THE VALENCY AND SPECIFIC HEAT OF THE METALS 589 



complex quantity including not only the increase of the energy of a 

 substance with its rise in temperature, but also the external work of 

 expansion 7 and the internal work accomplished in the molecules 

 only be connected by a complete theory of liquids, which may now soon be expected, 

 move especially as many sides of the subject have already been partially explained. 



7 .According to the above reasons the quantity of heat, Q, required to raise the tem- 

 perature of one part by weight of a substance by one degree may be expressed by the 

 eum Q = K + B + D, where K is the heat actually expended in heating the substance, or 

 what is termed the absolute specific heat, B the amount of heat expended in the 

 internal work accomplished with the rise of temperature, and D the amount of heat ex- 

 pended in external work. In the case of gases the last quantity may be easily deter- 

 mined, knowing their coefficient of expansion, which is approximately =0*00368. By 

 applying to this case the same argument given at the end of Note 11, Chapter I., we find 

 that one cubic metre of a gas heated 1 produces an external work of 10333 x 0*00368, 

 or 88*02 kilogrammetres, on which 38*02/424 or 0*0897 heat units are expended. This is 

 the heat expended for the external work produced by one cubic metre of a gas, but the 

 specific heat refers to units of weight, and therefore it is necessary in order to know D 

 to reduce the above quantity to a unit of weight. One cubic metre of hydrogen at 

 and 760 mm. pressure weighs 0*0896 kilo, a gas of molecular weight M has a density 

 M 2, consequently a cubic metre weighs (at and 760 mm.) 0*0448M kilo, and therefore 

 1 kilogram of the gas occupies a volume 1/0*0448M cubic metres, and hence the external 

 work D in the heating of 1 kilo of the given gas through 1=0*0896/0*0448M, or D = 2/M. 



Taking the magnitude of the internal work B for gases as negligeable if permanent gases 

 are taken, and therefore supposing B=0, we find the specific heat of gases at a constant 

 pressure Q=K + 2 M, where K is the specific he.at. at a constant volume, or the true 

 specific heat, and M the molecular weight. Hence K = Q - 2/M. The magnitude of the 

 specific heat Q is given by direct experiment. According to Begnault's experiments, for 

 oxygen it = 0*2175, for hydrogen 8*405, for nitrogen 0*2488; the molecular weights of 

 these gases are 82, 2, and 28, and therefore for oxygen K = 0*2175 -0*0625 = 0*1550, 

 lor hydrogen K = 8*4050 -1*000 =2*40^0, and for nitrogen K= 0*2488 -0*0714 =0*1724. 

 These true 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 fact, for oxygen 

 this product = 0*155x16 = 2* 48, for hydrogen 2*40, for nitrogen 0*7724x14 = 2*414, and 

 therefore if A stand for the atomic weight we obtain the expression K x A=a constant, 

 which may be taken as 2*45. This is the true expression of Dulong and Petit's law, 

 because E 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 =8*48, for hydrogen =8*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 1 

 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*45. 'When w=l this ratio k=V8 ; when 

 n = 2, k = 1*4, when n = 8, k = 1*8, 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 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 A is determined 

 by methods described in works on physics (for example, by the change of femperature 

 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 it 

 nearly 1*8. Kundt and Warburg (1875), by means of the approximate method mentioned 

 in Note 29, Chapter VII., determined k for mercury vapour when n=l, and found it to 

 k, =1-67 that is, a larger quantity than for atr, as would be expected from the above. 



It may be admitted that the true atomic heat of gases =2*48, only under the condition 



