86 HEAT. 



proportional to those which may be expected in the other. But only in 

 very few cases have the specific heats at constant volume been worked 

 out, and as yet only by Joly with the steam calorimeter.* He has found 

 that the specific heat alters with the density. Denoting the density by 

 p, he found that for air about a mean temperature of 50 specific heat 

 at constant volume = 0'17 151 + 0'02788/D, giving 0*17154 as the value 

 at and 760 mm. For carbon dioxide about a mean temperature of 

 55 and a range of pressure up to 80 atmospheres, he found 0-1650 

 + 0-2125/3 + 0-340p 2 . For hydrogen he found 2-40, with decided in- 

 dications of a decrease with increasing density. By varying the initial 

 temperature he was able to determine that there was no change in the 

 specific heat of carbon dioxide at constant volume between 10 0. and 

 100 0. if the density did not exceed -08, but that there was a rapid 

 increase at higher densities as the temperature decreased below 30. 



Swannf has employed the method of electrical heating to determine 

 the specific heats of air and carbon dioxide at atmospheric pressure. A 

 measured quantity of the gas was driven past a coil heated by an electric 

 current, and the energy given by the coil to the gas was measured 

 electrically. The rise in temperature of the gas was determined by 

 platinum resistance thermometers placed in the stream before it came to 

 and after it left the heating coil. Swann found that in terms of the 

 calory at 20 0. the specific heats were 



Air at 20 0., 0-24173; at 100 C., 0-24301. 

 CO 2 at 20 C., 0-20202; at 100 C., 0-22141. 



Extrapolating, we obtain for air at C. the value 0-24141, a result 

 nearly 2 per cent, higher than that of Regnault. 



Dulong and Petit'S Law. From their researches on specific heat 

 Dulong and Petit were led to conclude that for many solid elements the 

 product 



Atomic weight x specific heat = constant, 



a law now known by their name. As pointed out already, it implies 

 that if we take a weight of each element equal in grammes to the 

 number expressing the atomic weight, and therefore, on the atomic 

 theory, containing the same number of atoms, the capacity for heat is the 

 same. Or the heat capacity per atom is constant. 



Regnault made a very extensive series of researches to test this law, 

 and found that for most solid elements the product is nearly, but only 

 nearly, constant. This might be expected. For, as we have seen, the 

 specific heat changes with condition and temperature, and we could only 

 expect to find any exact relation for the different elements when we had 

 them in corresponding condition and at corresponding temperature, and 

 we do not yet know in what correspondence consists. On page 87 we 

 give a selection from Regnault's values of the specific heat, adding 

 carbon, boron, and silicon, with the limiting specific heats as given by 

 Weber. The product, Atomic weight x specific heat, the " Atomic Heat," 

 is given in the last column. 



* Phil. Trans., A., 1891, p. 73, and A., 1894, p. 943. 

 t Phil. Tram., A. 210, p. 199, 1910. 



