Linear Expansion. Increase in Bulk. 455 therefore, from any variation of temperature, would have a triple extent of motion. A linear dilatation of this kind is practically obtained in our mercurial thermometers, because the containing glass, although dilatable by heat, is much less dilatable than the fluid within it. As regards solids, we have to inquire so much more frequently respecting the dilatation in length, breadth, or thickness, that is to say, the linear dilatation in one direction, than respecting the increase of general bulk, that tables are commonly made stating only the linear dilatation. And this may be found at once from the above table by recollecting that it is one-third of the increase of bulk. Thus as glass, in passing from the freezing to the boiling heat of water, dilates one part in 416 of its bulk, it will dilate only one-third as much in length, namely one-1248th part.* The expansion of solids by heat has been ascertained by bringing microscopic instruments to bear on marked rods of the different substances heated to various degrees in some liquid. Ramsden invented an instrument which, by a micrometer, would measure the rate of linear expansion on a solid up to the 70,000th of an inch. Whitworth's measuring machine serves to indicate a still smaller amount of expansion by heat, i.e., up to the millionth part of an inch. The expansion of fluids, again, is found by filling a glass vessel with a known weight of a fluid, and then ascertaining how much is caused to run over or escape by a given increase of heat, or how much the fluid rises, when heated, into a long tubular neck like the stalk of a thermometer. This quantity, when the required allowance is made for the expansion of the heated glass vessel (already known), determines the increase in the fluid itself. The general and comparative expansion of solids by heat are exemplified in the following facts:— 660. An iron bullet, when heated, cannot be made to enter an opening through which, when cold, it passes readily. A leaden bullet, cast in a mould, occupies a greater space in the liquid than in the solid state. As it solidifies on the outside first, this leads to the curious results that in all cast bullets of any size there is a small vacuous space of the size of a barleycorn. This is easily observed by cutting the bullet through its axis. It is not Glass without lead expands in length and part, and platinum very ittle less, th. As they contract in these proportions glass may be fused to platinum by heat and they will cohere. All other metals, by reason of their great inequality in linear expansion, separate from glass on cooling. 456 Illustrations of Expansion formed in the centre of the sphere, but usually nearer to the surface. The vacuum thus left in the conversion of the liquids into the solid affects the centre of gravity of the bullet, and causes it to deviate from the line in which it is discharged. Owing to this defect bullets are made in the Royal Arsenal by compression, instead of by casting. In this case the bullet assumes the form of a solid sphere. A glass stopper sticking in the neck of a bottle may often be released by surrounding the neck with a cloth taken out of warm water, or by immersing the bottle in the water up to the neck, or by applying rapidly to the neck the flame of a spirit-lamp. By any one of these methods, the binding-ring of the neck is heated and expanded sooner than the stopper, and so becomes for a short time somewhat more loose upon it. Tapping gently at the same time on the stopper with a piece of wood favours the operation. Pipes of cast-iron for conveying hot water, steam, hot air, or coalgas, if of considerable length, must have joinings which allow a certain degree of shortening and lengthening, otherwise a change of temperature may destroy them. An incompetent person who undertook to warm a large manufactory by steam from one boiler, laid a rigid main pipe along a passage, with lateral branches passing tightly through holes into the several apartments. On his first admitting the steam, the expansion of the main pipe made many fractures at the branches. An iron gate which, during a cold day, may be loose and easily shut or opened, on a warm day may stick, owing to there being greater expansion of it and of the neighbouring railing, than of the earth on which they are placed. The iron bars of railways are now formed with oblique surfaces at their meeting ends, to allow of expansion with changes of weather. The lid of a kettle, which can easily be raised when the water is cold, becomes fixed when the water is boiling. Iron hoops fitted to barrels when hot, contract on cooling, and this contraction has the effect of binding the staves closer together. So the iron tires of wheels when put on in a heated state, contract on cooling and bind together more firmly the fellies and spokes of the wheels. The iron pillars commonly used to support the front walls of houses of which the ground floors are intended to serve as shops, lift up the wall which rests upon them in warm weather, and in cold weather allow it again to subside. The iron bridge which crosses the Thames between London and Southwark, is raised in summer to a higher level than it has in winter. In some vast structures of this kind compensation must be made for these effects of expansion by heat. In the Menai Bridge suspension rollers have been introduced in order to allow of free expansion and contraction. The diurnal effect of heat upon the vast mass of metal in this bridge, is sensible and admits of measurement. Even when the sun is not visible, owing to dense fog or clouds, the position of this luminary is indicated by the greater expansile effect of the direct rays of heat on the metal. When the stones of a building are held together by clamps or bars of iron driven into them, the expansion of these clamps in summer will force the stones apart sufficiently for dust or sandy particles to lodge between them: and then, on the return of winter, the stones, not being at liberty to close as before, will cause the ends of the shortened clamps to be drawn out, and the effect increasing with every succeeding year, the structure may at last be dangerously loosened. 661. The expansion of solids by heat, or their contraction on the withdrawal of it, is attended with considerable force. It is equal to that which would be required to elongate or condense the material to the same extent by mechanical means. According to Barlow a bar of malleable iron a square inch in section is stretched Tooth of its length by a ton weight. A similar elongation is produced by a rise of 16° F. In this climate there is often a variation of 80° between the cold of winter and the heat of summer. A wrought-iron bar, ten inches long, will vary th of an inch, and, if its two ends be securely fastened, will exert a strain equal to fifty tons on the square inch (Miller). These facts are of the greatest importance in the construction of buildings or bridges with iron pillars and girders. The pitch of a pianoforte or harp is lowered on a warm day or in a warm room, owing to the expansion of the, strings being greater than that of the wooden frame-work; and on a cold day, the reverse will happen. Thus an instrument, which has been well tuned in a morning drawing-room, may make discords when the crowded evening party has heated the room. Bell wires too slack in summer, may be of the proper length in winter. A difference of the 100th of an inch in the length of a common pendulum causes a clock to err about ten seconds in twenty-four hours, and a rise or fall of 25° of Fahrenheit's thermometer may produce this difference. In order to counteract this expansion and 458 Unequal Expansion of Solids. increase of length in the pendulum rod, a glass vessel containing mercury is substituted for the solid ball or weight. As the rod expands downwards so the liquid mercury expands upwards, and the centre of gravity is therefore raised just enough to compensate for the lengthening of the pendulum rod. Thin strips of two metals differently expansible by heat, may be soldered together throughout their length to form one long straight riband. If this be then heated or cooled, it bends or curls like damp paper held before a fire. A very sensitive thermometer has been constructed on this principle by Breguet. 662. As a rule all solids expand equally in their three dimensions, but owing to the force of cohesion in some crystalline solids being stronger in one direction or axis than in another, the effect of heat upon them is to expand them unequally. When a rhombic crystal of Iceland spar was heated from 32° to 212°, Mitscherlich observed that it was so elongated as to render the obtuse angles more acute. There was a difference of 8 degrees in the inclination of the surfaces of the crystal. Crystals when heated, do not expand quite equally in breadth and in length. The same is true of fibrous substances, as wood, which expands and contracts more in breadth than in length, hence wood is well fitted for the pendulum rods of astronomical clocks. This is also instanced in the leaking, during cold weather, of a ship's deck, which in warm weather is tight. Bodies expanded by heat, unless when their intimate structure is changed by it, regain exactly their former dimensions on being cooled. Heat produces no permanent change in them. They weigh the same before and after. As is seen in the preceding table (p. 454), the expansion of liquids by heat is much greater than of solids. 663. In a general way it may be stated that the same quantity of heat which would expand a solidoth part would expand a liquid th and a gas rd of its volume. In reference to gases, Regnault found that 1000 parts of atmospheric air in being heated from 32° tc 212° became 1367 parts. All gases and vapours expand in about equal proportions between these temperatures, and this may be taken at of their volume at 32°. This is equivalent to 19 of the volume at 32° for each degree of Fahrenheit between 32° and 212°, so that when heated 490°, air, or any gas or vapour at the temperature of 32o, would be doubled in volume. The expansion of gases differs remark Expansion of Liquids. 459 ably from that of liquids and solids in these respects; 1. It takes place equally for equal increments of heat, and thus an air-thermometer within a certain range, serves to measure degrees of tempe rature more accurately. 2. All gases, in spite of their great difference of density, expand equally for equal additions of heat. Thus carbonic acid and hydrogen expand in an equal ratio between 32° and 600°, although carbonic acid is 22 times heavier than hydrogen. 664. Expansion of Liquids.—The lighter the liquid and the lower its boiling point, the more it expands by heat. Thus alcohol at the same temperature increases in volume more than water, and ether more than alcohol. By the addition of 180°, alcohol is observed to expand th of its bulk, water st, and mercury th. Owing to this alteration in volume, hot water is lighter than cold, and when coloured with archil, it may be made to float visibly on cold water. Of all liquids there is none which undergoes such remarkable changes in bulk by the addition or withdrawal of heat, as water. A cubic inch of water in passing to the solid state forms rather more than a cubic inch of ice, and a cubic inch of water, heated to 212° degrees, is converted into 2000 cubic inches of aqueous vapour or steam. A cask quite filled with liquid in winter, must in summer force its plug or burst: and a vessel which has been filled to the lip with warm liquid, will not be full when the liquid has cooled. If a teakettle be quite full when placed on the fire, it overflows when heated to the boiling point. It is thus that the mercury rises and falls in the stalk of a thermometer, in proportion as that contained in the bulb is heated or cooled. 665. There exists, however, in the case of water, a singular exception, already mentioned, to the law of expansion by heat and contraction by cold, producing certain beneficial results in nature. Water contracts only down to the temperature of 40°, while, from that to 32°, which is its freezing point, it again dilates or expands. Water is the only liquid which is known to possess this remarkable property.* If we apply heat to a quantity of water at 39° * Some melted metals and alloys expand on passing from the liquid to the solid state. This property is observed in bismuth, in fusible metal, in type metal, and cast iron, especially that variety of iron which contains phosphorus. It is owing to this expansion in cooling that such exquisitely fine castings of iron are obtained, as may be seen in the Berlin iron ornaFor a similar reason type metal takes the sharpest impression in stereotype castings. ments. |