169.]

MEASURE OF SPECIFIC HEAT.

347

equal volumes of water, or of oil, or of any liquid, at different temperatures, are mixed with due precautions, they yield a mass the temperature of which is exactly the mean of the two. For instance, a litre of water at 32° F., added to a litre of water at 100°, gives two litres of water at 66°. But if two dissimilar liquids be used, the result is different. A litre of water at 32° mixed with a litre of mercury at 100°, gives a mixture the temperature of which is only 52°; but a litre of mercury at 32° mixed with a litre of water at 100°, gives a mixture having a temperature of 80°. Mercury is therefore often said to have less capacity for heat than water. It requires a smaller amount of heat to raise it a given number of degrees in temperature than is required to produce an equal elevation of temperature in the same volume of water. If equal weights of the two bodies be employed, instead of equal volumes, the difference is still more striking. A kilogramme of mercury at 20°, agitated with a kilogramme of water at 54°, gives a mixture the temperature of which is 53°. The water loses 1°, while the mercury gains 33°. The quantity of heat which would be required to raise any substance 1° C. in temperature, or more correctly, from 。° C. to 1° C., compared with the quantity of heat required to raise an equal weight of water through the same interval, is called its specific heat: therefore, taking the specific heat of water as 1, that of mercury will be 0033.

(169) Modes of Measuring Specific Heat.-Three modes of determining the specific heat of a body have been employed. The best is the method of mixtures just described; another method consists in determining the rate of cooling of equal masses of the different bodies under similar circumstances; and the third con-` sists in determining the amount of ice which a given mass of each body will melt when cooled from a fixed temperature, say 100° C., to the freezing point. This last method was employed by Lavoisier and Laplace; but though excellent in principle, the difficulties in practice render the results inaccurate.

If the body be in the solid form, the process of mixture may still be employed to ascertain the specific heat, by heating to the same degree of temperature, equal masses of the different solids which are to be compared, then immersing each in an equal volume of water, and observing the elevation of temperature produced in each case. Experiments conducted in this manner show that great differences in specific heats exist. Researches of this nature are necessarily attended with great difficulty, owing to the variety of sources of error, and the number of pre

348

MEASURE OF SPECIFIC HEAT.

[169.

Full particulars

cautions required in order to insure accuracy. upon these points are given in the papers of Dulong and Petit upon this subject (Ann. Chim. Phys. 1819 [2], x. 395), and of Regnault (Ib. 1840 [2], lxxiii. 5; 1841 [3], i. 129; 1843, ix. 322; 1849, xxvi. 261; 1856, xlvi. 257; and 1861, lxiii. 5).

In the Phil. Trans. for 1865 will be found an elaborate discussion by Kopp of the merits and defects of the various methods of determining specific heats. The following is the method which he has himself devised for determining speedily, and with considerable approach to accuracy, the specific heat of any substance either solid or liquid. If the material for trial be a liquid, it is introduced into a thin glass tube. The tube, with its contents, is heated by immersion in a mercury bath, which is maintained at a constant temperature, not exceeding 50° C., and then immediately plunged into a small calorimeter containing a known quantity of cold water, and the rise of temperature thus effected is accurately noted. If the calorific capacity of the tube without the liquid be first determined, and the amount so ascertained be deducted from the rise of temperature occasioned when the experiment has been repeated after the substance has been introduced into the tube, the specific heat of the substance under trial is easily calculated. If the material be solid, it is reduced to small fragments, or it is employed in the form of powder, and is placed in the glass tube with a known amount of a liquid in which it is not soluble, usually either water or coal naphtha. The calorific capacity of the tube with the naphtha is first ascertained, and then the experiment is repeated after the addition of the solid under trial.

The second mode of ascertaining the specific heat is founded on the different rates of cooling exhibited by equal masses of dissimilar composition; those which have the greatest specific heat cooling most slowly. The bodies are finely powdered, and introduced into an annular polished silver vessel, which is placed in a vacuous chamber coated internally with lamp-black, and surrounded by ice. By this arrangement the substances have virtually equal surfaces and equal radiating powers, and cannot be cooled by convection. The silver vessel, with a thermometer placed in its interior compartment, is heated to 30° or 40° C., and introduced into the chamber, from which the air is pumped as rapidly as possible; when the temperature indicated by the thermometer has fallen to 10° the time is noted, and again when the temperature has reached 5°, by determining the time occupied by each in cooling through this interval, aud by comparing this with the time required by an equal quantity of water to cool

169 a.]

MEASUREMENT OF SPECIFIC HEAT.

349

through the same thermometric interval, a series of numbers is obtained which represent approximately the specific heats of the bodies in question; making the time occupied by water in cooling, the unit of comparison, or 1. The differences in conductivity which varies greatly in the different bodies submitted to trial, is, however, a serious objection to the employment of this method for solids; for liquids it is less liable to error.

The following table gives a few of the results of Regnault upon specific heat, obtained by the process of mixture or im

mersion:

Specific Heats of Equal Masses between 。° C. and 100° C.

(169 a) Causes of Alteration of Specific Heat.-Any circumstance which alters the relative distances between the particles of which a body is composed, at the same time alters its specific heat. Mechanical compression sufficient to produce a permanent alteration in density is attended by a corresponding decrease in specific heat :-For instance, the specific heat of a piece of soft, well-annealed copper was found to be from o'09501 to 009455; the same copper, after hammering, had a specific heat of from 0'0936 to 00933; on being again thoroughly annealed, so as to recover its former density, its specific heat was from 009493 to 0'09479, or almost exactly the same as at first. Again, in dimorphous bodies (86) the densest form has in some cases been found to possess the lowest specific heat. Regnault (Ann. Chim. Phys. 1841 [3], i. 204) found that diamond, for example, has a specific heat of 01468; whilst graphite has a specific heat of o 2018, or one-third higher; and the specific heat of charcoal is still higher, or o'2415. Kopp, however, considers that this rule is not general; the specific heats of calc spar and aragonite, iron pyrites and marcasite, rutile and brookite being scarcely different. It has also been thought that to this diminution of specific heat by compression may be partially due the heating of cold metallic bars observed during the operation of rolling: they become denser, and consequently have less capacity for heat. It is, however, more probable that this is simply a case of the conversion of sensible motion into the molecular motion which produces heat, similar to that which attends friction or percussion.

350

SPECIFIC HEAT OF AERIFORM BODIES.

[169 a.

The sudden compression of aeriform bodies is likewise attended with the evolution of a very large amount of heat, which may even rise high enough to ignite tinder and other inflammable substances. On rarefying air the opposite effects are observed. One evidence of this fact is afforded by the mist which is formed within a glass receiver while it is undergoing exhaustion. On first working the pistons of the air-pump, the sudden expansion deprives the moisture which all air contains, of part of the heat necessary for its existence in the gaseous form, and it condenses in minute drops, which speedily evaporate again as the equilibrium of temperature is restored. If compressed air be allowed to expand suddenly, by escaping into the atmosphere, a similar phenomenon is produced; a demand for the heat which the air had lost in compression suddenly arises, and moisture is deposited as before.

It was formerly supposed that this absorption of heat attending the expansion of aeriform bodies was due to an alteration in their specific heat, but the careful and elaborate experiments of Regnault have proved that this is not the case, and the absorption of heat under these circumstances affords a strong argument in favour of the mechanical theory of heat.*

FIG. 133.

d

It may be worth while to examine the conditions under which this diminution of temperature takes place somewhat more fully. Suppose two equal volumes of air at o° C. be exposed to the action of a gradually increasing temperature until each is raised to a temperature of 273° C. If one of these volumes of air be allowed to expand unchecked, its pressure will remain unaltered, but its volume will be doubled; whilst if the other is confined within fixed limits, its volume will be unaltered, but its pressure will be doubled. The quantity of heat absorbed to produce the observed rise of temperature will, however, be very different in the two experiments. In the case where the air is allowed to expand, the heat required will be greater than where the volume of the air continues the same-in the ratio of 1413 to 1000; or the quantity of heat consumed when the air is not allowed to expand will be about less than when the expansion occurs under the usual atmospheric pressure. Let C, fig. 133, be an open rectangular vessel, the base of which is one square metre in area. If a a represent the surface of a cubic metre of air contained within it at a temperature of o°C., d d will represent the surface of the same cubic metre of air which has been raised to 273° C. The quantity of air which originally filled but one cubic metre will now occupy the space of two cubic metres; consequently it must have lifted the superincumbent column of atmospheric air, resting on the surface d d, through a height of one metre; but the weight of that superincumbent column of air, calculated at 103329 kilos. per square centimetre is 10,332'9 kilos. Now, a cubic metre of air at o° C. is 1293187 kilogr., and the specific heat of air was found by Regnault to be a little less than one-fourth of that of water, or o 2375, so that

a

C

a

169 a.]

DECREASE OF TEMPERATURE WITH ALTITUDE.

351

The absorption of heat by air when it undergoes rarefaction, will enable us to understand the general distribution of temperature in any vertical column of the atmosphere of our globe. If the atmosphere, without being altered in quantity, could be reduced to a stratum of uniform density throughout, with a uniform temperature of 30° C., it would extend to a height of about 54 miles, or 8690 metres. Now, suppose that this air, throughout the entire thickness of the stratum, suddenly expanded to the extent due to its elasticity; the temperature would immediately fall in every part of the column (except at its base, where it would remain stationary), in conseqneuce of the alteration in density; at 5000 metres it would be about o° C., and at 10,000 metres it would be about 22° C. It may be shown, indeed, that a column of air in equilibrium is at uniform temperature, but this is a condition which cannot occur in the atmosphere of the earth. Air allowing heat to pass through it without raising its temperature, the sun's rays produce very little effect on the atmosphere until they strike the surface of the earth, this being heated warms the air in contact with it, expanding it, and producing a rise of warm air. On rising, the air is submitted to reduced pressure, and the resulting expansion

-

the quantity of heat required to raise 1293187 kilogr. of air 273° will raise only 0307132 kilogr. of water through 273° C. Now, 0307132 kilogr. of water raised to 273° C. would be equal to 83.847 kilos. raised only Thus the heat required to double the volume of a cubic metre of air, and consequently to lift 10,332'9 kilos., would heat 83 847 kilos. of water 1° C., or would be 83,847 units of heat.

Suppose, in the next place, that the cubic metre of air, instead of being allowed to expand freely, be confined when heated, so that its volume shall remain constant; the quantity of heat required under these circumstances will be less than when it was allowed to expand freely in the ratio of 1413 to 1000, so that the quantity of water which would be heated 1° by this amount is easily seen to be only equal to 59'3397 kilos.; for 1413: 1000 :: 83.847: 59°3397.

Now, on deducting 59 3397 from 83 847, the difference, 24'5073, represents the number of kilogr. of water which would be raised 1° C. by the excess of heat imparted to the air when allowed to expand, in our imaginary experiment; but this excess, as already explained, has been engaged in lifting a column of air of 10,3329 kilogr. weight through a height of one metre. If now we divide 10,332 9 kilos. by 24'5073, we obtain a number 421625 kilos., and hence it appears that an expenditure of heat sufficient to raise one kilogr. of water 1° C. is competent to raise 421625 kilos. one metre; or we are by this means brought to nearly the same result as that deduced by Joule from his experiments. The reasoning employed above is that used by Mayer in his paper on the mechanical nature of heat. The numbers, however, have been supplied by subsequent experiments. We assume, however, in this experiment, that the interior energy of the air remains the same. (See Tyndall: Heat as a Mode of Motion, 4th edit. p. 68, et seq.)