory movement advances.

307. Law of Cooling.-It is often important to know the law according to which a body cools when placed in an inclosure of lower temperature than its own; for we are thus enabled to take account of the heat which a body loses during the progress of an experiment. This law, when stated in such terms as to be applicable to all possible differences of temperature and all possible conditions of the surrounding medium, becomes exceedingly complex; but when the difference of temperature is small, amounting only to a few degrees, the law known as Newton's law of cooling can be applied without sensible error. It is this: the rate at which the body loses heat is proportional to the difference between the temperature of its surface and

that of the inclosure. If the body be of sensibly uniform temperature throughout its whole mass, as in the case of a vessel with thin metallic sides containing water which is kept stirred, or of the quicksilver in the bulb of a thermometer, the fall of temperature is proportional to the loss of heat, and Newton's law as applied to such a body asserts that the rate at which the temperature falls is proportional to the excess of the temperature of the body above that of the inclosure.

To test this law experimentally, we observe from time to time the excess of the temperature of a thermometer above that of the air in which it is cooling. It is found, that, if the observations are made at equal intervals of time, the observed excesses form a decreasing geometric series.

To express this fact algebraically, let 。 denote the initial excess of temperature, and the ratio of the series. Then the excess at the end of a unit of time will be oo, at the end of two units, and after

Ꮎ

m

до

m

M29

t units o so that if o denote the excess at time t, we have

One pair of observations is sufficient to determine the value of the constant m, which is different for different thermometers.

By rate of cooling is meant the fall of temperature per unit time which is taking place at the instant considered. This is computed approximately by dividing the fall of temperature in a small interval of time by the length of the interval. Its exact value is given by the differential calculus, and is

which is proportional to 6, as asserted by Newton's law

A precisely similar law holds for warming.

307 A. Cooling by Radiation in Vacuo.-The cooling of a thermometer in air is effected partly by the contact of the air, and partly by radiation. When the thermometer is placed in the centre of a vacuous space, radiation alone can operate, namely, radiation from the thermometer to the walls of the inclosure. The law of cooling under these conditions has been investigated experimentally by Dulong and Petit, and was reduced by them to a formula which was found to be accurate within the limits of experimental error for all

the ranges of temperature employed, the excess of the temperature of the thermometer above that of the walls of the inclosure ranging from 20° to 240° C. They found that the rate of cooling did not depend upon the difference of temperature alone, but was faster at high than at low temperatures; also that, for a given temperature of the walls, the rate of cooling was not simply proportional to the excess, but increased more rapidly. Both these results are expressed by their formula

V = cat (a® - 1),

(3)

where V denotes the rate of cooling, c and a constants, t the temperature of the walls of the inclosure, and ✪ the excess of temperature, so that t+0 is the temperature of the thermometer. If we denote this by the formula may be thrown into the more symmetrical form

which suggests the idea that an unequal exchange of heat takes place between the thermometer and the walls, the thermometer giving to the walls a quantity of heat represented by a", and receiving in exchange1 only the quantity at. The former of these amounts remains the same at all temperatures of the inclosure, and the latter is the same for all temperatures of the thermometer.

When the temperatures are Centigrade, the constant a is 1·0077. When they are Fahrenheit it is 10043, the form of the expression for V being unaffected by a change of the zero from which the temperatures are reckoned. The value of c depends upon the size of the bulb and some other circumstances, and is changed by a change of

zero.

ао

By developing a in ascending powers of 0, it will be found that formula (3) agrees sensibly with Newton's law when the excess of temperature does not exceed a few degrees.

308. Law of Inverse Squares.-If we take a delicate thermometer and place it at successively increasing distances from a source of heat, the temperature indicated by the instrument will exceed that of the atmosphere by decreasing amounts, showing that the intensity of radiant heat diminishes as the distance increases. The law of varia

1

According to the theory of exchanges, the heat emitted by the thermometer is cat' plus a constant term depending on the zero of the temperature scale employed, and the heat absorbed by it is cat plus the same constant. It may be remarked that the factor c also depends upon the zero from which temperatures are reckoned as well as upon the length of the degrees, whereas a depends on the latter only.