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ture, the water froze, and thereby the copper index was fixed at the place which Fig. 16.
it occupied. The nipple of ice formed by the freezing of the water in the conic space at c was removed, the copper cone f introduced, and by means of the screw C driven in as strongly as possible. The whole apparatus was now again reversed, so that E was above and C below.
After the apparatus, in this last position, was firmly secured in a strong cross-piece between two bars, (Fig. 17,) and surrounded with the freezing mixture, the index d being thus plunged in the ice deep under g, the female screw or nut E was, by means of a lever sis decimetres long, gradually driven around, and thereby g more and more pressed downward. If the ice remained firm under the compression, there must, on the opening of the screw C, situated below, appear at the copper cone f first a cylinder of ice and then the index d; but if water has been produced by the pressure, the index d must descend to c, at the lower end of the cavity, and hence, on the with
drawal off, first the inFig. 17.
dex and next in order the massive ice cylinder respectively make their appearance.
In order to prevent the heating of the apparatus by mechanical work the depression of g was
very slowly conducted, the female screw E being turned only every five minutes to the extent of 45°, and the operation being thus protracted through the space of some four hours. When, after these processes, the lower terminal screw was opened, still under a very low temperature, the copper cone f immediately protruded and ice instantly formed on its sides. Directly behind the cone f followed the index d, and after this a thick cylinder of ice, which must have been formed at the moment of the opening
Tbus was the proof afforded that, by a sufficiently strong pressure, ice is converted into water at=18° C. The pressure to which the ice was subjected in this experiment is estimated by Mousson at some 13,000 atmospheres. This lowering of the melting point of ice through pressure plays an important part in the explanation of glacier-phenomena, and on that account will be again the subject of consideration in the section of cosmical physics.
The value of $, (in equation 111) is, for water, a negative one, because ice, in melting, contracts. For such substances, however, as are attended in melting with an augmentation of volume, o is positive, and for these therefore the melting
point must, through increased pressure, be heightened. The correct
Fig. 18. ness of this consequence has been experimentally proved by Bunsen, (Pogg. Annal., LXXXI, 1850,) and by Hopkins, (Dingler's Polyt. Journal, cxXXIV.) Bunsen conducted the experiment in the fol. lowing manner: A very thick-walled glass tube about a foot long, and having a bore of the size of a straw, was drawn out at one end into a fine capillary tube from 15 to 20 inches in length, which was made of as accurate calibre as possible. The lower end of this glass tube was also drawn out to a somewhat wider tube, one and a half inch long and curved, as is shown in Fig. 18.
By atmospheric pressure the whole apparatus was now filled with quicksilver, and the longer capillary tube was then soldered at a. After cooling, a small quantity of quicksilver was driven out at b by gentle heat, and in place of it, while the cooling was renewed, a small quantity of the substance to be tested was imbibed in a state of fusion. The apparatus was now soldered also at b, the longer capillary tube was then opened at a, and the whole apparatus heated one or two degrees above the melting point of the substance contained therein, through which process a part of the quicksilver is expelled from the open point at a. Finally, after renewed cooling, the range of the quicksilver in the capillary tube at c, together with the range of the thermometer and barometer, was noted; the point at a was then once more soldered, and thus a column of air of ascertained length was included.
Two such instruments of precisely similar form and contents, one of which was soldered at a, while the other remained open, were now, together with a sensitive thermometer, fastened on a small board in such manner that the two little tubes filled with the substance to be tested might stand close to the bulb of the thermometer. If this apparatus be immersed in water whose temperature is a few degrees above the melting point of the substance, to such a depth that only the tube b shall be submerged, it will be seen that, by gradual cooling of the water, molecular rigidity will ensue simultancously in both tubes. But were tlie apparatus sunk deeper in the warm water, there would follow, through the expansion of the quicksilver in the closed instrument, a pressure which can be readily measured by the compression of the air in the capillary tube cb, and which may be angmented or diminished at will by depressing the instrument in the warm fluid or partially withdrawing it therefrom. The pressure in the open instrument, on the other hand, remains unchanged during the whole experiment. The difference of temperature at which the substance grows rigid in the closed instrument sooner than in the open ono gives the elevation of the melting point for the observed pressure. An experiment made with spermaceti gave the following result: Pressure.
Point of rigidity. 1 atmosphere...
47.7° C. 96 atmospheres.
49.7° 156 atmospheres..
50.9° The same experiment repeated witli parafline gave : Pressure.
Point of rigidity. 1 atmosphere...
46.3° C 85 atmospheres.
48.9° 100 atmospheres....
By another method, Hopkins obtained the following results :
X. SPECIFIC HEAT IN THE ACCEPTATION OF THE MECHANICAL THEORY
By the specific heat of a substance is understood, we know, the number which specifies how many units of heat (calories) must be added to the unit of weight of that substance in order to produce an elevation of temperature from 0° to 1° C.
According to a law propounded by Dulong and Petit, the product obtained when the specific heat of a solid element is multiplied by its atomic weight should be a constant number; which is, indeed, nearly the case, as the following brief table will show:
The Dulong-Petit law admits of being expressed in this wise: Chemically equivalent quantities of solid elements require for like elevation of temperature quantities of heat of like amount. Still another expression of the same law is the following : The atoms of all simple substances have a like capacity for heat; or, in fine, the atomic heat of all simple substances is equal, if we denote by atomic heat the product of the atomic weight into the specific heat.
In the mean, the atomic heat of solid elements has the product p.sza, or the value 6.4. From this value, however, the atomic heat of carbon deviates considerably, since we have for
The atomic heat of the different forms of carbon is somewhat more approximate to the mean value of the atomic heat of the rest of the elements, if, according to Regnault's proposition, we take the atomic weight of carbon not as equal to 12, but to 24.
If we indicate the atomic weight of a compound body by P, its specific heat by S, and by N the number of single atoms which are associated with one atom of
P:s · the compound body, then, according to Garnier, we have very nearly -A,
N if a represent the mean atomic heat of the solid elements, and, therefore, the value 6.4. In effect there results, for example, for
Now the temperature of a bouy depends, according to the mechanical theory of heat, entirely on the living force with which the atoms composing it move. Two bodies have a like temperature when the living force with which each atom in the one vibrates is equal to the living force of an atom in the other. For the temperature of two bodies to be raised in an equal degree it is neces
cessary that the oscillatory work of the atoms in both should undergo an equal augmentation.
From this it might well be expected that like quantities of heat will be needed to produce a like elevation of temperature in two masses of different substanco of which one contains just as many atoms as the other; or, in other words, it would be expected that the magnitude, which we have above indicated as atomic beat, should for all elements be alike; that, hence, the Dulong-Petit law should not only be approximately, but rigorously, correct, that for chemically compounded substances the quotient which we obtain when we divide the atomic heat of the combination by the number of single atoms which are associated with
PS one atom of the composition, being the value must under all circumstances
N be perfectly equal to the atomic heat of the simple substance. This, however, experiment does not verify. The numbers of the last column of the above table,
PS in part, deviate considerably from 6.4, and thus the quotient Lis not equal for
N all combinations, as we have also seen above.
The contradiction in which experiment and the mechanical theory of heat seem here involved entirely vanishes, however, when it is considered that the quantity of beat which must be supplied to a body in order to raise its temperature is by no means wholly employed in exalting the living force of its molecular vibrations, but that a considerable part of the heat, which we designate as specific heat, is consumed in the performance of internal and external work. Let us indicate the specific heat of a simple substance by s; then is, s=k+ite
(1), if by k we denote the augmentation of the vibratory work which the unit weight (Gewichtseinheit) of the substance in question undergoes from an elevation of temperature of 1°, while i and e denote the heat equivalent of the internal and external work simultaneously executed. If we designate the atomic weight of the substance by p, then, according to the principles of the mechanical theory, the product kp must, of course, be the same for all simple substances; but it ly no means follows that sp also is a constant magnitude, since e and i are quantities which vary, not only from one substance to another, but for the same substance with the conditions of aggregation. We can realize the absolute validity
of the law of Dulong and Petit only when both quantities i and e are completely null. Only in special cases can the quantities e and i be small enough to admit of their being neglected. This circumstance, however, makes it possible to ascertain the value of the quantity k.
For solid and fluid bodies the expansion which corresponds to an elevation of temperature by 1° is so slight that we may overlook, without sensible error, the external work thereby executed; for this case, therefore, we have
s=k+i On the other hand, it may be assumed that, at least with the permanent gases, the internal work is null; whence, for these we have s=kte
(3), if by s the specific heat of these gases under constant pressure be indicated. For the case in which the gas is so confined as not to be capable of expanding from subsequent heating, e is also null; and we then have $==k
(4), if hy s' be indicated the specific heat of gases under constant volume.
According to the experiments of Regnault, the specific heat is, with constant volume, for oxygen gas, 0.1551 ; for hydrogen gas, 2.4153; for nitrogen gas, 0.1712; whenco the atomic heat is for oxygen gas, 0.1551 · 16=2.4816; for hydrogen gas, 2.4153 · 1=2.4153; for nitrogen gas, 0.1712 · 14=2.3968. We will take, then, 2.4 for the approximate value of the atomic heat under constant volume, for the gases named.
This value, 2.4, wo will now designate as absolute atomic heat. It would be the atomic heat for all elements, whether in a fluid, solid, or gascous state, if all the heat supplied to them inured exclusively to the angmentation of the vibratory work, and none of it were employed for internal and external work.
The knowledge of the absolute atomic heat 2.4 enables us to ascertain what part of the specific heat s of a body inures to the elevation of temperature, and what part thereof becomes latent through the performance of internal or esternal labor. For solid elements the atomic heat is, according to equation (2),
sp=(1+i)p. For the absoluto atomic licat kp of all elements we have found the value 2.4; whence,
2.4 (s-i)p=2.4, and s-i=
P 2.4 The quotient which we will call the absolute specific heat, or the absolute
P heat-capacity, is the same quantity which we designated above by k; we find it for each element if we employ its atomic weight p as a divisor for 2.4.
2.4 Thus, for examplo, wo obtain for copper ka -0.0378.
63.4 tity of heat 0.0949, which must be supplied to one gram of copper in order to raise its temperature 1°, only 0.0378 units of heat aro expended for the elevation of temperature, (increase of vibratory work ;) the rest, 0.0949—0.0378= 0.0571 units of heat, are consumed for internal work, and hence are latent.
In the same way we obtain for certain solid elements, which are exhibited together in the fol
Of the quan