284 MECHANICAL EQUIVALENT OF HEAT. [129. This water (between 55° and 60°) by 1° F. requires for its evolution the expenditure of work adequate to lift 772 lb. I foot. may be expressed in terms of the metrical system as follows:A unit of heat, or the heat capable of raising I gramme of water 1° C., is equivalent to work required to lift 423'55 grammes through a height of metre. FIG. 114. The apparatus employed in the determination of the amount of heat given out during the friction of water consisted of a brass paddle-wheel furnished with eight sets of vanes, revolving between four sets of stationary vanes. Fig. 114, No. 1, shows a vertical section of the paddle, and No. 2 a transverse section of the vessel and paddle. This paddle was fitted securely into a copper vessel, c, fig. 115, provided with a lid in which were two apertures, one allowing the passage of the axis without actual contact with it, the other t, for the insertion of the thermometer graduated to hundredths of a degree F. A weighed quantity of water was introduced into the vessel, or calorimeter, c, and its temperature ascertained with minute precision. The amount of heat produced was ascertained by again observing the temperature of the water in c, with the same precision, at the close of each experiment. In order to prevent loss of heat by conduction, the vessel was supported upon a wooden stool, and connected by a piece of boxwood, b, with the apparatus for producing rotation. Motion was given to the axis by the descent of two leaden weights, one of which is shown at w, fig. 115. These weights were suspended by strings over two wooden pulleys, one of which is shown at p, resting on friction rollers, f. ƒ, and the palleys were connected by fine twine with the roller r, which, by means of a pin, could be readily connected with, or detached from the calorimeter, c. The descent of the weights was measured on the scale, s. 129.] SOURCES OF HEAT-PERCUSSION. 285 A similar, but smaller apparatus, made of iron instead of brass, with six rotatory and eight stationary vanes, was used for measuring the heat produced by the friction of mercury. The apparatus for measuring the heat produced by the friction of solids, consisted of a vertical axis carrying a bevelled cast-iron wheel, against which a stationary bevelled wheel was pressed by a lever; the wheels were enclosed in a cast-iron vessel filled with mercury. The rise of temperature in each experiment amounted in the case of water to about 0° 313 C., or o°563 F. In the case of mercury, the mean rise during each experiment in one series was 1°339 C., or 2°41 F., and in case of cast-iron, it was 2°39 C., or 4°3 F. 3. Percussion, which is a combination of friction and compression, is a method of eliciting heat which is frequently practised, as is seen in the use of the common steel and flint, where the compression developes heat enough to set fire to the detached portions of steel. In firing iron shot against an iron target, as in the artillery trials at Shoeburyness, a sheet of flame is commonly seen at the moment of the collision, owing to the arrest of motion in the projectile, and its manifestation in the form of heat. Mr. Whitworth has indeed employed iron shells which are exploded simply by the heat developed by the concussion on striking the surface of the iron target. It is a practice not uncommon among blacksmiths, to show their agility and dexterity by hammering a piece of cold iron on the anvil until it becomes red-hot from the heat produced by compression. It is, however, remarkable that iron once treated in this way cannot again be made red-hot by hammering unless it has been subsequently heated in the forge. Many other similar instances might be adduced; in the rolling of brass and of copper, for example, the bars, as they issue from the rollers, between which they have been subjected to enormous pressure, become much heated, although they were quite cold when they entered the rolling mill. 4. Another source usually resorted to for procuring heat artificially is chemical action. Whenever this occurs with great intensity, heat is evolved, and it is very generally accompanied by evolution of light, of which a common fire affords the best practical illustration. The chemical actions which are constantly going on in living animals are also never-ceasing sources of a regulated emission of heat, and they differ only from those of the furnace in the more moderate and subdued amount of heat generated in a given time and in a given space. The quantity of heat generated by the combination of definite weights of the bodies which unite is perfectly definite in amount, depending only on the quantity and quality of the substances entering into combination. (199 et seq.) 5. Accumulated electricity is another source of intense heat. 286 THEORIES OF THE NATURE OF HEAT. [129. 6. In addition to the above-mentioned sources of heat, Pouillet (Ann. Chim. Phys. 1822 [2], xx. 141) has shown that the simple act of moistening any dry substance is attended with slight yet uniform disengagement of heat. With bodies of mineral origin, when reduced to a fine powder with a view of increasing the extent of surface, the rise of temperature does not exceed from 0°3 to 1°C.; but with some vegetable and animal substances, such as cotton, thread, hair, wool, ivory, and well-dried paper, a rise of temperature varying from 1° to even 6° C. has been observed. 7. Besides these sources of heat there can be no doubt of the existence of a nucleus of intensely heated matter within the body of the earth itself. If a thermometer be buried from 10 to 12 metres beneath the surface, it is found to undergo no change with the alternations of the seasons, but on proceeding to greater depths the thermometer is found to rise progressively, though not quite uniformly at all places. If it be assumed that on the average this increase of temperature is 1° C. for every 29:3 metres of descent,* and if this rate of progression be continued uniformly as the depth increases, it would be at the rate of 55° C. or 100° F. per mile; so that at a depth of a mile and a half the temperature would be as high as that of boiling water, and at the depth of 40 miles, a temperature of 2204° C. (4000° F.) would be attained, considerably beyond the melting point of cast-iron or even of platinum. The existence of this central heat, which rises to a degree sufficiently high to fuse the rocky constituents of the earth's crust, is abundantly manifested in the torrents of melted lava which are from time to time poured forth in volcanic eruptions; and the occurrence, at great depths, of rocks which bear evident marks of igneous action, attests the high temperature of the interior of the earth. (130) Nature of Heat-Mechanical Theory of Heat.-Two principal views of the nature of heat have been entertained since experimental science has been actively cultivated. One of those views, which is supported chiefly by the phenomena of latent heat and chemical combination, regards heat as an extremely subtle material agent, the particles of which are endowed with high selfrepulsion, are attracted by matter, but are not influenced by Cordier considers 1° C. in 25 metres, or 1° F. in 45 feet, not too high an estimate. In two shafts of the depth of 2000 feet, one near Durham and the other near Manchester, the temperature increases 1° F. for 65 to 70 feet; in the Saxon argentiferous lead mines, it was found to be 1° in 65 feet, and the increase of temperature observed in boring the well of Grenelle at Paris was 1o in 60 feet.-Lyell, Princ. Geol. 11th ed. ii. 205. 130.] TREORIES OF THE NATURE OF HEAT. 287 gravity. On the other theory heat is supposed to be the result of molecular motions or vibrations. The latter view was powerfully advocated by Count Rumford, and by Davy, who, in the early part of the present century, instituted an important series of experiments upon the production of heat by friction. Many philosophers were subsequently induced to adopt the theory of the vibratory nature of heat as maintained by these eminent men. The opinions of Davy upon this subject. are thus stated by him in his treatise on Chemical Philosophy, p. 95. 'It seems possible to account for all the phenomena of heat, if it be supposed that in solids the particles are in a constant state of vibratory motion, the particles of the hottest bodies moving with the greatest velocity, and through the greatest space; that in liquids and elastic fluids, besides the vibratory motion, which must be conceived greatest in the last, the particles have a motion round their own axes, with different velocities, the particles of elastic fluids moving with the greatest quickness; and that in etherial substances the particles move round their own axes, and separate from each other, penetrating in right lines through space. Temperature may be conceived to depend upon the velocities of the vibrations; increase of capacity, on the motion being performed in greater space; and the diminution of temperature during the conversion of solids into fluids or gases, may be explained on the idea of the loss of vibratory motion, in consequence of the revolution of particles round their axes, at the moment when the body becomes fluid or æriform, or from the loss of rapidity of vibration in consequence of the motion of the particles through greater space.' The experiments of Joule on the definite amount of heat developed by friction (Phil. Trans. 1850, 61) have recalled the attention of philosophers to these views; and the mathematical theory of heat propounded by S. Carnot, in accordance with them, has undergone recent revision, particularly by Mayer, Clausius, Rankine, and Sir W. Thomson, in consequence of which the hypothesis involved in the term the mechanical theory of heat has been favourably received. Upon this view, although the ideas of Davy quoted above have been adopted with extensions and modifications by some writers, it is not necessary to assume the particular kind of motion in the interior of bodies which may be conceived to be the cause of the peculiar phenomena of heat, but only to suppose that a motion of the particles exists, and that the heat is a measure of the kinetic energy of this motion. The important principle of the theory is this:-In all cases where mechanical work is produced by heat, a quantity of heat is used up, proportional to 288 DIFFERENCE BETWEEN HEAT AND TEMPERATURE. [130. the work done: and, conversely, the same quantity of heat can be again generated by the expenditure of just so much mechanical effect. Tyndall, in his work on Heat considered as a Mode of Motion, has applied the mechanical theory of heat to the explanation of many of its phenomena with great ingenuity and clearness. The chemical considerations, which are indeed the most difficult to reconcile with this theory, are, however, only incidentally touched upon by him. A simple view of the mathematical considerations involved is given in B. Stewart's Elementary Treatise on Heat, and Maxwell's Theory of Heat. § I. EXPANSION-MEASUREMENT OF TEMPERATURE. (131) Difference between Heat and Temperature.-The effect of a hot or of a cold substance upon our sensations enables us to distinguish the one from the other; but the impression thus produced is only comparative, and affords no exact criterion of the amount of heat, the sensation produced being referable to the temperature of that part of the body to which the substance is applied at the particular moment. Heat and cold are, in fact, merely relative terms; cold implying not a negative quality antagonistic to heat, but simply the absence of heat in a greater or less degree. It is singular that intense cold produces the same sensation as intense heat; and a freezing mixture, as well as boiling water, will blister the part to which it is applied. Heat produces no alteration in the weights of bodies; consequently the balance cannot be employed as a measure of its amount. All bodies, however, when heated, acquire an increase in volume, and return to their original volume in cooling, and the measure of the amount of expansion is universally employed as the measure of temperature. It is necessary to draw a distinction between the terms heat and temperature, which are applied to indicate very different things. By the term heat is meant, in philosophical language, the power, whatever it be, which excites in us the sensation of warmth; temperature is a measure of the tendency of a body to impart heat to other bodies: bodies are at equal temperatures when neither transfers heat to the other. If two or more masses of matter, of the same or of different kinds, such as mercury, oil, water, or spirit of wine, when brought into contact with a thermometer, cause the mercury which this instrument contains to stand at the same point, they are said to have the same tempeBut the temperature of a body affords no indication of rature. |