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EXPANSION OF SOLIDS.

the actual quantity of heat which it contains.

289

A pint of spring

water may raise a thermometer to the same degree as a gallon of the same water, though it is obvious that the larger quantity of the liquid contains the greater amount of heat. Again, suppose a thermometer to stand in water at 40° in one instance, and at 80° in another, in equal quantities of the liquid; it would be a mistake to suppose that in the latter case the water is twice as hot as in the former. The zero of the thermometer scale is an arbitrary point; the temperature of a body which contained no heat or the zero of a perfect thermometer scale would be - 273° C. or -459°4 F.

(132) Expansion of Solids.-Solids, as might be expected from the cohesion among the particles, expand less for equal elevations of temperature than either liquids or gases. Solids generally expand uniformly in all directions, and on cooling return to their original shape. Lead, however, is so soft that its particles slide over each over in the act of expansion, and do not return to their original position. A leaden pipe of a few feet long, if used for conveying steam, becomes permanently lengthened by some inches in a short time; and the leaden flooring of a sink which often receives hot water, becomes, in the course of use, thrown up into ridges and puckers.

Mitscherlich (Poggendorff's Ann. 1827, x. 137) discovered that all those crystals which possess a doubly refracting action upon light, expand unequally in different directions when heated. The shape of a crystal of calcareous spar, for instance, is slightly altered when heated: the obtuse angles become more acute, and the inclination of the faces of the crystal to each other becomes lessened 8 by an elevation of temperature from 0° to 100° C. The crystal elongates most in the direction of the optic axis, and indeed it actually contracts at the same time in directions at right angles to this. Such crystals, however, form no exception to the general rule that the volume of bodies is increased by heat. It has been ascertained, for instance, that a crystal of calc-spar increases in volume between o° and 100° C., to the extent of I part in 510.

Different solids expand very unequally for equal increase of temperature: zinc, for example, expands much more than iron, and iron more than glass. The cubical expansion of a body may be obtained very nearly by multiplying the linear expansion (or expansion in length) by 3. The following table gives some measurements of the expansion both in length and in volume which is experienced by various solid bodies:

The following results, which were obtained by Daniell, with bars heated in a cylinder of baked black-lead ware, and measured by his pyrometer scale (140), show the expansion of certain solids at high temperatures. (Phil Trans. 1841, 456.)

The addition of heat beyond a certain point overcomes the cohesion of the solid, and it assumes the liquid form. The temperature at which this change takes place varies greatly with the nature of the substance, some solids melting at a much lower temperature than others.

(133) Expansion of Liquids.-Liquids expand much more than solids. They differ also in expansibility to a much greater

133.]

EXPANSION OF LIQUIDS.

291

extent generally the most volatile are most expansible. This is remarkably shown in the case of the liquids obtained by the condensation of the gases (196), which are even more dilated by heat than aëriform bodies.

It has, however, been found that in many liquids of analogous chemical composition the expansion is very nearly uniform, if the comparison be made, not at the same temperature, but at corresponding temperatures, that is to say, at equal distances from the boiling point, the point at which cohesion is just about to yield to the repulsive action of heat. The same thing has also been observed between some liquids which present no analogies in their nature, as was originally observed by Gay-Lussac in comparing the expansion of alcohol and carbonic disulphide. The subject has more recently been investigated with great care by Pierre (Ann. Chim. Phys. [3], 1845, xv. 325; 1847, xix. 193; 1847, xx. 5; 1847, xxi. 336; 1851, xxxi. 118) and by Kopp (Pogg Annal. 1847, lxxii. 1 and 223; Liebig's Annal. 1855, xciii. 157; xciv. 257; and xcv. 303). In most instances there is a very satisfactory agreement between the results obtained by these observers upon the same liquid. Some of their results are embodied in the following table. The volume of each liquid at its boiling point is taken at 10,000. The numbers in the table indicate the volume of the liquid, first at 40° C. below the boiling point of each liquid, and again at a still lower temperature, 70° C. below that point; the most expansible liquids being placed first in the table.

The expansion of the different liquids used in these experiments was determined by enclosing in tubes similar to those employed for thermometers, known volumes of the liquid at a particular temperature, and measuring the expansion experienced in each case, making the necessary correction for the dilatation of the glass envelope. In fact, a number of thermometers were prepared, in each of which one of the various liquids under experiment was substituted as the expansible material in place of mercury.

In comparing corresponding compounds obtained from wood-spirit and from alcohol (two homologous organic liquids), a remarkable parallelism in their rates of expansion has been observed. The ethyl and methyl acetates correspond closely with each other, and with the butyrates of the same substances. The ethyl and methyl bromides also correspond. So do the ethyl and methyl iodides. Wood-spirit and alcohol do not differ greatly from each other, or from an allied compound produced during fermentation, which has received the name of fusel oil; but the rates of expansion of the homologous butyric, acetic, and formic acids differ rather more widely. Ethyl formiate is metameric with methyl acetate

135.]

EXPANSION OF GASES-THERMOMETERS.

293

(that is to say, it is composed, in 100 parts, of the same chemical elements, in precisely the same proportions), and both expand also at exactly the same rate; but this uniformity of expansion in metameric bodies is not always observable: considerable differences are found to exist, for example, between the rates of expansion of the metamerides Dutch liquids and monochlorinated hydrochloric ether, and between monochlorinated Dutch liquid and dichlorinated hydrochloric ether.

Two elements, however, such as chlorine and bromine, which are most closely allied in chemical properties, and which form compounds possessing the same crystalline form, may yet combine with the same element, and produce liquids which have totally different rates of expansion. For instance, Dutch liquid and ethylene dibromide differ considerably, and no correspondence exists between the expansion of silicic bromide and silicic chloride.

(134) Expansion of Gases.-When the temperature rises beyond a certain point in liquids, they change their state, cohesion is entirely overcome, repulsion predominates, and the aëriform condition supervenes. Expansion for equal increments of temperature is in gases far greater than in solids or in liquids. If the open extremity of a tube, on the other end of which a bulb is blown, be plunged into water, the heat of the hand will be sufficient to dilate the air in the bulb so as to cause a

part of the enclosed air to escape. In gases where cohesion is entirely overcome, no such variety in expansion is exhibited as in the case of liquids and of solids; and it may, without sensible error, be assumed that in gases, and also in vapours at considerable distances above their points of condensation, the rate of expansion is the same in all. From the freezing to the boiling point of water, they increase in volume more than onethird, or, 1000 parts at o° becoming 1367 at 100° C.*

(135) Thermometers -Whether the body be in the solid, the liquid, or the gaseous condition, the change of volume is very nearly proportionate to the change of temperature; and the same body, with the same initial temperature, always expands to the same extent for the same increase of temperature: for example, a body at the temperature of 20° will, however often it be heated to 100°, always expand to the same volume; and on cooling to its original temperature of 20°, it will always return to its original volume.

By ascertaining exactly the extent of this expansion, a ready and available measure of temperature is afforded; and accord

Regnault (Ann. Chim. Phys. 1842 [3], iv. 5 and v. 52) and Magnus (Ib. [3], iv. 330) have published independent and elaborate investigations on the expansion which various gases undergo on the application of heat. According to their experiments, the coefficient of expansion is not rigidly uniform for all gases; the expansion being greatest for those which are most readily condensible, whilst for the gases which have resisted all efforts to liquefy them, scarcely any appre