Heat, atomic

The researches of F. Neumann (1831), Regnault (1840), and H. Kopp (1864), indicated that solid elements preserve unchanged their atomic heats when they unite to form solid compounds. Thus, the product molecular weight) X s )ecific heat) = (molecular heat) is composed additively of the atomic heats MC = niaiCi + h2 2c2 + n t s + (9)... 

The law was stated in this form by J. P. Joule in 1844 it is usually referred to as AVoestyn s law (1848). It shows that the carriers of heat in a solid compound are not the molecules of the latter, but the atoms of its constituent elements. Joule s law enables one to calculate the molecular heats of compounds from the atomic heats of their elements, and the atomic heats of elements in the solid state when the latter are not readily directly accessible (solid oxygen, from c(CaC03) — c-(Ca) — c(C) = 3c(0), or 100 X 0 203 — 6 4 — P8 = 3 X 4 0). 

Assumption (7) implies that the molecular heat of each compound gas is the sum of the atomic heats of its constituents (a hypothesis introduced on the basis of experiment by Delaroche and Berard (1818), and afterwards defended by Buff (1860), and Clausius (1861) ), and also that the molecular heats are independent of temperature. This rule is only very approximate, the deviations sometimes exceeding 30 per cent., although (8) is often useful over a small range of temperature. 

Abnormally low atomic heats were explained by Richarz on the assumption of a diminution of freedom of oscillation consequent on a closer approximation of the atoms, which may even give rise to the formation of complexes. This is in agreement with the small atomic volume of such elements, and with the increase of atomic heat with rise of temperature to a limiting value 6 4, and the effect of propinquity is seen in the fact that the molecular heat of a solid compound is usually slightly less than the sum of the atomic heats of the elements, and the increase of specific heat with the specific volume when an element exists in different allotropic forms. 

There is, however, a fatal objection to the theory of Boltzmann. At very low temperatures the oscillations will be small, and should conform to the theory. But the atomic heats, instead of approaching the limit 5 955 at low temperatures, diminish very rapidly, and in the case of diamond the specific heat is already inappreciable at the temperature of liquid air. A new point of view is therefore called for, and it is a priori very probable that this will consist of a replacement of the hypothesis of Equipartition of Energy adopted by Boltzmann. This supposition has been verified, and the new law of partition of energy derived... 

By means of the experimental methods briefly referred to in 9 a large number of specific-heat measurements have been made at very low temperatures. In Fig. 91 we haye the atomic heats of some metals, and of the diamond, represented as functions of the temperature. The peculiar shape of the curves will. be at once apparent. At a more or less low temperature, the atomic heat decreases with extraordinary rapidity, then apparently approaches tangentially the value zero in the vicinity of T = 0. The thin curves represent the atomic heats calculated from the equation ... 

The values of v obs. were determined from the atomic heats by means of Einstein s formula, those of v calc. were obtained from equation (6) ... 

According to Joule s law ( 9), the molecular heat of a compound is the sum of the atomic heats of its components, and since this holds good even when the atomic heats are irregular, i.e., not equal to 6 4, it seems that the heat content of a solid resides in its atoms, and not in the molecular complexes as such. This agrees with Einstein s theory. Hence the molecular heat of a compound should be calculable by means of the formula ... 

Energy of individual atoms Heat of atomization of real molecule... 

Though silica supports are amorphous, the surface may exhibit some local order, such as that of the mineral /3-crystoballite (Fig. 5.23). The surfaces of silica support contain OH groups at densities of between 4 and 5.5 OH per nm that of cristobal-lite is 4.55 OH per nm. Silica surfaces contain only terminal OH groups, i.e. bound to a single Si atom. Heating leads to dehydroxylation, and at high temperatures only the isolated OH groups remain. 

Isoprenoid fatty acids (4,8,12 trimethyl tetradecanoic acid and phytanic acid), acids with 16, 18 and 20 carbon atoms Heated marine lipids [42,43]... 

An Arrhenius plot of the hydrogen penetration depth is shown in Fig. 7. The activation energy derived from the Arrhenius plot is 0.39 eV. This activation energy is believed to be the energy for breaking an Si—H bond near a B atom. Heating above 40°C appears to be necessary to cause the... 

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