Note 6 — Chapter XIV · THE VALENCY AND SPECIFIC HEAT OF THE METALS. MAGNESIUM. CALCIUM, STRONTIUM, BARIUM, AND BERYLLIUM

If W be the amount of heat contained in a mass m of a substance at a temperature t, and dW the amount expended in heating it from t to t + dt, then the specific heat Q = dW(m × dt). The specific heat not only varies with the composition and complexity of the molecules of a substance, but also with the temperature, pressure, and physical state of a substance. Even for gases the variation of Q with t is to be observed. Thus it is seen from the experiments of Regnault and Wiedemann that the specific heat of carbonic anhydride at 0° = 0·19, at 100° = 0·22, and at 200° = 0·24. But the variation of the specific heat of permanent gases with the temperature is, as far as we know, very inconsiderable. According to Mallard and Le Chatelier it is = 0·0006 / M per 1°, where M is the molecular weight (for instance, for O2, M = 32). Therefore the specific heat of those permanent gases which contain two atoms in the molecule (H2, O2, N2, CO, and NO) may be, as is shown by experiment, taken as not varying with the temperature. The constancy of the specific heat of perfect gases forms one of the fundamental propositions of the whole theory of heat and on it depends the determination of temperatures by means of gas-thermometers containing hydrogen, nitrogen, or air. Le Chatelier (1887), on the basis of existing determinations, concludes that the molecular heat—that is, the product MQ—of all gases varies in proportion to the temperature, and tends to become equal (= 6·8) at the temperature of absolute zero (that is, at -273°); and therefore MQ = 6·8 + a(273 + t), where a is a constant quantity which increases with the complexity of the gaseous molecule and Q is the specific heat of the gas under a constant pressure. For permanent gases a almost = 0, and therefore MQ = 6·8—that is, the atomic heat (if the molecule contains two atoms) = 3·4, as it is in fact (Chapter IX., Note 17 bis. As regards liquids (as well as the vapours formed by them), the specific heat always rises with the temperature. Thus for benzene it equals 0·38 + 0·0014t. R. Schiff (1887) showed that the variation of the specific heat of many organic liquids is proportional to the change of temperature (as in the case of gases, according to Le Chatelier), and reduced these variations into dependence with their composition and absolute boiling point. It is very probable that the theory of liquids will make use of these simple relations which recall the simplicity of the variation of the specific gravity (Chapter II., Note 34), cohesion, and other properties of liquids with the temperature. They are all expressed by the linear function of the temperature, a + bt, with the same degree of proximity as the property of gases is expressed by the equation pv = Rt.

As regards the relation between the specific heats of liquids (or of solids) and of their vapours, the specific heat of the vapour (and also of the solid) is always less than that of the liquid. For example, benzene vapour 0·22, liquid 0·38; chloroform vapour 0·13, liquid 0·23; steam 0·475, liquid water 1·0. But the complexity of the relations existing in specific heat is seen from the fact that the specific heat of ice = 0·502 is less than that of liquid water. According to Regnault, in the case of bromine the specific heat of the vapour = 0·055 at (150°), of the liquid = 0·107 (at 30°), and of solid bromine = 0·084 (at -15°). The specific heat of solid benzoic acid (according to experiment and calculation, Hess, 1888) between 0° and 100° is 0·31, and of liquid benzoic acid 0·50. One of the problems of the present day is the explanation of those complex relations which exist between the composition and such properties as specific heat, latent heat, expansion by heat, compression, internal friction, cohesion, and so forth. They can only be connected by a complete theory of liquids, which may now soon be expected, more especially as many sides of the subject have already been partially explained.