578 PRINCIPLES OF CHEMISTRY 



could not be determined Recording to Avogadro-Gerhardt's law, was 

 made about 1860 by the Italian professor Carmizzaro. 



Exactly the same conclusions respecting the bivalence of magnesium 

 and its analogues are obtained by comparing the specific heats of their 

 compounds, especially of the halogen compounds as the most simple, with 

 the specific heats of the corresponding alkali compounds. Thus, for in- 

 stance, the specific heat of magnesium and calcium chlorides, MgCl 2 and 

 CaCl 2 , equal O194 and 0'164, and of sodium and potassium chlorides, 

 NaCl and KC1, 0*214 andO'172, and therefore their molecular heats (or 

 the products QM, where M is the weight of the molecule) are 18 '4 and 

 18*2, 12'5 and 12 '8, and therefore the atomic heats (or the quotient of 

 QM by the number of atoms) are all nearly 6, as with the elements, 

 Whilst if, instead of the actual atomic weights Mg=24 and Ca=40, 

 their equivalents 12 and 20 be taken, then the atomic heats of the 

 chlorides of magnesium and calcium would be about 4'6, whilst those of 

 potassium and sodium chlorides are about 6'3. 5 



As the specific heat or the amount of heat required to raise the 

 temperature of a unit of weight one degree 6 is a complex quantity 



5 It must be remarked that in the case of oxygen (hydrogen and carbon) compounds 

 the quotient of MQ/w, where n is the number of atoms in the molecule, is always less 

 than 6 for solids; for example, in the case of MgO = 5*0, CuO= 5'1, MnOo = 4'6, ice 

 (Q = 0-504) = 3, Si0 2 = 3'5, &c. At present it is impossible to say whether this depends 

 on the smaller specific heat of the atoms of oxygen in its solid compounds (Kopp, Note 4) 

 or on some other reason ; but, nevertheless, taking into account this decrease, depending 

 on the presence of oxygen, a reflection of the atomicity of the elements may to a certain 

 extent be seen in the specific heat of the oxides. Thus in the case of alumina, A1 2 O 5 

 (Q = 0'217), MQ = 22'3, and therefore the quotient MQ/n, = 4'5, which is nearly that 

 given by magnesium oxide, MgO. But if we ascribe the same composition to alumina as 

 to magnesia that is, if aluminium were counted as divalent we should obtain the figure 

 3'7, which is much less. In general, in compounds of identical atomic composition 

 and of analogous chemical properties the molecular heats MQ are nearly equal, as 

 many investigators have long remarked. For example, ZnS = 11'7 and HgS = 11'8 ~ 

 MgSO 4 = 27'0 and ZnSO 4 = 28'0, &c. 



6 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 t (m x 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 = 0'19, 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 in- 

 considerable. Therefore the specific heat of those permanent gases which contain two 

 atoms in the molecule (H 2 , Oo, N 2 , 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 sup- 

 ports 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 propor- 

 tion 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 



