the large amount of heat radiated by the lamp-black surface falls on the silver surface, for in this case only a small proportion of the incident heat is absorbed. 247*. The Relation between the Amount of the Radiation and the Temperature of the Body.-In order to determine the connection between the amount of the radiation and the temperature of a body, Dulong and Petit used as radiating body the spherical bulb of a large thermometer. The bulb was heated to about 300°, and then introduced into a hollow copper sphere, which was kept at a constant temperature, and the sphere was exhausted. The temperature of the bulb was indicated by the position of the mercury thread in the stem of the thermometer, which projected from the copper vessel, and was read at equal short intervals of time. The fall of temperature v in one second they called the velocity of cooling, so that if W is the water value of the thermometer bulb, the loss of heat in unit time, Q, is given by Q=Wv. As a result of their experiments, Dulong and Petit came to the conclusion that if t is the temperature of the radiating body, and t' that of the chamber, then v=k(a2 — a''), where k and a are constants depending on the nature and area of the surface of the radiating body. Dulong and Petit's law, which is quite empirical, has, however, been found only to hold over a small range, and Stefan, from an examination of their results, has been led to the conclusion that the total radiation emitted by a body is proportional to the fourth power of the absolute temperature. Thus if 7 is the absolute temperature of the body, the total radiation will be represented by aT4, where a is a constant depending on the extent and nature of the surface of the body. In the same way the heat radiated by the walls, if they are at an absolute temperature To, will be proportional to 74. The quantity of this radiation absorbed by the body will be a T4, since the emissive power and absorbing power of a body are the same. Hence the total loss of heat, 2, by the body in unit time is Q=a(T1 - T1). If S is the area of the radiating surface of the body, then a=Sc, where c is a constant depending on the nature of the surface only. Hence Q=Sc(T1- T4). If the temperature of the enclosure is the absolute zero, and that of the body 1°, so that 7=0 and 71=1, and the surface of the body is unity, we get 2=c, or the quantity represents the heat radiated per second from a square centimetre of the surface of the body, when the temperature of the body is 1° on the absolute scale, and the enclosure is at the absolute zero. If the difference between the temperature of the body and the enclosure is 0, we have Q=Sc{(To+0) — T ̧1}, and if is small, so that we may neglect terms in 2 and higher powers. Hence for small changes in the difference of temperature between the body and the enclosure Q is proportional to 8. In the case of a body surrounded by a gas, as we have already pointed out, the cooling is partly due to convection currents and conduction. In such a case Newton supposed that the rate of cooling, i.e. the quantity of heat lost by the body in unit time, was proportional to the difference in temperature between the body and the surrounding medium. This law, which is known as Newton's law of cooling, only holds good for small excesses of temperature. For such excesses, however, as ordinarily occur in calorimetry Newton's law is sufficiently accurate. 248*. Measurement of Specific Heat by the Method of Cooling. -According to Newton's law of cooling, the quantity of heat Q1 lost by a body during the time t, when its temperature is degrees above the surrounding medium, is given by Q1=kSot, where S is the area of the cooling surface, and k is a constant dependent on the nature of the surface. If in a time the temperature falls by an amount d0, the quantity of heat lost must be Ms80, where M is the mass of the body and s is its specific heat. Hence Ms. 0.80.=Q1=kSOt. If now the experiment be repeated, using the same radiating surface and starting at the same temperature 0, and the time 1 be noted in which a second body of mass M1 and specific heat s1 cools through 80, we shall have Hence, if we know M, M1, t, and 1, we can obtain the ratio of the specific heats of the bodies. In an actual experiment the bodies to be experimented on are contained in a calorimeter, the outer surface of which is coated with lampblack. This calorimeter is suspended inside a vessel with double walls, the space between the walls being filled with water so as to keep the temperature of the enclosure constant. Of course, due allowance must be made for the water value of the calorimeter, thermometer, and stirrer. This method of measuring specific heats is found only to work satisfactorily in the case of liquids, since it is only with these that the contents of the calorimeter can be kept at a uniform temperature throughout during the cooling, this condition being obtained by continuous stirring. The further consideration of radiant heat will be deferred till the chapters dealing with the emission, absorption, &c., of light, since there is no sharp physical line of demarcation between what we recognise by one set of senses as radiant heat, and what we recognise by our sense of sight as light. CHAPTER VI THE MECHANICAL THEORY OF HEAT 249. Theories as to the Nature of Heat.-Up to the end of the eighteenth century there existed two rival theories as to the nature of heat. According to one of these theories, known as the caloric theory, heat was supposed to be a subtle, elastic, imponderable fluid called caloric, which permeated all kinds of matter existing in the interstices between the molecules. According to the other theory, which was only held by very few, heat was supposed to be due to the rapid motion of the molecules of matter. It was well known that heat could be produced by friction or percussion, and the supporters of the caloric theory explained these facts by supposing that in the case of percussion the caloric was squeezed out of the body, and hence flowed into a neighbouring body such as a thermometer, and, in the case of friction, that during the friction some of the body was rubbed off, and that the capacity of matter for caloric was less in the form of a powder than in the form of a solid block. That this explanation of the production of heat by friction was untenable was first shown by Count Rumford in 1798. Being struck by the large amount of heat developed when cannon were being bored at the arsenal at Munich, Rumford performed an experiment in which a blunt steel borer was rotated while kept pressed against the bottom of a hole in a large mass of gun-metal. The borer was rotated nearly a thousand times, and the heat developed was sufficient to raise the temperature of the whole block, which weighed 113 lbs., about 70° F., while the amount of metal rubbed off from the bottom of the hole was only 837 grains troy. Rumford, in the account of his experiments, draws attention to the fact that the supply of heat obtained in this way from a given lump of metal seems quite inexhaustible, and hence cannot be a material substance, but must be "motion." The supporters of the caloric theory, however, still maintained that the source of heat was the abraded metal, till this explanation was completely refuted by an experiment performed by Davy. He rubbed together two blocks of ice at a temperature below o° C., and found that heat was developed and the ice melted. Since it was allowed by the calorists that water contained more caloric than ice, if we can produce water by the friction of ice, the heat developed must be due to some other cause than the extrusion of caloric. We have seen, when dealing with radiant heat, that a hot body is continually radiating heat into surrounding space; and when we come to the consideration of the subject of light, we shall see that there is conclusive evidence that radiant heat, after it leaves the hot body, exists as a wave-motion in some medium surrounding the body. Now in order to set up waves in a medium, we must have a body which is itself in motion in the medium. Thus, since a hot body can set up such waves, we infer that it must be in a state of motion. Also, since the highest-power microscope is quite unable to detect any motion in a hot body, we infer that this motion must be a motion of the molecules as a whole, or of the parts of a molecule, or both combined. We are hence reduced to the theory that heat is a "mode of motion." 250. Dynamical Equivalent of Heat-First Law of ThermoDynamics.-In Rumford's experiments, the heat produced in the cannon was indirectly due to the work done by the horse which turned the boring tool, and it is obviously of interest to see what connection there is between the work done by the horse and the amount of heat produced. We shall see in later sections, that whenever mechanical work is converted into heat, or mechanical work performed at the expense of heat, there exists a constant relation between the work done and the heat produced or lost. The quantity of work which must be done in order that, when all the work is converted into heat, the unit quantity of heat energy may be produced is called the mechanical or dynamical equivalent of heat. If is the value of the mechanical equivalent, then the relation between the work W converted into heat and the quantity of heat H produced is given by the equation W=JH. This equation, which we shall justify subsequently, expresses symbolically what is known as the first law of thermo-dynamics, which may be stated as follows:- Whenever mechanical energy is converted into heat, or heat into mechanical energy, the ratio of the mechanical energy to the heat is constant. 251. The Determination of the Mechanical Equivalent of Heat. The first to experimentally show that the first law of thermodynamics is true, and determine the value of the mechanical equivalent of heat, was Joule, who between 1840 and 1878 carried on a classic series of experiments on this subject, in which he showed that the value for the mechanical equivalent was always the same, although the methods employed for converting the mechanical energy into heat differed greatly. The first method employed by Joule consisted in measuring the heat developed when a known amount of work was done in stirring water. The apparatus used consisted of a copper vessel B (Fig. 201), inside which a brass paddle-wheel worked. A system of partitions were fixed |