TIIK VALKNCV AND SPKCIKK 1 HEAT OK TIIK M KTA Ls 579 



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 



which incro uses with the complexity of the gaseous molecule. The magnitude lOOOa for 

 ammcmia = <>-ll, for chloric anhydride = 7'42, for ethylene, C 2 H 4 = 12-7, for chloroform, 

 CHC1 3 = 29'5, \-c. For permanent gases a = 0, and MQ = 6'8 that is, the atomic heat (if 

 tin- molecule contains two atoms) = 8'4, as it is in reality. As regards liquids (as well as the 

 rapoun formed by them), the specific heat always rises with the temperature: Thus for 

 benzene, it equals 0'38 + 0'0014. 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 varia- 

 tion of the specific gravity (Chap. II. Note 84), cohesion, and other properties of liquids 

 with the temperature. They are all expressed by the linear function of the temperature, 

 <t + bt, with the same degree of proximity as the property of gases is expressed by the 

 equation pv = Itt. 



As regards the relation between the specific heats of liquids (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*18, 

 liquid 0"28 ; steam 0*475, liquid water I'O. But the whole complexity of the relation > 

 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 80), and of solid bromine 

 = 0'084 (at 15). The specific heat of solid benzoic acid (according to experiment and 

 call illation, BoBfl L888) between J 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 other like properties. 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. 



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 

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

 that which 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, Chap I., we find 

 that one cubic metre of a gas heated by 1 produces an external work of 10333 x 0'00868, 

 or :;.^-ii2 kilngriimmi-uv>, 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 by 1 = 0-0896/0'0448M, or D = 2/M. 



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

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

 pre>-ure Q = K + 2 M. wh.Te K is the specific heat 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 Regnault's experiments, for 

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

 are 32, 2, and 28, and therefore for hydrogen K = 0'2438 - 0-0714 = 0'1724. These true 



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