580 PRINCIPLES OF CHEMISTRY 



internal work accomplished in the molecules inciting them to decom- 

 position according to the rise of temperature 8 - therefore it is irnpos- 



specific heats of elements are in inverse proportion to their atomic weights that is, their 

 product by the atomic weight is a constant quantity. In reality, for oxygen this product 

 = 0-155 x 16 = 2'48, for hydrogen 2'40, for nitrogen 0'7724 x 14 = 2'414, and therefore if A 

 stand for the atomic weight we obtain the expression K x A a constant, which may be 

 counted as 2'45; and this is the true expression of Dulong and Petit's law, because K is 

 the true specific heat and A the weight of the atom. It should be remarked, moreover, 

 that the product of the observed specific heat Q into A is also a constant quantity (for 

 oxygen = 3'48, for hydrogen = 3'40), because the external work D is also inversely propor- 

 tional to the magnitude of the atomic weight. 



In the case of gases we distinguish the specific heat at a constant pressure c' (we 

 designated this quantity above by Q), and at a constant volume c. It is evident that 

 the relation between both specific heats, Jc, judging from the above, is the ratio of Q 

 to K, or equal to the ratio of 2'45?i + 2 to 2'45w. When n = 1 this ratio k = 1'8 ; when 

 n=2 A- = 1-4, when n = 8 A = 1'3, and with an exceedingly large number, n, of atoms in the 

 molecule, Jc=l. That is, the ratio between the specific heats decreases from 1'8 to I'O as 

 the number of atoms, n, contained in the molecule increases. This deduction is verified 

 to a certain extent by direct experiment. For such gases as hydrogen, oxygen, nitrogen, 

 carbonic oxide, air, and others in which ->i = 2, the magnitude of k is determined by 

 methods described in physics (for example, by the change of temperature with an altera- 

 tion of pressure, by the velocity of sound, &c.), and is found in reality to be nearly 1*4, 

 and for such gases as carbonic anhydride, nitric peroxide, and others it is nearly 1'8. 

 Kundt and Warburg (1875), by means of the approximate method mentioned on p. 321, 

 determined k for mercury vapour when n = l, and found it to be = 1'07 that is, a larger 

 quantity than for air, as would be expected from the above. 



It may be admitted that the true atomic heat of gases =2' 43, only under the condition 

 that they are distant from a liquid state, and do not undergo a chemical change when 

 heated that is, when no internal work is produced in them (B = 0). Therefore this 

 work may to a certain extent be judged by the observed specific heat. Thus, for instance, 

 for chlorine (Q = 0'12, Eegnault; A; = 1'33, according to Straker and Martin, and therefore 

 K = 0'09, MK = 6'4), the atomic heat (3'2) is much greater than for other gases containing 

 two atoms in a molecule, and one must consider, therefore, that when heated some great 

 internal work is accomplished of whose nature it is at present impossible to form an 

 opinion. And as in the case of such gases as ethylene, C 2 H 4 (Q = 0'39), according to 

 "Wiedemann k = l'2, K = 0'88, MK = 9'2 ; hence the true atomic heat is less than for con- 

 stant gases =1'5. Therefore the question as to the relation between the specific heats of 

 gases and the number of atoms and composition cannot be counted as sufficiently 

 general if we do not consider Le Chatelier's deduction (Note 6) as proved by the asso- 

 ciation of data. If the latter! be verified, then it will have to be admitted that Dulong 

 and Petit's law is not applicable to any gases besides those which are permanent and 

 possess a comparatively low molecular weight. The question might be solved by deter- 

 mining the specific heat of mercury vapour at different temperatures, but as yet there 

 are no exact methods of doing this. 



All the more remarkable is the adaptability of Dulong and Petit's law to the mass of 

 the common elements in a solid state. In order to generalise the facts concerning the 

 specific heat of gases and solids, it appears to me possible to accept the following general 

 proposition : the atomic heat (that is, AQ or QM/w, where M is the molecular weight 

 and n the number of molecules) is less (greatest for solids, 6'8 ; for gases, 8'4) the more 

 complex the molecule (that is, the greater the number (n) of the atoms forming it), 

 and to a certain extent (with similar physical states of substances) the less the mean 

 (M/n) weight of the atom. 



8 For an example, it is enough to point out the specific heat of nitrogen tetroxide, 

 N a O 4 , which, when heated, gradually passes into NO a that is, chemical work of decom- 



