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Weber (loc. cit.) found that the specific heats of carbon, boron, and silicon increase rapidly as the temperature is raised, but that at high temperatures the velocity of the increase becomes much smaller. The following table gives a synopsis of Weber's results :
Specific heats of Boron, Carbon, and Silicon. (WEBER.)
These numbers show that the specific heat of boron increases with increase of temperature, and that the value of this increase, for a given interval, is considerably less at high than at low temperatures. The variations in the rate of this increase are almost identical with the variations noticed in the case of carbon; hence at temperatures above 233°
1 Dewar (Phil. Mag.  44. 461) found for the specific heat of gas-carbon between 20° and 1040° the number o‘32, for diamond the number oʻ366; and between 20° and a temperature estimated to be 2000°, for "carbon' the number Silicon-crystallised
this identity will probably remain. Calculated on this assumption, the specific heat of boron at about 1000° is o 50. Specific heats of Boron, Carbon, and Silicon. (WEBER) continued.
Sp. ht. x at. wt.
1'95 0-99 0:1935
2'07 0°-223° 0*2385
2.84 These numbers show that the specific heat of carbon increases from – 50° upwards, the value found at 600° being about seven times as great as that found at 50°; but that the rate of this increase is very small at high temperatures,from a red heat upwards the rate is about one-seventeenth of that from oo to 100°.
The specific heats of diamond and graphite differ at temperatures below about 600°, but from this point upwards they are practically identical; the numbers given for porous wood carbon are almost the same as those for graphite at the same temperature-intervals, hence it may be said that at high temperatures (above 600°) the various modifications of carbon have probably all the same specific heat.
Sp. ht. x at, wt.
3.81 5:13 5:50 563 568
The specific heat of silicon attains an almost constant value at about 200°.
30. It is evident that the specific heat of an elementary body is not a constant number, but varies with the temperature, and that the relation between the variation of specific heat and that of temperature differs for each element. The following formulæ calculated from experimentally determined numbers, express the relation in question for some of the elements.
2 Copper 2 Zinc 2 Lead
2 Iron 9 Tin
1 Carbon-diamond sp. ht.=0*4408 +0'0000405 t, where t varies from
600°—800° =0°4408 +0'0000561 t
800°-1000° graphite =04454 +0'0000472 t
600°- 800° =094454 +0'0000840 t
800-1000 =0'0910 +0'000023 ť
0°—250° =0°0865 +0'000044 t
=0'0286 +0'000019t 3 Platinum =0'0317 +0.000006 t
0°-1200° 3 Iridium
=0'0317 +0'000006 t
0-250 ° =0*050 +0'000044 t 2 Antimony
=0'0466 +0'000020 t 2 Bismuth
=O‘0269 +0'000020 t The specific heat of any substance also varies with variations in the physical state of that substance—thus : Sp. heat.
Sp. heat. Bromine-solid
o'o843 Mercury- gaseous
Oʻ1175 O'0934 Titanium oxide as rutile ... 0:1666 Iron sulphide as strahlite 01332
brookite 0:1610 pyrites ... O'1279
artificial ... 0*1716 Chlorine-solid
Oʻ180 Calcium carbonate as calc4 gaseous 0'093
as arragonite 0*204 The specific heats of the elementary bodies have generally been determined at temperatures situated at very varying
1 Weber (loc. cit.). 2 Bede, Mém. Couronn. de l'Acad. Brux. 27. 3 (1855). 3 Violle, Compt. rend. 85. 543. 4 Calculated for constant volume.
intervals from the melting points of these elements; the physical aggregation of the specimens examined has also varied much ; hence the values found for the specific heats of the elements cannot be regarded as strictly comparable.
There appears to be a certain interval of temperature within which the value of the specific heat of an element becomes nearly constant, and for this interval only can the element be said approximately to obey the law of Dulong and Petit, as stated on p. 56. This temperature-interval varies for each element, especially for the nonmetallic elements with small atomic weights; for many elements it may be roughly taken as from oo to 100°.
Kopp (loc. cit.) has supposed that the atoms of certain elements—more especially of boron, carbon and silicon-are built up of simpler parts, have themselves a grained structure, and that at high temperatures the atoms of these elements are composed of a smaller number of those little parts than at lower temperatures. Heat added at low temperatures is supposed, on this hypothesis, to be used in separating the atomic groups. Kopp's hypothesis will be again referred to in the chapter on the nature of the elements; meanwhile it may be observed, that the facts of spectroscopy seem to point to the existence of a more complex structure in the nonmetallic than in the metallic molecules; that allotropy occurs markedly only among the nonmetals; that the molecules of the two metallic elements whose vapourdensities have been determined are monatomic; that the atomic heat of tellurium, a metal-like nonmetal belonging to the oxygen group, is 6'o, of the less metal-like selenion about 5:8, of the decidedly nonmetallic sulphur about 5-5, and of the typical nonmetal oxygen probably not more than 4; and finally that the molecular structures of oxygen, sulphur, and selenion vapours are more complex than that of tellurium vapour.
31. A consideration of the data which has been summarised in the preceding paragraphs shews, I think, that the application of Avogadro's law is of more value to the chemist as a means of determining the atomic weights of elements, than the law of Dulong and Petit. From a general consideration of the inolecular theory of matter it is also apparent that a deduction which does not necessitate an exact hypothesis as to the internal structure of molecules is more trustworthy and more appropriate, in the present state of knowledge, than another which does necessitate some such hypothesis.
The molecular explanation of the gaseous laws expressing relations between volume, pressure and temperature, and of Avogadro's law, may be considered as fairly complete; but in order to explain the law of molecular specific heats more knowledge of the internal structure of molecules than we now possess is necessary! For the specific heat of a substance depends on the rate at which the whole energy of the molecule increases with increase of temperature: but this energy is made up of two parts, (1) the energy of agitation, that is, the energy the molecule would possess if it moved as a whole with the motion of its centre of mass, or in other words without rotation; and (2) the energy of rotation, that is, the energy the molecule would possess if its centre of mass were reduced to rest, in other words the energy due to the motion of the parts relatively to the centre of mass of the molecule”. If it is assumed that the energy due to the rotational motions of the parts of the molecule tends towards a value having a constant ratio to the energy of agitation of the molecule, then a simple expression is found for the whole energy; but this expression contains a factor which varies in different gases, and the value of which has been determined only in a few cases. And moreover it is probable that when the energy due to the rotational motions of the parts of a molecule becomes greater than a certain quantity, the molecule separates into parts; hence when heat is imparted to a mass of molecules work is probably in many cases done in destroying some of the molecules as such. Hence the molecular expla
i Clerk Maxwell, C. S. Journal  13. 507.
4 See Hicks, Phil. Mag. (5). 4. 80, and 174. On some effects of Dissociation on the Physical Properties of Gases.'