In fact, for oxygen this product = 0·155 × 16 = 2·48, for hydrogen 2·40, for nitrogen 0·7724 × 14 = 2·414, and therefore if A stand for the atomic weight we obtain the expression K × A = a constant, which may be taken as 2·45. 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 proportional to 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 the two specific heats, k, judging from the above, is the ratio of Q to K, or equal to the ratio of 2·45n + 2 to 2·45n. When n = 1 this ratio k = 1·8; when n = 2, k = 1·4, when n = 3, k = 1·3, and with an exceedingly large number n, of atoms in the molecule, k = 1. That is, the ratio between the specific heats decreases from 1·8 to 1·0 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 n = 2, the magnitude of k is determined by methods described in works on physics (for example, by the change of temperature with an alteration 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 dioxide, and others it is nearly 1·3. Kundt and Warburg (1875), by means of the approximate method mentioned in Note 452, Chapter VII., determined k for mercury vapour when n = 1, and found it to be = 1·67—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, Regnault; k = 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 it must be assumed, therefore, that when it is heated some great internal work is accomplished.
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/n, where M is the molecular weight and n the number of molecules) is smaller (in solids it attains its highest value 6·8 and in gases 3·4), the more complex the molecule (i.e. the greater the number (n) of atoms forming it) and so much smaller, up to a certain point (in similar physical states) the smaller the mean atomic weight M/n.
As an example, it will be sufficient to refer to the specific heat of nitrogen tetroxide, N2O4, which, when heated, gradually passes into NO2—that is, chemical work of decomposition proceeds, which consumes heat. Speaking generally, specific heat is a complex quantity, in which it is clear that thermal data (for instance, the heat of reaction) alone cannot give an idea either of chemical or of physical changes individually, but always depend on an association of the one and the other. If a substance be heated from t0 to t1 it cannot but suffer a chemical change (that is, the state of the atoms in the molecules changes more or less in one way or another) if dissociation sets in at a temperature t1. Even in the case of the elements whose molecules contain only one atom, a true chemical change is possible with a rise of temperature, because more heat is evolved in chemical reactions than that quantity which participates in purely physical changes. One gram of hydrogen (specific heat = 3·4 at a constant pressure) cooled to the temperature of absolute zero will evolve altogether about one thousand units of heat, 8 grams of oxygen half this amount, whilst in combining together they evolve in the formation of 9 grams of water more than thirty times as much heat.