According to H. Schroeder the silver salts of the fatty acids exhibit additive relations; an increase in the molecule of CH2 causes an increase in the molecular volume of about 15.3.

Thermal Relations.

Specific Heat and Composition.—-The nature and experimental determination of specific heats are discussed in the article CALORIMETRY; here will be discussed the relations existing between the heat capacities of elements and compounds.

In the article [Thermodynamics] it is shown that the amount of heat required to raise a given weight of a gas through a certain range of temperature is different according as the gas Specific heat of gases. is maintained at constant pressure, the volume increasing, or at constant volume, the pressure increasing. A gas, therefore, has two specific heats, generally denoted by Cp and Cv, when the quantity of gas taken as a unit is one gramme molecular weight, the range of temperature being 1° C. It may be shown that Cp - Cv = R, where R is the gas-constant, i.e. R in the equation PV = RT. From the ratio Cp/Cv conclusions may be drawn as to the molecular condition of the gas. By considerations based on the kinetic theory of gases (see [Molecule]) it may be shown that when no energy is utilized in separating the atoms of a molecule, this ratio is 5/3 = 1.67. If, however, an amount of energy a is taken up in separating atoms, the ratio is expressible as Cp/Cv = (5+a)/(3+a), which is obviously smaller than 5/3, and decreases with increasing values of a. These relations may be readily tested, for the ratio Cp/Cv is capable of easy experimental determination. It is found that mercury vapour, helium, argon and its associates (neon, krypton, &c.) have the value 1.67; hence we conclude that these gases exist as monatomic molecules. Oxygen, nitrogen, hydrogen and carbon monoxide have the value 1.4; these gases have diatomic molecules, a fact capable of demonstration by other means. Hence it may be inferred that this value is typical for diatomic molecules. Similarly, greater atomic complexity is reflected in a further decrease in the ratio Cp/Cv. The following table gives a comparative view of the specific heats and the ratio for molecules of variable atomic content.

The abnormal specific heats of the halogen elements may be due to a loosening of the atoms, a preliminary to the dissociation into monatomic molecules which occurs at high temperatures. In the more complex gases the specific heat varies considerably with temperature; only in the case of monatomic gases does it remain constant. Le Chatelier (Zeit. f. phys. Chem. i. 456) has given the formula Cp = 6.5 + aT, where a is a constant depending on the complexity of the molecule, as an expression for the molecular heat at constant pressure at any temperature T (reckoned on the absolute scale). For a further discussion of the ratio of the specific heats see [Molecule].

Molecular Content. Examples.Cp. Cv. Cp/Cv.
Monatomic Hg, Zn, Cd, He, Ar, &c. 5 3 1.66
DiatomicH2, 02, N2 (0°-200°) 6.83 4.83 1.41
Cl2, Br2, I2 (0°-200°) 8.6 6.6 1.30
HCl, HBr, HI, NO, CO . . . . . . 1.41
Triatomic H2O, H2S, N2O, CO2 9.2 7.2 1.28
TetratomicAs4, P413.4 11.4 1.175
NH3, C2H211.6 9.6 1.21
Pentatomic CHCl314 12 1.17
Hexatomic C2H4, C2H3Br16.4 14.4 1.14

Specific Heats of Solids.—The development of the atomic theory and the subsequent determination of atomic weights in the opening decades of the 19th century inspired A.T. Petit and P.L. Dulong to investigate relations (if any) existing between specific heats and the atomic weight. Their observations on the solid elements led to a remarkable generalization, now known as Dulong and Petit’s law. This states that “the atomic heat (the product of the atomic weight and specific heat) of all elements is a constant quantity.” The value of this constant when H = 1 is about 6.4; Dulong and Petit, using O = 1, gave the value .38, the specific heat of water being unity in both cases. This law—purely empirical in origin—was strengthened by Berzelius, who redetermined many specific heats, and applied the law to determine the true atomic weight from the equivalent weight. At the same time he perceived that specific heats varied with temperature and also with allotropes, e.g. graphite and diamond. The results of Berzelius were greatly extended by Hermann Kopp, who recognized that carbon, boron and silicon were exceptions to the law. He regarded these anomalies as solely due to the chemical nature of the elements, and ignored or regarded as insignificant such factors as the state of aggregation and change of specific heat with temperature.

The specific heats of carbon, boron and silicon subsequently formed the subject of elaborate investigations by H.F. Weber, who showed that with rise of temperature the specific (and atomic) heat increases, finally attaining a fairly constant value; diamond, graphite and the various amorphous forms of carbon having the value about 5.6 at 1000°, and silicon 5.68 at 232°; while he concluded that boron attained a constant value of 5.5. Niison and Pettersson’s observations on beryllium and germanium have shown that the atomic heats of these metals increase with rise of temperature, finally becoming constant with a value 5.6. W.A. Tilden (Phil. Trans., 1900, p. 233) investigated nickel and cobalt over a wide range of temperature (from -182.5° to 100°); his results are:—

Cobalt.Nickel.
From -182.5° to -78.4°4.16874.1874
-78.4° to 15°5.49785.6784
15° to 100°6.03246.3143

It is evident that the atomic heats of these intimately associated elements approach nearer and nearer as we descend in temperature, approximating to the value 4. Other metals were tested in order to determine if their atomic heats approximated to this value at low temperatures, but with negative results.